tag:blogger.com,1999:blog-607253412379764662024-03-13T08:48:28.692-07:00John Lottery's Bimonthly Lottery ArticlesA collection of lottery articles analyzing specific aspects of Mega Millions, Powerball, Lotto Max, Lotto 649, Euromillions, and other lottery games. Examples of topics include advice on: when to buy and play guides; rule and format changes; benefits of buying the Megaplier, Powerplay, Sizzler options; how much money the lottery keeps; cash verses annuity analysis; implied yields; lottery odds of single and multiple tickets; etc. Includes annuity and multi-ticket calculator gadgets for your use.John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.comBlogger150125tag:blogger.com,1999:blog-60725341237976466.post-77220590224930032282016-01-08T10:50:00.001-08:002016-01-08T16:43:39.002-08:00Will there be a Powerball Winner on Saturday? - And, What is the probability there will be?<a href="http://www.moremonmouthmusings.net/wp-content/uploads/2012/11/How-to-read-your-losing-powerball-ticket.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://www.moremonmouthmusings.net/wp-content/uploads/2012/11/How-to-read-your-losing-powerball-ticket.jpg" height="200" width="190" /></a>The Powerball jackpot for tomorrow night's drawing (Saturday January 9 2016) has just been increased to $800 million for the annuity value, and to $496 million for the cash value. Based on this, we are estimating that around 400 million tickets will be sold in total for the next drawing.<br />
<br />
Since the total number of combinations is 292.2 million, one would think that the jackpot will be won for sure (because 400 is greater than 292).<br />
<br />
But you would be wrong.(See <b style="text-align: center;"><a href="http://www.lotterypowerpicks.com/poissondistribution.htm" target="_blank">Probability of Winning the Lottery</a>)</b><br />
<b style="text-align: center;"><br /></b>
The real probability that the winning ticket will be sold is only:<br />
<br />
<div style="text-align: center;">
<span style="color: red; font-size: large;"><b>a 74.6% probability that Powerball will be won </b></span></div>
<div style="text-align: center;">
<span style="color: blue;">(if 400 million tickets are sold).</span></div>
<div style="text-align: center;">
<br /></div>
<b>This means that there is a 25.4% chance that there will be no winner</b>, and that the jackpot will continue to grow!<br />
<br />
<b>The explanation for estimating this lower probability lies with the principal of randomness and duplicates.</b><br />
<br />
Since every combination is randomly generated independently from another, the chance that a newly printed number set is a duplicate increases as the number of combinations are sold. Eventually, it becomes more likely that new combination is a duplicate, rather than being a unique combination.<br />
<br />
According to the <a href="http://lottoreport.com/"><b>LottoReport.com</b></a> website, approximately 176 million tickets were sold in the Wednesday January 6th drawing and there was no jackpot winner. This is not surprising because there was only a 45.3% chance that a winning ticket would be sold.<br />
<br />
Likewise, when 200 million combinations are sold, there is only a 49.6% chance of winning; and when 300 million combinations are sold, there is a 64.2 chance of wining (but more than 1 in 3 chance of losing).<br />
<br />
You can access our:<br />
<br />
<div style="text-align: center;">
<span style="font-size: large;"><b> <a href="http://www.lotterypowerpicks.com/poissondistribution.htm" target="_blank">Probability of Winning the Lottery</a></b> </span></div>
<br />
page to analyse the chances of winning the Powerball and other lotteries based on the number of tickets sold.John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-57539647652795467872015-09-05T04:35:00.000-07:002015-09-05T04:35:30.397-07:00When to Play Lotto Max or Lotto 649 Guide - Includes 2015 Lotto Max Changes + 2013 Lotto 649 Changes<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="http://www.chfi.com/contests/win-with-lotto-649-lotto-max/" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="http://www.chfi.com/files/LottoMax649.jpg" height="133" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Lotto Max or Lotto 649?<br />
<span style="font-size: xx-small;">(from http://www.chfi.com/contests/win-with-lotto-649-lotto-max/)</span></td></tr>
</tbody></table>
<b><span style="color: blue;">Introduction</span></b><br />
The purpose of this post is to provide Canadian Lotto Max and Lotto 649 players with sufficient information to help them decide on which game they should spend their money. As background, we have firs summarized the most recent changes to both of these games. This is followed by our player recommendation advice.<br />
<br />
<b><span style="color: blue;">Lotto Max Modifies the Game</span></b><br />
In July 2015, the first format change to Lotto Max was implemented. As changes go, this was very modest because the ticket price, number of balls, and number of prizes remained the same. Only the prize amounts of the top three second tier prizes (5/7, 6/7, and 6/7 + bonus) were lowered.<br />
<br />
This was done in order to allow the Lotto Max Jackpot cap to be increased from $50 to $60 million.<br />
<br />
No change was made to the MaxMillions feature, which begin to be offered at $50 Million. However, the number of MaxMillion prizes will be at the discretion of the organizers when the Jackpot level is between $50 and $60 million. In this range, they may increase the Jackpot, the number or MaxMillions, or both. Once the jackpot reaches $60 million, it remains fixed and only the number Max Million prizes increase.<br />
<br />
<b><span style="color: blue;">Effect of 2015 Lotto Max Changes</span></b><br />
From an executive viewpoint, three of the game characteristics remain unchanged.<br />
<ul>
<li>The percent of winners remains at 5.05% </li>
<li>The overall odds stays at 19.8</li>
<li>The return sensitivity stays constant at $0.006985.</li>
</ul>
But, the overall return is decreased to $0.353 (from $0.364), and payout per dollar spent is reduced to $7.00 versus $7.21.<br />
<br />
<b><span style="color: blue;">Review of the Lotto 649 Changes in 2013</span></b><br />
Since we first published our "<b><i>When to Play Guide</i></b>" for Lotto Max and Lotto 649 in 2009, we have not updated it since (although 649 was changed).<br />
<br />
In September 2013, four significant changes were made to the Lotto 649 format:<br />
<ul>
<li>First, the ticket price was increased to $3.00 (up from $2.00)</li>
<li>Second, the minimum jackpot prize was increased to $5 Million (up from $2.5)</li>
<li>Third, a new "Free Ticket" prize was added for those matching only 2 of the 6 main balls (not including the bonus ball).</li>
<li>Fourth, a separate $1 Million Guaranteed Prize drawing was added.</li>
</ul>
While the underlying concept of drawing 6 of 49 balls and one bonus ball remained the same, these changes produced very noticeable results, mainly:<br />
<ul>
<li>The number of winners increased to 15.1% (up from 3.1%),</li>
<li>The overall odds dropped to 1 in 6.62 (from 1 in 32.31)</li>
<li>The overall return increased slightly to $0.333 per dollar (from $0.318)</li>
<li>The return sensitivity flattened to $0.023837 (from $0.035736)</li>
<li>And, the payout per dollar spent was cut to an average of $2.20 (from $10.27)</li>
</ul>
<br />
<b><span style="color: blue;">Break-even Jackpot</span></b><br />
Using the Overall Returns and Return Sensitivities of the latest 2015 Lotto Max and the 2015 Lotto 649 games, <b>we have calculated the break-even jackpot to be $4.15381 Million</b>.<br />
<br />
<hr />
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" />
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As shown above, the break-even amount is below both the minimum $5.0 Million Lotto 649 jackpot and the $10.0 Million Lotto Max minimum jackpot. Thus, for any level where the jackpots of both Lotto 649 and Lotto Max are equal, one should always purchase the Lotto 649 game because the return is higher.<br />
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However, we rarely have the situation when the jackpot offerings of both games is the same. This is because the Lotto Max minimum is $10.0 Million, and it increases by a minimum of $5.0 million, whereas the Lotto 649 minimum is only $5.0 and typically increases by just $2.0 to $5.0 million.<br />
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<b><span style="color: blue;">The "When to Play" Guide</span></b><br />
Therefore, we need to view a cross-jackpot matrix to identify the various levels where it is more beneficial to play one game versus the other. Using the return information from the above graph, we have constructed a "When to Buy" graph showing the break-even Lotto 649 jackpots for Lotto Max jackpots ranging from $10.0 million to $100.0 million<br />
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<img 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" /><br />
<br />
<hr />
<br />
<b><span style="color: blue;">Choosing the Game to Play - Our Advice</span></b><br />
Based on the above, we see 10 vertical bars. The horizontal spacing indicates the Lotto Max jackpots labeled 10M to 100M. Immediately below them are the corresponding Lotto 649 break-even jackpots.<br />
<br />
For example, we see that if the Lotto Max jackpot is $10 million, we should purchase this game whenever Lotto 649 is below $5.87 million. But, if the Lotto 649 jackpot is higher ($7M for instance), we should then buy Lotto 649.<br />
<br />
Similarly, when Lotto Max is $50 Million, we should buy that game unless Lotto 649 is above $17.59 million.<br />
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Note that once Lotto Max reaches $50 Million, we must consider the total jackpot offering to determine the return., This is the total of both the advertised jackpot amount plus the total number of Max Millions. This is why we can consider Lotto Max jackpots from $50 to $100 Million. For example, if the Lotto Max jackpot was $60 million plus 20 Max Millions, we would use the total of $80 million as the Lotto Max value when reading the graph above.<br />
<br />
Lastly, to evaluate jackpot levels not displayed, one should simply use the values shown above and interpolate.<br />
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<br />
<div>
<b><span style="color: blue;">Learn More </span></b><br />
You can learn more by visiting our references:<br />
<ul>
<li><b><a href="http://jlotterysbimonthlyarticles.blogspot.com/2009/09/lotto-max-analysis-when-to-play-guide.html" target="_blank"><span style="font-size: small;">The 2009 Lotto Max Analysis - When to Play Guide</span></a></b></li>
<li><a href="http://www.lotterypowerpicks.com/expandedOdds/CDA_LM_expanded.htm" target="_blank"><b>Lotto Max Expanded Odds (2013)</b></a></li>
<li><a href="http://www.lotterypowerpicks.com/expandedOdds/CDA_649_expanded.htm" target="_blank"><b>Lotto 649 Expanded Odds (2015) </b></a></li>
<li><a href="http://jlotterysbimonthlyarticles.blogspot.com/2013/09/a-review-of-lotto-649-september-2013.html" target="_blank"><span style="font-size: small;"><b>A Review of the Lotto 649 September 2013 Game Changes</b></span></a></li>
</ul>
</div>
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-50595392961065843732013-10-18T11:07:00.001-07:002013-10-18T11:07:31.494-07:00The October 19 2013 Mega Millions Lottery Changes<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="http://www.ctlottery.org/Modules/Games/default.aspx?id=11" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;" target="_blank"><img border="0" src="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcSsdzRQQxtRkxDd-HWB_XUIrUNRA1rpyUc4AhcKk-hrzYFqmcZPFQ" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">(from <a class="irc_hol irc_itl" data-ved="0CAQQjB0" href="http://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&docid=7YUPTZrk5HOdXM&tbnid=UGR7j8XmslJdXM:&ved=0CAQQjB0&url=http%3A%2F%2Fwww.ctlottery.org%2FModules%2FGames%2Fdefault.aspx%3Fid%3D11&ei=Z15hUpHvDfG74AOgi4FQ&bvm=bv.54176721,d.dmg&psig=AFQjCNFJ4jKtGnQeO8_ujsb8ESQB9oyI7A&ust=1382199245911311"><span class="irc_ho" dir="ltr" style="text-align: left;">www.ctlottery.org</span></a><span class="irc_dim">)</span></td></tr>
</tbody></table>
Last Spring, <span style="color: red;">Mega Millions</span> announced that it was going to make major changes to its nationwide lottery game. This came in response to the Powerball price increase last year, and to the realization that the playing public is eager to frantically buy lottery tickets when the offered jackpots are absurdly high.<br />
<br />
So to capitalize on the players desire to win gigantic jackpots and to derive larger revenue profits, the <span style="color: red;">Mega Millions</span> format was changed to make the probability of winning the jackpot even more difficult. By doing this, it is believed that the the average jackpot prize offerings will be in the $200 to $800 million range. And, by keeping the ticket cost at the same single dollar price, players will be more eager to purchase multiple tickets at once.<br />
<br />
Truthfully, this logic is brilliant, and we believe that Mega Millions will accomplish its goals.<br />
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<hr style="height: 1px;" />
<span style="color: red;"></span><br />
<div style="color: red;">
<b>The 2013 Mega Millions Changes <br />
</b></div>
The table below shows a summary of the 2013 Mega Millions changes. Most notably, players will find that the cost of ticket prices will remain the same $1 cost, prize payouts will be substantially lower, and the chances of winning will be much harder.
<br />
<br />
<table border="1">
<tbody>
<tr>
<td style="background-color: red; color: white; text-align: center;"><b>Summary of 2013 Mega Millions Changes
</b></td><td style="background-color: red; color: white; text-align: center;"><b>Megaplier Prizes
</b></td></tr>
<tr>
<td valign="top"><ul>
<li>White Balls increased to 1 to 75 (19 more) </li>
<li>Megaball lowered 1 to 15 (down from 46)</li>
<li>Starting jackpot at $15 million (up from $12 million)</li>
<li>Jackpot will increase by $5 million minimum</li>
<li>Match 5 prize fixed at $1 million (up from $250,000)</li>
<li>Regular Ticket Costs $1 (no change)</li>
<li>Chance of winning 258,890,850 (up 83M or 47.4%) </li>
<li>Annuity payout moved to 30 years (up from 26)</li>
<li>Annuity payments increase by 5% every year</li>
<li>Overall chance of winning any prize 14.7</li>
</ul>
</td>
<td valign="top"><ul>
<li>Megaplier Ticket still Costs $2 (no change)</li>
<li>All prizes multiplied by 2, 3, 4 or 5 times (5 times is new)</li>
<li>Average megaplier value is 3.87 times</li>
</ul>
</td></tr>
</tbody></table>
<br />
Because the number of white balls increased to 75, the chances of winning the 2nd tier prize of 5+0 has grown to 1 in 18,492,204. Comparing this to the old 1 in 3,904,701 value for 1 in 56, we see that it is 5.975 times harder to win this prize. This means that the the 2nd tier 5+0 prize is undervalued in the new Mega Millions game. <br />
<br />
However, since the number of Megaballs decreases to 15, the overall chance of winning any prize drops to in in 14.7 verses one in 40 in the old format. <br />
<div style="color: red;">
<br />
<hr style="height: 1px;" />
<span style="color: red;"></span><b>Start Date<br />
</b></div>
The new Mega Millions will become effective on <b>Saturday October 19, 2013</b>, and the first drawing will be held on Tuesday October 22, 2013.<br />
<br />
<hr style="height: 1px;" />
<span style="color: red;"></span><br />
<div style="color: red;">
<b>Mega Millions's Reasons for Changes.</b></div>
According to summaries, the main reason that the <span style="color: red;">Mega Millions</span> format is changing is that they want to make the game more exciting by offering larger jackpots. To do this, they increased the number of combinations to make the jackpot more difficult to win. However, they wanted to be competitive with Powerball. So, they kept ticket price at the same $1 cost. Thus:
<br />
<ol>
<li>to increase jackpots, they increased the odds of winning to 1 in 258.9 million;</li>
<li>by keeping the price at $1, a player who spends $2 on Powerball can get 2 Mega Million Tickets;</li>
<li>for the same Powerball price, the odds of winning are only 1 in 129.45 million (lower than Powerball);</li>
<li>by offering the match 5 prize of $1 million, they are consistant with Powerball;</li>
<li>by offering the Megaplier, a player matching 5 white balls only could win $2 to $5 million;</li>
<li>by changing the annuity payment to 30 years, they are consistant with all the other major lottery annuities.</li>
<li>and lastly, by lowering the Megaballs to only 15, the will be more overall winners. </li>
</ol>
<div>
<hr style="height: 1px;" />
<span style="color: red;"></span><span style="color: red;"><b>Game Variety</b></span></div>
Now that the odds of winning have increased by 47%, it is easy to see that winning Mega Millions will be more difficult. Further, the value of individual prizes has been reduced substantially.
<br />
<br />
To help understand the impact of the Mega Millions changes, the table below lists the Mega Millions and Powerballs differences side by side. Powerball is shown in the light blue columns, and the new Mega Millions is shown in the pink columns.<br />
<br />
<table border="1" cellpadding="0" cellspacing="0" style="width: 100%;"><colgroup><col style="width: 74pt;" width="99"></col>
<col span="2" style="width: 74pt;" width="98"></col>
<col style="width: 63pt;" width="84"></col>
<col style="width: 48pt;" width="64"></col>
<col style="width: 62pt;" width="83"></col>
<col style="width: 63pt;" width="84"></col>
<col style="width: 62pt;" width="83"></col>
<col style="width: 63pt;" width="84"></col>
</colgroup><tbody>
<tr height="17" style="height: 12.75pt;">
<td class="xl73" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><b><span style="font-size: x-small;">Match</span></b></td>
<td class="xl73" style="background-color: red; text-align: center; width: 74pt;" width="98"><b><span style="font-size: x-small;">MM 5/75+1/15</span></b><br />
<b><span style="font-size: x-small;">Odds</span></b></td>
<td class="xl74" style="background-color: #9fc5e8; text-align: center; width: 74pt;" width="98"><b><span style="font-size: x-small;">PB 5/59+1/35</span></b><br />
<b><span style="font-size: x-small;">Odds</span></b></td>
<td class="xl73" style="background-color: red; text-align: center; width: 63pt;" width="84"><b><span style="font-size: x-small;">Winners</span></b><br />
<b><span style="font-size: x-small;">MM </span></b></td>
<td class="xl74" style="background-color: #9fc5e8; text-align: center; width: 48pt;" width="64"><b><span style="font-size: x-small;">Winners</span></b><br />
<b><span style="font-size: x-small;">PB </span></b></td>
<td class="xl73" style="background-color: red; text-align: center; width: 62pt;" width="83"><b><span style="font-size: x-small;">Prize $</span></b><br />
<b><span style="font-size: x-small;">MM </span></b></td>
<td class="xl74" style="background-color: #9fc5e8; text-align: center; width: 63pt;" width="84"><b><span style="font-size: x-small;">Prize $</span></b><br />
<b><span style="font-size: x-small;">PB </span></b></td>
<td class="xl73" style="background-color: red; text-align: center; width: 62pt;" width="83"><b><span style="font-size: x-small;">Prize $</span></b><br />
<b><span style="font-size: x-small;">Megaplier</span></b></td>
<td class="xl74" style="background-color: #9fc5e8; text-align: center; width: 63pt;" width="84"><b><span style="font-size: x-small;">Prize $</span></b><br />
<b><span style="font-size: x-small;">Power Play</span></b></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">5+1</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">258,890,850.00</span></b></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">175,223,510.00</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">1</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">1</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$15,000,000 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$40,000,000 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$15,000,000 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$40,000,000 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">5+0</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">18,492,203.57</span></b></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">5,153,632.65</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">14</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">34</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$1,000,000 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$1,000,000 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$3,866,667 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$2,000,000 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">4+1</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">739,688.14</span></b></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">648,975.96</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">350</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">270</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$5,000 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$10,000 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$19,333 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$40,000 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">4+0</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">52,834.87</span></b></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">19,087.53</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">4,900</span></b></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">9,180</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$500 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$100 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$1,933 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$200 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">3+1</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">10,720.12</span></b></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">12,244.83</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">24,150</span></b></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">14,310</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$50 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$100 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$193 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$200 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">3+0</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">765.72</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">360.14</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">338,100</span></b></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">486,540</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$5 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$7 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$19 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$14 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">2+1</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">472.95</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">706.43</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">547,400</span></b></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">248,040</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$5 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$7 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$19 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$14 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">2+0</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">33.78</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">20.78</span></td>
<td class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;"><br /></span></b></td>
<td class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;"><br /></span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;"> </span></b><br />
<b><br /></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;"> </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;"> </span></b><br />
<b><br /></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;"> </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">1+1</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">56.47</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">110.81</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">4,584,475</span></b></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">1,581,255</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$2 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$4 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$8 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$12 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">1+0</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">4.03</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">3.26</span></td>
<td class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;"><br /></span></b></td>
<td class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;"><br /></span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;"> </span></b><br />
<b><br /></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><br /></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;"> </span></b><br />
<b><br /></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;"> </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">0+1</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">21.39</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">55.41</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;">12,103,014</span></b></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">3,162,510</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$1 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$4 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;">$4 </span></b></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$12 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">0+0</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><b><span style="font-size: x-small;">1.53</span></b></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">1.63</span></td>
<td class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><b><span style="font-size: x-small;"><br /></span></b></td>
<td class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;"><br /></span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;"> </span></b></td>
<td class="xl69" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;"><br /></span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><b><span style="font-size: x-small;"> </span></b></td>
<td style="background-color: #9fc5e8;"><span style="font-size: x-small;"><br /></span></td>
</tr>
</tbody></table>
<br />
Illustrated above are the odds (or chances), number of winners, prize payout for normal tickets, and prize payout for the multiplier (Megaplier and Power Play) tickets of both games.<br />
<br />
Because the differences are rather large, we have decided not to illustrate these in graphic form.<br />
<br />
<hr style="height: 1px;" />
<span style="color: red;"><span style="font-weight: bold;">Summary</span></span><br />
In summary, we believe that the increased odds of winning both the <span style="color: red;">Mega Millions</span> Match 5 and Jackpot will result in a far fewer number of players winning prizes of $1 million or more. But, since few people win these now, most players will not realize the importance of this improbability.
<br />
<br />
Correspondingly, players will obtain a "false" sense of security thinking that they really have a chance to win the jackpot because it seems there are more winners. Compared to Powerball, there will be 3 times more players who match the Megaball than those matching the Powerball number. But, those who win at Mega Millions will only receive $1 verses those Powerball players who receive $4.
<br />
<br />
So just think, you will get 1/4th the amount of money but 3 times the number of winners. So, in reality, things are much worse on a dollar to dollar basis.
<br />
<br />
But, those who play the Megaplier option will fare much better. In this case, one should compare the Megaplier payouts to the normal $2 Powerball ticket. When this is done, it is easier to see that Mega Millions odds are lower than Powerball and the payouts are much better.
<br />
<br />
However, we believe the new <span style="color: red;">Mega Millions</span> game will be very successful. Indeed, jackpots will be typically be large and the frequency of winning will keep players hooked on the game.
<br />
<span style="font-size: 78%;"><br /></span>
<br />
<hr style="height: 1px;" />
<span style="color: red;"><span style="font-weight: bold;">More Information:</span></span><br />
The following links provide you with more information about the 2013 Mega Millions lottery.<br />
<ul>
<li><b><a href="http://www.lotterypowerpicks.com/expandedOdds/US_MM_expanded.htm" target="_blank">2013 Mega Millions Complete Odds and Returns</a></b></li>
<li><b><a href="http://www.lotterypowerpicks.com/mm_megaplierAnalysis.htm" target="_blank">Megaplier Analysis for the 2013 Mega Millions</a> </b></li>
</ul>
<br />
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-65531144570532401472013-09-13T11:04:00.001-07:002013-09-16T09:04:55.092-07:00A Review of the Lotto 649 September 2013 Game Changes<b>Canada's national <span style="font-size: large;"><span style="color: #45818e;">Lotto 649</span></span> game will change beginning September 15, 2013</b>. Most notably, players of this lottery game will find four changes:<br />
<ul>
<li>Ticket prices will be $3 each (increased from $2),</li>
<li>Minimum jackpots will begin at $5 million,</li>
<li>A new match 2 prize (2 of 6 white balls) earns a free play,</li>
<li>A separate second draw game with a guaranteed $1 million prize is included. </li>
</ul>
The rational behind raising the ticket price is that the increased minimum jackpot and the $1 million guaranteed prize draw will lure more players. Plus, to help make the players believe they are not wasting their money, the addition of the match 2 prize will increase the number of winners by approximately 12%.<br />
<br />
<span style="color: blue;"><b>Notes:<span style="font-size: x-small;"> </span></b></span><br />
<ul>
<li><span style="color: blue;"><span style="font-size: x-small;"><b><span style="color: red;">This post was revised on Monday September 16, 2013</span>. </b></span></span></li>
<li><span style="color: blue;"><span style="font-size: x-small;"><b>This is Part I of a 2 part series which reviews the changes to the September 2013 Canadian Lotto 649 game.</b></span></span></li>
<li><span style="color: blue;"><span style="font-size: x-small;"><b>Our second post, Part II (next week), will provide a "2013 Lotto 649 vs Lotto Max - When to Play Guide</b></span> "</span><b> </b></li>
</ul>
Wow, more winners and higher prizes, all for a single buck more!<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.newswire.ca/en/story/1223799/sales-for-the-new-lotto-6-49-start-this-sunday" imageanchor="1" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" height="260" src="http://photos.newswire.ca/images/download/20130912_C6492_PHOTO_EN_30731.jpg" width="320" /></a></div>
<br />
<div style="text-align: center;">
<span style="color: #45818e;"><span style="font-size: large;"><b>Is this a good deal for the Canadian Lottery player?</b></span></span></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<span style="color: blue;"><span style="font-size: large;"><b>No, not really.</b></span></span></div>
<br />
Why? Because the increased jackpot, $1 million prize, and match 2 prize payouts are all funded by the ticket price increase, and little goes back to the players.<br />
<br />
<span style="color: blue;"><b>Prize Payout Structure</b></span><br />
Under the new <span style="color: #3d85c6;"><b>Lotto 649 </b></span>game rules, all Pool's Fund payouts (5/6+, 5/6, and 4/6) are approximately 10% lower under the $3 play:<br />
<ul>
<li>Match 6/6 = $5 million (vs $2 million) </li>
<li>5/6+ = $77,145.29 (vs 87,357.71) - down 11.7%</li>
<li>5/6 = $1,530.66 (vs 1,718.22) - down 10.9%</li>
<li>4/6 = $54.11 (vs $60.57) - down 10.7%</li>
<li>3/6 = $10 (same)</li>
<li>2/6+ = 5 (same)</li>
<li>2/6 = Free Ticket (new)</li>
<li>(1) Guaranteed Prize of $1 million to be paid on a raffle basis</li>
</ul>
<br />
<span style="color: blue;"><b>Why are these down?</b></span><br />
There are 6 reasons why these will be lower:<br />
<ul>
<li>Regardless of whether the <span style="color: #3d85c6;"><b>Lotto 649</b></span> ticket cost $2 or $3, <b>47%</b> of the ticket sales are dedicated to the <b>Main Prize fund</b>. This is the amount that will be paid out to players. The remaining 53% will be kept by the lottery organizers.</li>
<li>Next, the payouts for the fixed 3/6, 2/6+, and 2/6 prizes are deducted from the Main Prize fund.</li>
<li>The remainder is then called the Pool's Fund.</li>
<li>According to a predefined percentage, the Pool's fund is allocated to the jackpot 6/6 prize, as well as the 5/6+, 5/6, and 4/6 prizes.</li>
<li>Although the absolute amount of the Main Prize and Pool's Fund has increased, the individual allocation of prize percentages were revised: 6/6 jackpot = 79.50% (was 80.5%); 5/6+ = 6.0% (was 5.75%), 5/6 = 5.0% (was 4.75%), and 4/6 = 9.5% (was 9.0).</li>
<li>This all means that: if we assume that all 13.98 million tickets are sold, then the amount in the Pool's Fund (amount to be used for paying the 6/6, 5/6+, 5/6, and 4/6 prizes) decreases by $1.401 million, which is a 15.37% decrease.</li>
<li><span style="color: red;">However, allocation for the funding of the Guaranteed $1 Million Prize, which is 7%, is deducted from the 47% proportioned for the Main Prize Fund (and not the organizers 53%).</span></li>
</ul>
If we consider that the Lotto 649 ticket price increased by 50%, then we realize that the Pool's Fund value decrease is quite substantial. <br />
<br />
<br />
<span style="color: blue;"><b>What about the $5 Million Minimum Jackpot Prize?</b></span><br />
This is a good offering. The old $2 game listed a minimum prize of $2 million. However, this was rarely used. Instead, most starting jackpots were valued at either $3.0 or $3.5 million. Since the cost of a 649 ticket increases by 50%, the new $5 million minimum is in line with the ticket price increase. <br />
<br />
<br />
<span style="color: blue;"><b>And the new Free Ticket 2/6 match prize?</b></span><br />
The $3 Lotto 649 game adds a new "free ticket" prize for those matching only 2 of the 6 white balls. This change means two things.<br />
<ul>
<li>First, the number of possible winners increases by 12.01%; bringing the overall percent of winners to 15.1% (as opposed to 3.1%),</li>
<li>Second, the overall odds if winning is decreased from 32.31 to 6.62.</li>
</ul>
While this sounds good, we believe this is only a marketing ploy which guarantees future sales.<br />
<br />
<span style="color: blue;"><b>Why?</b></span><br />
Remember, this is a "Free Ticket" prize, not a $3 cash prize. This means that the prize can only be used in the next (or subsequent) drawings. Thus, 12% of the winning players must redeem their prize for new tickets, which means that they will only have a 15% chance of winning once again. Even though some players may later win, most will have lost this value without having a choice of keeping the money.<br />
<br />
<div style="text-align: center;">
<span style="color: #3d85c6;"><span style="font-size: large;"><b>But I can also win the Guaranteed $1 Million prize.</b></span></span></div>
<br />
<span style="color: blue;"><b>Yes, But will there be a Guaranteed $1 Million Winner?</b></span><br />
<span style="color: red;">Yes there will be a winner. </span>At the original time of this writing, the documentation did not specifically indicate if there would be a winner. <span style="color: red;"><b>However, newly published game rules by the ALC and WCLC indicate that there will always be a single winner</b></span>. For this to happen, then the additional ticket selection numbers must be sequential and known at the time of the drawing.<br />
<br />
The BCLC documentation lists:<br />
<ul>
<li>Guaranteed Prize Draw prizes are not shared.</li>
<li>Guaranteed Prize Draw prizes are not carried over to the next draw.</li>
<li>Guaranteed Prize Draw winning selection is exact match only, in the order that they appear.</li>
</ul>
<span style="color: red;">Thus, if the prize is not carried over, then it sounds like there remains a possibility that a winner will not be drawn.</span><br />
<br />
<span style="color: blue;"><b>Why Sequential Numbering is Important: because Winning may be Rare.</b></span><br />
Based on the Guaranteed Prize Draw Selection number format, your chances of winning this prize are about 1 in 1 billion (yes, 1 billion). As stated in their documents, in order for a player to win this prize, they must match a 10 digit number (in the format of xxxxxxxx-xx). Since there are 10 digits that can range from 0 to 9, there is a total of 1 billion combinations. Using our Poisson Distribution Probability of Winning page, we can learn that ticket sales must be 10.04 million in order for there to be a 1% chance of someone winning the Guaranteed $1 Million prize. If all ticket combination are sold, there is only a 1.39% chance that there will be a winner (for 28 million sold, a 2.76% chance; and for 42 million tickets, only a 4.12% chance).<br />
<br />
<span style="color: blue;"><b>Perhaps No Guaranteed $1 Million Winners.</b></span><br />
So you see that the chance that anyone winning this prize is extremely small if it is not limited to the total ticket sales. Therefore, we are discounting the value of this prize to zero. Note, however, that this prize will not be shared. Should there be more than 1 winner in a drawing, then all winners will receive $1 million.<br />
<br />
Because the methodology of generating this extra prize number on your ticket is not defined, we are unsure if there could be multiple winners. If the number is assigned sequentially (or a sorted variation thereof), then there will not be multiple winners. If the number is randomly generated, then there is a possibility that there will be multiple winners.<br />
<br />
<span style="color: red;"><b>However, the ALC Game Rules state that there will always be 1 winner and that there will be no duplicates.</b></span><br />
<br />
<span style="color: blue;"><b>Conclusion</b></span><br />
Players were alerted to the <span style="color: #3d85c6;"><b>Lotto 649</b></span> changes almost 6 months ago, but the details of the prize allocation and distribution was not made public until last week. After analyzing the impact of these changes, it becomes apparent that the lottery organizers did not want the public to understand that the changes do not benefit the players because:<br />
<ul>
<li>total allocation of lottery sales revenue to winners prize payouts remains the same (47%)</li>
<li>the Guaranteed $1 Million Prize consumes 7% of this revenue,</li>
<li>the Lotto 649 portion of distribution is lowered to 40% of sales,</li>
<li>the the 2/6 free ticket only assures future lottery sales and not cash to players,</li>
<li>the values of the remaining prizes (except for the jackpot) do not increase in proportion to the 50% ticket price increase; instead, they decrease in value. </li>
</ul>
<div style="text-align: center;">
<span style="color: red;"><span style="font-size: large;"><b>Therefore, we do NOT look favorably</b></span></span></div>
<div style="text-align: center;">
<span style="color: red;"><span style="font-size: large;"><b>on the 2013 </b></span></span></div>
<div style="text-align: center;">
<span style="color: red;"><span style="font-size: large;"><b>$3 - Lotto 649 game.</b></span></span></div>
<br />
<span style="color: blue;"><b>Fortunately, Canadian lottery players can play Lotto Max and the regional games at a relatively much cheaper cost.</b></span>John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-42018686047287796032013-05-09T09:38:00.000-07:002013-05-09T09:38:18.191-07:00Hot Lotto Changes on March 12, 2013 - Not so Hot!<span style="color: blue;"><b>Beginning with the March 15, 2013 drawing, the MUSL Hot Lotto game format will change.</b></span><br />
<br />
While we normally welcome improvements to the various lottery games, we do not believe that the new 2013 Hot Lotto changes will assist in attracting more players. Overall, the odds of winning any prize increase from 1 in 16.09 to 1 in 17.22, while the amount of money returned to the players decreases from 32.9% to 27.4%. This means it will be harder to win less money!<br />
<br />
Hot Lotto used to be a small niche game offering a chance to win a minimum of $1 million at odds less than a Pick 6 game. Now, a player can win a little more than a million dollars at twice the odds of Pick 6.<br />
<br />
<div style="text-align: center;">
<span style="color: red;"><b>Thus, we think the new 2013 Hot Lotto game is not as hot as advertised!</b></span></div>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://www.powerball.com/hotlotto/hl_main.asp%E2%80%8E" imageanchor="1" style="margin-left: auto; margin-right: auto;" target="_blank"><img border="0" height="119" src="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcTIrZGw91ebuWqHMnSchkz-eVoeTWRpPI64TJ1gxW3lFrjZigIKWA" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: red;"><b>Not So</b></span></td></tr>
</tbody></table>
<br />
<span style="color: blue;"><b>The Changes</b></span><br />
First, the number of white balls will increase from 39 to 47 numbers. This means that the chance of winning the jackpot prize will increase from approximately 1 in 11 million to 1 in 29 million. Thus, it will be almost 3 times more difficult to win the top prize.<br />
<br />
To offset this increased risk of losing, the guaranteed jackpot minimum will be increased by 1.4 to 1.5 times, depending in which state which the jackpot winners lives. This is achieved because the federal and state taxes on the jackpot prize will be paid directly by the lottery association. This means the minimum jackpot increase is only a quarter of the increase in the odds. So, when the jackpot value is low, we are not very keen on this new game format.<br />
<br />
No longer will the jackpot winner have the choice to taking a single discounted cash prize, or a 25 payment annuity. Instead, all prizes will be paid straight out, as cash.<br />
<br />
In the game, players must still choose a Hot Ball number in the range of 1 to 19. This has not changed.<br />
<br />
To help make the game more attractive to players, payouts for several prizes will be increased. But, as shown below, only 2 prize levels have increase more than the odds have increased. <br />
<br />
Lastly, players will still have the option to purchase the Sizzler option at a cost of $1 more per ticket. The prize payouts to winners with this option will have their prize value multiplied by 3. This does not apply to jackpot winners however.<br />
<br />
The tables below summarize and compare 4 aspects of the new Hot Lotto game format to that of the existing game.<br />
<br />
<span style="color: blue;"><b>Chances of Winning 2013 Hot Lotto</b></span><br />
First we will examine the odds of winning and the the number of winning combinations in the new Hot Lotto Game.<br />
<br />
<table border="1">
<tbody>
<tr>
<td width="300px"><table border="1" cellpadding="0" cellspacing="0"><colgroup><col span="2"></col>
<col span="2"></col>
<col></col>
</colgroup><tbody>
<tr bgcolor="HOTPINK">
<td align="center" colspan="5"><span style="font-size: x-small;">Table HL-1</span></td>
</tr>
<tr bgcolor="HOTPINK">
<td colspan="2" style="text-align: center;"><span style="font-size: x-small;">Hot Lotto<br />Balls<br />Matched</span></td>
<td colspan="3" style="text-align: center; width: 76pt;"><span style="font-size: x-small;">Odds (Chances) of Winning</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">White</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">HB</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">Old Format</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2013 Format</span></td>
<td style="text-align: center;"><span style="font-size: x-small;"> Change</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">10,939,383.00</span></td>
<td align="right"><span style="font-size: x-small;">29,144,841.00</span></td>
<td align="right"><span style="font-size: x-small;">166.4%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">607,743.50</span></td>
<td align="right"><span style="font-size: x-small;">1,619,157.83</span></td>
<td align="right"><span style="font-size: x-small;">166.4%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">64,349.31</span></td>
<td align="right"><span style="font-size: x-small;">138,784.96</span></td>
<td align="right"><span style="font-size: x-small;">115.7%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">3,574.96</span></td>
<td align="right"><span style="font-size: x-small;">7,710.28</span></td>
<td align="right"><span style="font-size: x-small;">115.7%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">1,949.98</span></td>
<td align="right"><span style="font-size: x-small;">3,385.00</span></td>
<td align="right"><span style="font-size: x-small;">73.6%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">108.33</span></td>
<td align="right"><span style="font-size: x-small;">188.06</span></td>
<td align="right"><span style="font-size: x-small;">73.6%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">182.81</span></td>
<td align="right"><span style="font-size: x-small;">253.87</span></td>
<td align="right"><span style="font-size: x-small;">38.9%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">10.16</span></td>
<td align="right"><span style="font-size: x-small;">14.10</span></td>
<td align="right"><span style="font-size: x-small;">38.8%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">47.18</span></td>
<td align="right"><span style="font-size: x-small;">52.08</span></td>
<td align="right"><span style="font-size: x-small;">10.4%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">2.62</span></td>
<td align="right"><span style="font-size: x-small;">2.89</span></td>
<td align="right"><span style="font-size: x-small;">10.3%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">39.31</span></td>
<td align="right"><span style="font-size: x-small;">34.26</span></td>
<td align="right"><span style="font-size: x-small;">-12.8%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">2.18</span></td>
<td align="right"><span style="font-size: x-small;">1.90</span></td>
<td align="right"><span style="font-size: x-small;">-12.8%</span></td>
</tr>
<tr>
<td style="text-align: center;">-</td>
<td style="text-align: center;">-</td>
<td align="right">-</td>
<td align="right">-</td>
<td align="right">-</td>
</tr>
<tr>
<td align="left" colspan="5"><span style="font-size: x-small;">
Table HL-1 above compares the chances of winning the 2013 Hot Lotto Game with the existing game format. As we can see, the odds of matching 5 white balls increased by 166.4%.
<br />
<br />
In fact, the odds of matching 1 or more of the balls selected all increased. The only odds that decreased are those that do not match any white balls.
<br />
</span></td>
</tr>
</tbody></table>
</td>
<td width="300px"><table border="1" cellpadding="0" cellspacing="0"><colgroup><col span="2"></col>
<col span="2"></col>
<col></col>
</colgroup><tbody>
<tr bgcolor="HOTPINK">
<td align="center" colspan="5"><span style="font-size: x-small;">Table HL-2</span></td>
</tr>
<tr bgcolor="HOTPINK">
<td colspan="2" style="text-align: center;"><span style="font-size: x-small;">Hot Lotto<br />Balls<br />Matched</span></td>
<td colspan="3" style="text-align: center; width: 76pt;"><span style="font-size: x-small;">Number of Winners</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">White</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">HB</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">Old Format</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2013 Format</span></td>
<td style="text-align: center;"><span style="font-size: x-small;"> Change</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">0.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">18</span></td>
<td align="right"><span style="font-size: x-small;">18</span></td>
<td align="right"><span style="font-size: x-small;">0.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">170</span></td>
<td align="right"><span style="font-size: x-small;">210</span></td>
<td align="right"><span style="font-size: x-small;">23.5%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">3,060</span></td>
<td align="right"><span style="font-size: x-small;">3,780</span></td>
<td align="right"><span style="font-size: x-small;">23.5%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">5,610</span></td>
<td align="right"><span style="font-size: x-small;">8.610</span></td>
<td align="right"><span style="font-size: x-small;">53.5%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">100,980</span></td>
<td align="right"><span style="font-size: x-small;">154,980</span></td>
<td align="right"><span style="font-size: x-small;">53.5%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">59,840</span></td>
<td align="right"><span style="font-size: x-small;">114,800</span></td>
<td align="right"><span style="font-size: x-small;">91.8%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">1,077,120</span></td>
<td align="right"><span style="font-size: x-small;">2,066,400</span></td>
<td align="right"><span style="font-size: x-small;">91.8%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">231,880</span></td>
<td align="right"><span style="font-size: x-small;">559,650</span></td>
<td align="right"><span style="font-size: x-small;">141.4%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">4,173,840</span></td>
<td align="right"><span style="font-size: x-small;">10,073,700</span></td>
<td align="right"><span style="font-size: x-small;">141.4%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">278,256</span></td>
<td align="right"><span style="font-size: x-small;">850,668</span></td>
<td align="right"><span style="font-size: x-small;">205.7%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">5,008,608</span></td>
<td align="right"><span style="font-size: x-small;">15,312,024</span></td>
<td align="right"><span style="font-size: x-small;">205.7%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;"></span></td>
<td style="text-align: center;"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;">10,939,383</span></td>
<td align="right"><span style="font-size: x-small;">29,144,841</span></td>
<td align="right"><span style="font-size: x-small;">166.4%</span></td>
</tr>
<tr>
<td align="left" colspan="5"><span style="font-size: x-small;">
</span>
<span style="font-size: x-small;">Table HL-2 shows the number of possible combinations that will occur assuming that all the tickets are sold.
<br />
<br />
Note that the number of winners that match the 5 white balls with or without the Hot Ball, do not change.
<br />
<br />
<br />
<br />
</span>
</td>
</tr>
</tbody></table>
</td></tr>
</tbody></table>
<br />
From the above two tables, we can make two observations:<br />
<ol>
<li>Although the odds of winning either the jackpot or second tier prize increased substantially, the absolute possible of winners in those categories did not change at all. </li>
<li>The chance of holding a losing ticket combination has increased proportionately more than the increase in total overall odds (205.7% increase in losers verses 166.4% increase in odds).</li>
</ol>
Thus, from an odds viewpoint, we see that the new format only benefits the MUSL, and not the Hot Lotto players.<br />
<br />
<span style="color: blue;"><b>New Payouts</b></span><br />
Now let's examine the change to the payout structure.<br />
<br />
<table border="1">
<tbody>
<tr>
<td><table border="1" cellpadding="0" cellspacing="0"><colgroup><col span="2"></col>
<col span="2"></col>
<col></col>
</colgroup><tbody>
<tr bgcolor="HOTPINK">
<td align="center" colspan="5"><span style="font-size: x-small;">Table HL-3</span></td>
</tr>
<tr bgcolor="HOTPINK">
<td colspan="2" style="text-align: center;"><span style="font-size: x-small;">Hot Lotto<br />Balls Matched</span></td>
<td colspan="3" style="text-align: center; width: 76pt;"><span style="font-size: x-small;">Winning Prize Payouts</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">White</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">HB</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">Old Format</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2013 Format</span></td>
<td style="text-align: center;"><span style="font-size: x-small;"> Change</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$1,000,000</span></td>
<td align="right"><span style="font-size: x-small;">$1,400,000</span></td>
<td align="right"><span style="font-size: x-small;">40.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">$10,000</span></td>
<td align="right"><span style="font-size: x-small;">$30,000</span></td>
<td align="right"><span style="font-size: x-small;">200.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$500</span></td>
<td align="right"><span style="font-size: x-small;">$3,000</span></td>
<td align="right"><span style="font-size: x-small;"><span style="font-size: x-small;">5</span>00.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">$50</span></td>
<td align="right"><span style="font-size: x-small;">$100</span></td>
<td align="right"><span style="font-size: x-small;">100.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$50</span></td>
<td align="right"><span style="font-size: x-small;">$50</span></td>
<td align="right"><span style="font-size: x-small;">0.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">$4</span></td>
<td align="right"><span style="font-size: x-small;">$6</span></td>
<td align="right"><span style="font-size: x-small;">50.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$4</span></td>
<td align="right"><span style="font-size: x-small;">$6</span></td>
<td align="right"><span style="font-size: x-small;">50.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$3</span></td>
<td align="right"><span style="font-size: x-small;">$3</span></td>
<td align="right"><span style="font-size: x-small;">0.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$2</span></td>
<td align="right"><span style="font-size: x-small;">$2</span></td>
<td align="right"><span style="font-size: x-small;">0.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
</tr>
<tr>
<td align="left" colspan="5"><span style="font-size: x-small;">
Table HL-3 above illustrates the changes to the prize payouts for a straight $1 ticket. As we can see, several of the payouts have been increased. However, the amounts for those matching 3 white + HB, 1 white + HB, and HB only remain the same.
<br />
<br />
Note that we have entered a minimum of $1.4 million for the jackpot. We chose this value because it includes an approximate taxes paid value. This value will change as the jackpot increases.
<br />
</span></td>
</tr>
</tbody></table>
</td><td><table border="1" cellpadding="0" cellspacing="0"><colgroup><col span="2"></col>
<col span="2"></col>
<col></col>
</colgroup><tbody>
<tr bgcolor="HOTPINK">
<td align="center" colspan="5"><span style="font-size: x-small;">Table HL-4</span></td>
</tr>
<tr bgcolor="HOTPINK">
<td colspan="2" style="text-align: center;"><span style="font-size: x-small;">Hot Lotto<br />Balls Matched</span></td>
<td colspan="3" style="text-align: center; width: 76pt;"><span style="font-size: x-small;">Sizzler Payouts</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">White</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">HB</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">Old Format</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2013 Format</span></td>
<td style="text-align: center;"><span style="font-size: x-small;"> Change</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$1,000,000</span></td>
<td align="right"><span style="font-size: x-small;">$1,400,000</span></td>
<td align="right"><span style="font-size: x-small;">40.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">$30,000</span></td>
<td align="right"><span style="font-size: x-small;">$90,000</span></td>
<td align="right"><span style="font-size: x-small;">200.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$1,500</span></td>
<td align="right"><span style="font-size: x-small;">$9,000</span></td>
<td align="right"><span style="font-size: x-small;">500.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">$150</span></td>
<td align="right"><span style="font-size: x-small;">$300</span></td>
<td align="right"><span style="font-size: x-small;">100.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$150</span></td>
<td align="right"><span style="font-size: x-small;">$150</span></td>
<td align="right"><span style="font-size: x-small;">0.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;">$12</span></td>
<td align="right"><span style="font-size: x-small;">$18</span></td>
<td align="right"><span style="font-size: x-small;">50.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$12</span></td>
<td align="right"><span style="font-size: x-small;">$18</span></td>
<td align="right"><span style="font-size: x-small;">50.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$9</span></td>
<td align="right"><span style="font-size: x-small;">$9</span></td>
<td align="right"><span style="font-size: x-small;">0.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td align="right"><span style="font-size: x-small;">$6</span></td>
<td align="right"><span style="font-size: x-small;">$6</span></td>
<td align="right"><span style="font-size: x-small;">0.0%</span></td>
</tr>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">0</span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
<td align="right"><span style="font-size: x-small;"></span></td>
</tr>
<tr>
<td align="left" colspan="5"><span style="font-size: x-small;">
Table HL-4 above illustrates the changes to the prize payouts for the Sizzler option. As we see, all of the payouts (except the jackpot) have been multiplied by 3.
<br />
<br />
Note that we have entered a minimum of $1.4 million for the jackpot. We chose this value because it includes an approximate taxes paid value. This value will change as the jackpot increases.
<br />
<br />
<br />
</span></td>
</tr>
</tbody></table>
</td></tr>
</tbody></table>
<br />
Here we see that the prizes that increased the most in value are for those who: match 5 white balls and not the Hot Ball; and match 4 white balls and the Hot Ball.<br />
<br />
Wow, these to prizes go from $10,000 to $30,000 and $500 to $3,000 respectively!<br />
<br />
But, remember, that there are very few people who will win these prizes. There will still be only 18 possible winners of the $30,000 prize, and only 210 of the $3,000 prize.<br />
<br />
What this means is that the MUSL is relying on a players dream to win a larger amount, and hoping that they do not understand that the dream is fruitless.<br />
<br />
Think of it this way. The odds of winning the $3,000 Hot Lotto prize is 1 in 138,784.96. But, a person who plays the Pick 4 game has a 1 in 10,000 chance to win between $2,500 to $3,000. Meaning it is 13 time easier to win the same amount of money.<br />
<br />
<span style="color: blue;"><b>Conclusion</b></span><br />
We find it difficult to rationalize the changes made to the 2013 Hot Lotto Game. We do not believe the minimum jackpot level of $1 million will attract more players. Instead, we find that there will be less winners, 5.81% compared to 6.21%, and there will be many more losers.<br />
<br />
Players hoping to win equivalent prize payouts will have better opportunities playing their state's Pick 4 and Pick 6 games.<br />
<br />
<br /><span style="color: blue;"><b>To learn more, visit our full game analysis at:</b></span><br />
<ul>
<li><b><a href="http://www.lotterypowerpicks.com/expandedOdds/US_HL_expanded-May13.htm" target="_blank">US Hot Lotto Complete Odds and Returns to Players - Analysis of May 2013 Changes</a></b></li>
</ul>
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com2tag:blogger.com,1999:blog-60725341237976466.post-3087699441077352562013-03-15T11:00:00.001-07:002014-05-30T16:00:03.543-07:00New Lotto Texas 2013 - Review of the Game Changes <a href="http://3.bp.blogspot.com/-j1N-t8loftQ/UUNVoUzMMEI/AAAAAAAAATs/6eKCvYRwFKQ/s1600/lottotexas-v3.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://3.bp.blogspot.com/-j1N-t8loftQ/UUNVoUzMMEI/AAAAAAAAATs/6eKCvYRwFKQ/s1600/lottotexas-v3.png" /></a><span style="color: red;"><b>Revised: Friday, April 26, 2013</b></span><br />
<br />
<b>For the 4th time since the game began in 1992, the Texas Lottery Commission (TLC) will be making changes to Lotto Texas. </b><br />
<b><br /></b>
<b>These changes will become effective beginning with the <span style="color: blue;">April 17 2013</span> drawing.</b><br />
<br />
<span style="font-size: small;"><b>This is our summary of the changes and our evaluation of them.</b></span><br />
<br />
<span style="color: blue;"><b>The basic Lotto Texas format will remain the same. </b></span><br />
Players will still be required to pick 6 numbers from a set of 54. If the full 6 number combination matches the one drawn that evening, the player will win the jackpot prize. Each single ticket will continue to cost $1 each, and the lower tier prizes will remain the same (i.e. those matching 3, 4, and 5 of the white balls). Should a player be lucky enough to win the jackpot, he will still have the option to receive either the lump sum cash payout, or the full advertised annuity amount paid over a number of years.<br />
<br />
<span style="color: blue;"><b>What Changes</b></span><br />
However, there will be 4 differences in the new Lotto Texas 2013 game.<br />
<ul>
<li>First, a "<b>Extra!</b>" option is added to the game. Players can choose to pay $1 more for the chance to win higher cash amounts for the lower tier prizes. This means that those holding the <i>Extra!</i> option will earn higher prizes if they match 3, 4, or 5 balls. Plus, a new $2 prize payout will be added for those matching only 2 of the 6 balls. (This is in effect a "multiplier" option).</li>
<li>Second, the minimum annuity jackpot prize will be increased to $5.0 million.</li>
<li>Third, the annuity payout period will increase from 25 to 30 payments.</li>
<li>Forth, the annuity jackpot will increase in increments of $250,000 rather than the current $1 million.</li>
</ul>
While we rarely like the idea of raising lottery ticket prices, we have found that those games with a "multiplier" option usually offer better returns to the lottery players. Since players have the option (or choice) to pay more for a ticket, they have more control over the amount of money they spend. Thus, we believe this is fairer to them because they can control their own spending.<br />
<br />
To help players understand how these changes will affect them, we discuss each of these 4 changes below.<br />
<br />
<span style="color: blue;"><b>Summary of Lotto Texas 2013 Changes and Payout Structure</b></span><br />
To begin, we have prepared the summary <b>Table 1</b> below illustrating the prize payouts for a single $1 ticket and the new $2 <i>Extra!</i> ticket.<br />
<br />
<center>
<table border="1" style="width: 400px;">
<tbody>
<tr> <td bgcolor="BLUEVIOLET" colspan="6" style="text-align: center;"><span style="color: white; font-size: large;"><b>Table 1: New Lotto Texas 2013</b></span><br />
<span style="color: white; font-size: large;"><b>Payout Structure
</b></span></td></tr>
<tr bgcolor="BLUEVIOLET"> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b><span style="color: black;"> </span>Match </b></span></span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b>Chances </b></span></span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b>Occurs </b></span></span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b>Probability</b></span></span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b> Single<span style="font-size: x-small;"> </span>$1 <span style="font-size: x-small;"> </span></b></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b><span style="font-size: x-small;">Ticket</span> </b></span></span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b>New</b></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b>$2</b></span></span></span><br />
<span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"><span style="color: white;"><b>Extra!
</b></span></span></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">6</span></b></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"> 25,827,165.00 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">1 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">0.000004% </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"> Jackpot </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;"> Jackpot
</span></b></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">5</span></b></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">89,677.66 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">288 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">0.001115% </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">$2,000 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;"> $1<span style="font-size: x-small;">2</span>,000
</span></b></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">4</span></b></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">1,526.43 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">16,920 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">0.065512% </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">$50 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">$1<span style="font-size: x-small;">5</span>0
</span></b></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">3</span></b></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">74.66 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">345,920 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">1.339365% </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">$3 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">$1<span style="font-size: x-small;">3</span>
</span></b></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">2</span></b></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">8.85 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">2,918,700 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">11.300892% </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">- </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">$2
</span></b></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">1</span></b></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">2.51 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">10,273,824 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">39.779140% </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">- </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">-
</span></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;">0</span></b></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">2.10 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">12,271,512 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">47.513972% </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">- </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">-
</span></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><b><span style="font-size: x-small;"><br /></span></b></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">Total </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"> 25,827,165 </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;"> 100.000000% </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">- </span></span></td><td style="text-align: center;"><span style="font-family: Verdana,sans-serif;"><span style="font-size: x-small;">-
</span></span></td></tr>
</tbody></table>
</center>
<br />
Here we can see that there is no change to the single $1 ticket<span style="background-color: black;"></span> set of prizes. However, the <i>Extra!</i> ticket offers increased prizes for those matching 3, 4, and 5 balls. The match 5 prize moves from $2,000 to $10,000; the Match 4 prize moves from $50 to $100; and the Match 3 prize moves from $3 to $10.<br />
<br />
And, we can also see the new $2 prize for those matching 2 of the balls. The addition of this new prize is what makes the <i>Extra!</i> ticket attractive. Assuming all possible combinations were purchased, there will be nearly 3 million new winning tickets, an increase of 11.3% over those who did not buy <i>Extra!</i>. Further, those matching: 5 balls have a 5 times multiplier; 4 balls have a 2 times multiplier; and 5 balls have a 3.33 times multiplier.<br />
<br />
On a $ return basis, we look to see what will be returned to the players if the jackpot prize is not won. In the case of the single $1 ticket, we find that 9.52% is returned. Whereas, the <i>Extra!</i> ticket returns 31.61% of the money back to the players. This is an increase of 3.32 times, and it exceeds the 2 times cost in <i>Extra!</i> ticket. Thus, we believe that the <i>Extra! </i>option is attractive and should be played.<br />
<br />
<b>The Breakeven: When to buy <i>Extra!</i></b> - Like all other multiplier games, the new Lotto Texas <i>Extra!</i> option has an implied breakeven value. This is the jackpot amount where the returns of a single ticket equals that of the <i>Extra! </i>ticket. For Lotto Texas, we calculate this value to be: $11.4 million. Thus:<br />
<br />
<div style="text-align: center;">
<b><span style="color: #38761d;">Buy <i>Extra!</i> when the jackpot is less than or equal $11.4 million;</span></b></div>
<div style="text-align: center;">
<span style="color: red;"><b>Do not buy <i>Extra!</i> when the jackpot is more than $11.4 million.</b></span></div>
<br />
<span style="color: blue;"><b>Minimum Jackpot Increases to $5 Million</b></span><br />
There are two components to increasing the minimum jackpot. First, people tend to buy more lottery tickets when the jackpot increases. This means that increasing the minimum jackpot from $4 to $5 million will result in higher ticket sales. Second, the addition of the new <i>Extra!</i> option will most likely increase the Texas Lottery Commission profits since many players will be willing to pay $2 for their ticket rather than $1 because of the improved prize payouts. <br />
<br />
Thus, it is noteworthy that the Texas Lottey Commission recognized the potential for increased profits and raised the minimum Jackpot accordingly.<br />
<br />
<span style="color: blue;"><b>Annuity Payout Period increases to 30 payments.</b></span><br />
However, changing the annuity payout period from 25 to 30 payments only benefits the Texas Lottery Commission, not the players.<br />
<br />
On the surface, players may be indifferent to this change because most jackpot winners opt for the cash value payment. But, the value of the cash prize offering is directly proportional to the length of time established by the annuity. This means that for any given annuity value, the longer the annuity term to maturity (years of payments), the lower the cash value will become.<br />
<br />
Thus, even though we have a higher annuity value, the corresponding cash value payout will be proportionately lower than what currently exists. <br />
<br />
In theory, the Texas Lottery Commission (TLC) should not care whether a player chooses to take the cash option or the annuity payment. The reason is that the cash value should be valued at the amount the TLC must invest in order to achieve the annuity payments. <br />
<br />
But since the discounted cash value will be lower after the 2013 changes are implemented, the TLC will profit more from the difference it is saving. <br />
<br />
Further, some players who would have previously opted for a 25 payment annuity may shy away from a 30 period annuity: First because it is 5 years longer (which increases the uncertainty period); and Second because the yearly annuity payment will be lower.<br />
<br />
Lets assume the annuity value is set at $5 million and the investment yield is 2.80%. Under the current rules of 25 payments, the cash value will be $3.66 million and each of the annuity payments will be $200,000.<br />
<br />
However, under the new 2013 rules of 30 payments, the cash value will be lowered to $3.45 million and each annuity payment will be reduced to $167,000.<br />
<br />
Under this scenario, the TLC will profit by $210,000 simply by the difference in the cash values. And, the players yearly payment will decrease by $33,000. <br />
<br />
<center>
<table border="1" style="width: 400px;">
<tbody>
<tr align="center" bgcolor="BLUEVIOLET"> <td colspan="7"><span style="color: white; font-size: large;"><b>Table <span style="font-size: large;">2</span>:<span style="font-size: large;"> Annuity to Cash and</span></b></span><br />
<span style="color: white; font-size: large;"><b><span style="font-size: large;">Yearly Payouts<span style="font-size: large;"> <span style="font-size: large;">Scenarios</span></span><span style="color: black;"><span style="background-color: white;"></span> </span></span></b></span></td></tr>
<tr bgcolor="BLUEVIOLET"> <td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b> Jackpot </b></span></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b> Yield </b></span></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b> Old</b></span></span></span><br />
<span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b> Cash </b></span></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b> New</b></span></span></span><br />
<span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b> Cash </b></span></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b> Cash </b></span></span></span><br />
<span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b> Diff </b></span></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b>Old Yearly</b></span></span></span><br />
<span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b>Payout </b></span></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b>New Yearly</b></span></span></span><br />
<span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><span style="color: white;"><b>Payout </b></span></span></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$4M </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">2.8% </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$2.93 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$2.76 </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">-$0.17 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">Old Yrly </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>- na -</b></span></span></td></tr>
<tr bgcolor="LIGHTBLUE"> <td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$5M </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">2.8% </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$3.66 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$3.45 </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">-$0.21 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$0.200 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$0.167</b></span></span></td></tr>
<tr bgcolor="LIGHTBLUE"> <td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$5M </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">4.0% </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$3.25 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$3.00 </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">-$0.25 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$0.200 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$0.167</b></span></span></td></tr>
<tr bgcolor="LIGHTBLUE"> <td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$5M </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">6.0% </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$2.71 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$2.43 </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">-$0.28 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$0.200 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$0.167</b></span></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$10M </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">2.8% </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$7.32 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$6.89 </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">-$0.43 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$0.400 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$0.333</b></span></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$10M </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">4.0% </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$6.50 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$5.99 </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">-$0.51 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$0.400 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$0.333</b></span></span></td></tr>
<tr> <td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$10M </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">6.0% </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$5.42 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$4.86 </b></span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">-$0.58 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;">$0.400 </span></span></td><td style="text-align: center;"><span style="font-size: x-small;"><span style="font-family: Verdana,sans-serif;"><b>$0.333</b></span></span></td></tr>
</tbody></table>
</center>
<br />
<b>Table 2</b> above illustrates various annuity to cash
values for 3 different yield values: 2.8% (current value); 4.0%; and
6.0%. As we can see, the new jackpot cash value for 30 payments is
always less than the current 25 payout structure. Additionally, we can
see that the annuity payout in the new 2013 game will be less than what
winners receive now.<br />
<br />
<span style="color: blue;"><b>Jackpot Increases by $0.250 million </b></span><br />
The last major change with the new 2013 Lotto Texas will be the increments by which the annuity jackpot will grow.<br />
<br />
Under the new rules, the jackpot will grow in increments of $0.250 compared to the existing $1.0 million increment. This does not mean that the jackpot will only grow by 1/4 million dollars between consecutive non-winning drawings. Instead, it means that the annuity will be set to the closest 1/4 million.<br />
<br />
While this may appear to be a detriment, we believe it is a good improvement to the game because it will be fairer to both the Lotto Texas players and the TLC as well.<br />
<br />
The reason is that the annuity can be adjusted more proportionately to actual ticket sales.<br />
<br />
For example, when the jackpot is set to the minimum, ticket sales are low. But, as the jackpot increases, the ticket sales increase as well. Thus, when the jackpot is set at $5.0 million, the next drawing jackpot may only be $5.25 or $5.50 million. But, when the jackpot grows to $10 million, the subsequent jackpot might be set at $10.750 or $11.250 million.<br />
<br />
In the past, the TLC would have to adjust jackpot growth more randomly because increments would be rounded to the nearest $1.0 million. This would have the effect of the TLC offering a lower annuity jackpot than what its profits would permit.<br />
<br />
Setting the Lotto Texas jackpot increment to $0.250 will now be the same as that of Texas Two Step. A review of that game's jackpot history shows that growth appears to be exponential, rather than linear. We believe this same pattern will be repeated by the Lotto Texas game as well.<br />
<br />
<span style="color: blue;"><b>Summary</b></span><br />
In summary, four new rules to Lotto Texas will go into effect beginning with the April 17, 2013 drawing.<br />
<br />
These changes include: offering a new <i>Extra!</i> option that will increase the non-jackpot prize payouts; increase the minimum annuity jackpot to $5 million; lengthening the annuity payout period from 25 to 30 payments; and, lowering the minimum annuity jackpot growth to $0.250 million.<br />
<br />
Overall, we believe these changes will be beneficial to lottery players in Texas, and to the Texas Lottery Commission as well. The <i>Extra!</i> option increases payout returns to the players and will increase the potential number of winners by 3 million. Increasing the minimum jackpot amount will help to attract more players when the annuity is at its minimum. And, changing the jackpot growth will help to increase the annuity offerings because it eliminates precautionary rounding. The only detriment to the new rules is the lengthening of the jackpot payout period. This may influence more players to choose the cash value payment. But, we believe the annuity is still better because the cash value will be lower than what it is today.<br />
<br />
Please not that at the time of this writing, the official rules have not been published on the Texas Lottery website. When they become available, we will add the link to this post and make any modifications necessary.<br />
<br />
<span style="color: blue;"><b>Sources:</b></span><br />
<ul>
<li>Lotto Texas Change Announcement </li>
<li><a href="http://www.lottoreport.com/LT2013Change.htm" target="_blank">The Lotto Report review of changes</a></li>
<li><a href="http://www.lotterypowerpicks.com/expandedOdds/US_TX6_expanded.htm" target="_blank">Lotto Texas 2013 Complete Odds and Return to Players</a></li>
<li><a href="http://www.lotterypowerpicks.com/tx6_extraAnalysis.htm" target="_blank">When to buy Lotto Texas Extra - Recommendation Analysis</a></li>
<li><a href="http://www.lotterypowerpicks.com/beta/?pageID=1I230" target="_blank">Texas Two Step Jackpot Growth History</a></li>
</ul>
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-35917219870072652982013-03-12T08:34:00.001-07:002013-03-12T08:39:03.020-07:00Draft 2 - Post DeletedDraft Post Deleted - published by mistakeJohn Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-4966646168903959292013-02-07T08:00:00.002-08:002013-02-07T08:03:30.072-08:00Whittaker's Luck - Explains why two unrelated men won their country's large lottery jackpots!<span style="color: blue;"><b>If you want to win the lottery, perhaps you should change your name to Whittaker.</b></span><br />
<a href="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcRSbR4B0ix343MGMmaM8mselBlLYFP_muAQr-0if1GkeShuMFD7hA" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcRSbR4B0ix343MGMmaM8mselBlLYFP_muAQr-0if1GkeShuMFD7hA" width="147" /></a><br />
Within the strange coincidence of luck, we read that two unrelated men with the same last name have both won a large jackpot in different countries. This article explains why they won.<br />
<br />
Most recently, <b>James Whittaker</b> of Edmonton Alberta won $15.7 million playing Canada's Lotto 649. James's winning was in the January 16, 2013 drawing. His numbers were: 14 21 27 34 37 38 (he did not need the Bonus ball 10). James bought his ticket at a 7-Eleven store.<br />
<br />
A little more than 10 years ago, <b>Andrew Jackson “Jack” Whittaker</b> won $314.9 million playing the U.S. Powerball lottery. Jack's winning occurred in the December 25 2002 drawing. His lucky numbers were: 5, 14, 16, 29, 53, and Powerball 7. Jack purchased his ticket at the C&L Super Serve convenience store.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right; margin-left: 1em; text-align: right;"><tbody>
<tr><td style="text-align: center;"><a href="http://www.cbc.ca/gfx/images/news/topstories/2013/01/22/li-lottery-winner.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="112" src="http://www.cbc.ca/gfx/images/news/topstories/2013/01/22/li-lottery-winner.jpg" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">James Whittaker</td></tr>
</tbody></table>
The lives of these two men are quite a bit different. James is a young and unmarried Canadian. He always wanted to win the lottery, and now that he did, he plans to invest his winnings and do some traveling. Because Canada does not tax lottery winnings, James will get to keep his full $15.7 million.<br />
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQaHUyiW6iD0CqMQOL5FTxmaP__zbpyGoLpeMXu0b5n4W_FxJ91jg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQaHUyiW6iD0CqMQOL5FTxmaP__zbpyGoLpeMXu0b5n4W_FxJ91jg" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">"Jack" Whittaker</td></tr>
</tbody></table>
Jack, on the other hand, was a 55 year old United States citizen living in Jumping Branch, WV. He was married and owned a construction company. Although the official lottery picture shows Jack with a check for $314.9 million, Jack chose to take the cash option. After taxes were withheld, Jack received only $93 million (still quite a nice sum).<br />
<br />
After winning, Jack had many personal and family problems. Hopefully, young James will learn from Jack's experiences and manage both his money and his life differently so that he avoids the pitfalls that Jack and other lottery winners encountered.<br />
<br />
If you're wondering, the name Whittaker is a variation of the common name Whitaker (only 1 "T"). It's origin is from Old English and means "white acre" or "white field" depending on which source is used.<br />
<br />
Uniquely though, both Jack and James spell their last name the exact same way (with two "T"s).<br />
<br />
<span style="color: blue;"><b>So, why did they both win the lottery? The only logical explanation is: Whittaker's Luck!</b></span><br />
<br />
Now that we know of Whittaker's Luck, maybe we should all rush out: change our last name to Whittaker; and then buy some lottery tickets at a local convenience store. Note that it doesn't matter: if you are married or not, which country you live in; or how old you are. Only your last name and where you buy the ticket are important! But, make sure that your name has 2 "T"s in it.<br />
<br />
Gotta go now. I'm rushing off to the courthouse to change my name!<br />
<br />
<span style="color: blue;"><b>Sources</b></span><br />
<ul>
<li><a href="http://www.huffingtonpost.ca/2013/01/22/james-whittaker-edmonton-lottery-win-_n_2529513.html" target="_blank">James Whittaker Wins Edmonton Lottery Of $15.6 Million Lotto 6/49 </a></li>
<li><a href="http://www.cbc.ca/news/canada/edmonton/story/2013/01/22/edmonton-lotto649-winner.html" target="_blank">Edmonton man wins $15.7M in Lotto 649 </a></li>
<li><a href="http://en.wikipedia.org/wiki/Jack_Whittaker_%28lottery_winner%29" target="_blank">Jack Whittaker (lottery winner)</a></li>
<li><a href="http://www.businessweek.com/articles/2012-12-13/lottery-winner-jack-whittakers-losing-ticket" target="_blank">Lottery Winner Jack Whittaker's Losing Ticket</a></li>
<li><a href="http://www.cosmoloan.com/investments/5-worst-cases-of-lottery-disasters.html" target="_blank">5 Worst Cases Of Lottery Disasters</a></li>
<li><a href="http://wiki.answers.com/Q/What_does_the_name_Whitaker_mean" target="_blank">What does the name Whitaker mean?</a></li>
<li><a href="http://www.ourbabynamer.com/meaning-of-Whitaker.html" target="_blank">Whitaker</a></li>
</ul>
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-60755830917914124082012-11-26T11:14:00.000-08:002012-11-27T12:32:47.906-08:00Should you buy all 175.2 million Powerball combinations?<b><span style="color: blue;">Update 1</span>: <span style="color: red;">The Powerball annuity jackpot has been increased to $500 million, and the cash value is now $327 million. (Tuesday, Nov 27 3:31 PM)</span></b><br />
<b> </b><br />
<b>With the Powerball jackpot now at $425 million, it is logical for players to wonder if they should buy tickets for all the possible combinations. At first glance, one might think this would be a winning strategy for picking up an easy $74.6 million. </b><br />
<br />
However, before one recklessly spends this much money, there are several factors that that must be considered.<br />
<ol>
<li>In the 2012 Powerball game, each ticket costs $2. Since there are approximately 175.2 million combinations, one would have to spend $350.4 million to accomplish this.</li>
<li>The $425 million jackpot is the annuity value which is paid in 30 varying installments (29 years). This implies that the breakeven 0 profit financing rate is 1.144%. So, if one borrowed the $350.4 million, the borrowing rate must be less than this interest rate in order to make a profit. If the borrowing rate is more than 1.144%, you will lose money.</li>
<li>The cash value being offered today is $278.3 million. If you take the cash, you will immediately lose $72.1 million.</li>
<li>In order to guarantee yourself a winning ticket, you must buy all the 175.2 unique combinations. If you are lazy and buy 175.2 quick picks, then there is a 36.8% chance that you will not have the winning combination.</li>
<li>When the jackpot is this high, we can expect that approximately 120 million other tickets will be sold. Of these, there will be a 50% chance that one of these will be a winning ticket. This means that there is a 50% chance that you will have to share the jackpot prize with at least 1 other winner. If this happens, you might win only $212.5 million annuity or $139.2 million cash or less. Again, you will take a loss.</li>
</ol>
As you can quickly see, there is a very high probability that even if you buy all the unique combinations, you will end up losing millions of dollars if you purchase all the combinations. Thus, our advice is:<br />
<br />
<div style="text-align: center;">
<span style="color: blue;"><b>No, You should NOT but all the Powerball combinations.</b></span></div>
<br />
<b>But, what if no one wins the jackpot in the next drawing and the Powerball grows to $600 million. Should you buy the combinations then?</b><br />
To help you answer this, we present the two graphs below. The first shows the chances of there being a losing Powerball as ticket sales grow to 500 million. As you can see, the chances decrease as sales increase. When 200 million tickets are sold. there is a 30% chance that nobody will win. When ticket sales hit 500 million, there is less than a 6% chance that there will be no winner.<br />
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<img alt="" 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" /></div>
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The second graph shows the probabilities of having more than one winner. At sales of 200 million, there is a 40% chance of multiple winners. When sales reach 500 million, there is a 67% chance that there will be more than one winning ticket.<br />
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<img alt="" 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" /></div>
<div style="text-align: center;">
<br /></div>
So, even as the temptation to purchase all combinations increases as the jackpot value grows, the likelihood that the prize will be shared by more than one winner also increases. So, even if the annuity jackpot reached $1 trillion, it would most likely be shared by 2 or more winners, which means that each winner would only receive a jackpot prize equal to or less than the $425 million currently offered.<br />
<br />
Thus, we continue to recommend that you should:<span style="color: blue;"></span><br />
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<span style="font-size: large;"><span style="color: blue;"><b>NEVER buy all the Powerball combinations!</b></span></span></div>
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com1tag:blogger.com,1999:blog-60725341237976466.post-71395302093616605732012-10-18T12:51:00.000-07:002012-10-18T12:51:38.902-07:00Why you should play the Pick 4 LotteryThe primary goal of a lottery player is to win money. However, the motive behind this goal varies from person to person. Some do this to win a large jackpot, and to be set for life. Others play to supplement their income by trying to continually win smaller prizes. And, a smaller group are addicted gamblers, hooked on the thrill of winning regardless of the prize.<br />
<br />
<a href="http://i.nbc40.net/lottery/pick4.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://i.nbc40.net/lottery/pick4.png" /></a>This article is aimed at the second group of players, i.e. those who play to supplement their income. These are the people who treat the lottery expenditures as an investment. Their objective is to continually win smaller prizes and not to lose any of their own money. Their mindset is similar to those who invest in options. They know that they will:<br />
<ul>
<li>lose a little,</li>
<li>lose a little,</li>
<li>make a lot!</li>
</ul>
<span style="color: blue;"><b>Play Pick 4 </b></span><br />
To accomplish a viable cash flow of winnings, we suggest that playing the Pick 4 lottery game in your individual states. <br />
<br />
While there are slight variations in cost and payouts, the basic format of the game is identical in most states. To win, the player must select 4 numbers that range from 0 to 9 in each of the positions. This means that there are 10,000 possible combinations. In general, the cost of each ticket is $0.50 and the payout is $2,500. And, in most states, the Pick 4 drawings are held twice a day, seven days a week.<br />
<br />
In some states, the cost of the ticket is double ($1.00), but the payout is also double ($5,000). Further, many states pay out a fixed prize, and others determine the winning prize on a pari-mutuel basis. In these instances, we can still assume that the average payout per $0.50 spent is $2,500.<br />
<br />
<span style="color: blue;"><b>A Winning Strategy</b></span><br />
To limit one's costs, we recommend that a player select only number that they wish to play. Then, we suggest that they play that number in every drawing until it wins. <br />
<br />
By doing this, a player will be spending only $0.50 to win $2,500. Thay is a return of 5,000 to 1. <br />
<br />
However, we recognize that the players number may not be drawn immediately. This means that the player will be spending $1.00 per day until it wins. This represents $365 per year and 700 drawings. If the number is not drawn for a while, the player has approximately 6.9 years (6 years 10 months) until he reaches the breakeven level (which is 5,000) drawings.<br />
<br />
<span style="color: blue;"><b>Comparison</b></span><br />
To help understand this strategy, we have prepared the table and graphs below comparing the Pick 4 lottery game to Powerball (PB), Powerball with Powerplay (X PB), Mega Millions, Mega Millions with Megaplier (X MM), Lotto 649 (L6), Lotto Max (LM), and Pick 3. The charts only consider prizes in those games where the player matches 4 balls. <br />
<br />
<table border="1" cellpadding="0" cellspacing="0" style="width: 540px;"><colgroup><col style="mso-width-alt: 2779; mso-width-source: userset; width: 57pt;" width="76"></col>
<col style="mso-width-alt: 2779; mso-width-source: userset; width: 57pt;" width="76"></col>
<col style="width: 48pt;" width="64"></col>
<col style="width: 48pt;" width="64"></col>
<col style="width: 48pt;" width="64"></col>
<col style="mso-width-alt: 2523; mso-width-source: userset; width: 52pt;" width="69"></col>
<col style="mso-width-alt: 2596; mso-width-source: userset; width: 53pt;" width="71"></col>
<col style="width: 48pt;" width="64"></col>
<col style="mso-width-alt: 2377; mso-width-source: userset; width: 49pt;" width="65"></col>
<col style="width: 48pt;" width="64"></col>
</colgroup><tbody>
<tr height="20" style="background-color: #999999; height: 15.0pt;">
<td class="xl66" height="20" style="height: 15pt; text-align: center; width: 57pt;" width="76"><span style="font-size: x-small;"><br /></span></td>
<td class="xl66" style="text-align: center; width: 57pt;" width="76"><span style="font-size: x-small;">Cost per</span><br />
<span style="font-size: x-small;">Ticket</span></td>
<td class="xl67" style="text-align: center; width: 48pt;" width="64"><span style="font-size: x-small;">Prize</span></td>
<td class="xl65" style="text-align: center; width: 48pt;" width="64"><span style="font-size: x-small;">Odds</span></td>
<td class="xl67" style="text-align: center; width: 48pt;" width="64"><span style="font-size: x-small;">Winnings</span><br />
<span style="font-size: x-small;">per $</span></td>
<td class="xl67" style="text-align: center; width: 52pt;" width="69"><span style="font-size: x-small;">Return </span></td>
<td class="xl67" style="text-align: center; width: 53pt;" width="71"><span style="font-size: x-small;">Dwgs</span><br />
<span style="font-size: x-small;">per Week</span></td>
<td class="xl67" style="text-align: center; width: 48pt;" width="64"><span style="font-size: x-small;">Weeks to Prize</span></td>
<td class="xl67" style="text-align: center; width: 49pt;" width="65"><span style="font-size: x-small;">Years to Prize</span></td>
<td class="xl67" style="text-align: center; width: 48pt;" width="64"><span style="font-size: x-small;">Cost per Year</span></td>
</tr>
<tr height="20" style="height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">Pick 4</span></b></span></td>
<td class="xl66" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">$0.50</span></b></span></td>
<td class="xl67" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">$2,500</span></b></span></td>
<td class="xl65" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">10,000</span></b></span></td>
<td class="xl67" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">$5,000</span></b></span></td>
<td class="xl66" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">$0.25</span></b></span></td>
<td style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">14</span></b></span></td>
<td class="xl68" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">357.1</span></b></span></td>
<td class="xl68" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">6.9</span></b></span></td>
<td class="xl68" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">364.0</span></b></span></td>
</tr>
<tr height="20" style="background-color: #cfe2f3; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">PB 4/5+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$2.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$10,000</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">648,976</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$5,000</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.02</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">2,500.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">48.1</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">208.0</span></td>
</tr>
<tr height="20" style="background-color: #cfe2f3; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">PB 4/5</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$2.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$100</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">19,088</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$50</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.01</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">25.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">0.5</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">208.0</span></td>
</tr>
<tr height="20" style="background-color: #cfe2f3; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">PB 3/5+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$2.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$100</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">12,245</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$50</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.01</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">25.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">0.5</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">208.0</span></td>
</tr>
<tr height="20" style="background-color: #cfe2f3; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">X PB 4/5+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$3.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$40,000</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">648,976</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$13,333</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.06</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">6,666.7</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">128.2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">312.0</span></td>
</tr>
<tr height="20" style="background-color: #cfe2f3; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">X PB 4/5</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$3.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$200</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">19,088</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$67</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.01</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">33.3</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">0.6</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">312.0</span></td>
</tr>
<tr height="20" style="background-color: #cfe2f3; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">X PB 3/5+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$3.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$200</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">12,245</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$67</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.02</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">33.3</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">0.6</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">312.0</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">MM 4/5+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$1.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$10,000</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">689,065</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$10,000</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.01</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">5,000.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">96.2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">104.0</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">MM 4/5</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$1.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$150</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">15,313</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$150</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.01</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">75.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">1.4</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">104.0</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">MM 3/5+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$1.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$150</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">13,781</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$150</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.01</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">75.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">1.4</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">104.0</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">X MM 4/5+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$2.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$40,000</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">648,976</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$20,000</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.06</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">10,000.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">192.3</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">208.0</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">X MM 4/5</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$2.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$400</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">19,088</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$200</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.02</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">100.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">1.9</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">208.0</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">X MM 3/5+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$2.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$400</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">12,245</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$200</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.03</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">100.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">1.9</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">208.0</span></td>
</tr>
<tr height="20" style="background-color: #cfe2f3; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">L6 5/6</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$2.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$2,478</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">55,491</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$1,239</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.04</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">619.5</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">11.9</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">208.0</span></td>
</tr>
<tr height="20" style="background-color: #cfe2f3; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">L6 4/6</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$2.00</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$87</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">1,033</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$44</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.08</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">21.8</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">0.4</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">208.0</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">LM 6/7</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$1.67</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$6,973</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">299,305</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$4,184</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.02</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">4,183.8</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">80.5</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">86.7</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">LM 5/7</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$1.67</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$138</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">4,751</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$83</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.03</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">82.8</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">1.6</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">86.7</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">LM 4/7</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$1.67</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$20</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">214</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$12</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.09</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">12.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">0.2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">86.7</span></td>
</tr>
<tr height="20" style="background-color: #f4cccc; height: 15pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="font-size: x-small;">LM 3/7+</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$1.67</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$20</span></td>
<td class="xl65" style="text-align: center;"><span style="font-size: x-small;">230</span></td>
<td class="xl67" style="text-align: center;"><span style="font-size: x-small;">$12</span></td>
<td class="xl66" style="text-align: center;"><span style="font-size: x-small;">$0.09</span></td>
<td style="text-align: center;"><span style="font-size: x-small;">1</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">12.0</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">0.2</span></td>
<td class="xl68" style="text-align: center;"><span style="font-size: x-small;">86.7</span></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">Pick 3</span></b></span></td>
<td class="xl66" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">$0.50</span></b></span></td>
<td class="xl67" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">$250</span></b></span></td>
<td class="xl65" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">1,000</span></b></span></td>
<td class="xl67" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">$500</span></b></span></td>
<td class="xl66" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">$0.25</span></b></span></td>
<td style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">14</span></b></span></td>
<td class="xl68" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">35.7</span></b></span></td>
<td class="xl68" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">0.7</span></b></span></td>
<td class="xl68" style="text-align: center;"><span style="color: blue;"><b><span style="font-size: x-small;">364.0</span></b></span></td>
</tr>
</tbody></table>
<br />
As you can see, the games with the highest return to the players are both the Pick 4 and Pick 3 games. <br />
<br />
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" /><br />
<br />
Next, we examine the Per Dollar Prize amounts. Here, we see that only 4 prize levels return as much money per dollar spent as that of Pick 4. These are the Powerball and Mega Millions payouts for matching 4 white balls and the Power or Mega ball.<br />
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<img alt="" 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" /><br />
<br />
Now lets consider the amount of time we have before we reach the $0 (zero dollar) profit level. Of the 6 prizes that exceed the 6.9 year level, total amount spent is substantially higher than the Pick 4 total of $2,500.<br />
<br />
<img alt="" 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" /><br />
<br />
Lastly, we illustrate the yearly cost of purchasing one single ticket for each of the games. Here, we see that the Pick 4 and Pick 3 cost is highest. However, this is primarily a function of there being 14 drawings held in a week verses 2 for most games (and 1 for Lotto Max).<br />
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<img alt="" 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" /><br />
<br />
<span style="color: blue;"><b>Summary</b></span><br />
In summary, we believe that playing 1 Pick 4 combination continually in each drawing is a viable strategy for those lottery players looking to earn investment income at a relatively low and affordable cost!<br />
<br />
JL ..............<br />
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-23691138218946566552012-10-01T13:11:00.000-07:002012-10-03T08:14:24.092-07:00Introducing the Lottery Probability SurfaceIn an effort to help players find a financially feasible strategy for playing the lottery, we discovered an important organization inherent in all lottery games. By reducing all the combinations of a particular game into individual sum and range buckets, and then totaling those occurrences, have identified each game's "probability surface".<br />
<br />
The surface is constructed using the only the primary white balls and not the bonus balls. One axis of the surface consist of the Sum of all the balls. And, the second axis is defined by subtracting the last ball from the first ball (the X and Y axis are interchangeable). <br />
<br />
Doing this, for Pick 3 and 4 games which allow all selection for replacement, the resulting surface is that of a diamond. The reason for this pattern is that the last ball may be less than, equal to, or greater than the first ball, thus allowing the Range to progress from negative to positive values. The illustration below is a 3-D view of the Pick 4 probability surface.<br />
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-JVNPamaGFlk/UGntyjEQ0LI/AAAAAAAAAKA/HKi0OZUKBic/s1600/pick4_surf_3d.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Pick 4 Lottery Probability Surface (3-D)" border="0" height="264" src="http://3.bp.blogspot.com/-JVNPamaGFlk/UGntyjEQ0LI/AAAAAAAAAKA/HKi0OZUKBic/s320/pick4_surf_3d.jpg" title="3-D Image of Pick 4 Lottery Probability Surface" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: blue;"><b>3-D Image of Pick 4 Lottery Probability Surface</b></span></td></tr>
</tbody></table>
<br />
For those games which do not have replacement (such as Mega Millions, Powerball, Lotto 649, Texas 2 Step, etc), we ignore the order drawn and sort the numbers from lowest to highest value. Doing this, we define a shape that is trapezoidal in shape. The illustration below is a 3-D view of the Texas 2 Step probability surface. This shape similar to that of Powerball, Mega Millions, etc. However, its scale is more condensed.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-zZWvrB_1_0w/UGnut5kfMUI/AAAAAAAAAKQ/9Hp1lgdf4lU/s1600/tx2_surf_3d.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img alt="Texas 2 Step Lottery Probability Surface (3-D)" border="0" height="264" src="http://1.bp.blogspot.com/-zZWvrB_1_0w/UGnut5kfMUI/AAAAAAAAAKQ/9Hp1lgdf4lU/s320/tx2_surf_3d.jpg" title="3-D Image of Texas 2 Step Lottery Probability Surface" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="color: blue;"><b>Texas 2 Step Lottery Probability Surface (3-D)</b></span></td></tr>
</tbody></table>
<span id="goog_212208217"></span><span id="goog_212208218"></span><br />
During the coming months, we will publish the probability surface characteristics for each of the lottery games that we cover. In addition, we will be adding new analytic pages to our website summarizing the historical data of each game.<br />
<br />
Our first application using this new discovery will be the Pick 4 games. We are well into the development of studying the New Jersey Pick 4 and hope to release this in the next few weeks. Following that, we will apply the same template to analyzing the Pick 4 games which we can easily obtain the complete drawing histories (California, Texas, North Carolina).<br />
<br />
JL ..........John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-44041666174873451102012-09-03T03:30:00.000-07:002012-09-03T03:30:02.288-07:00Lottery Power Picks turns 6 year old this SeptemberThis has been an exciting year for us at Lottery Power Picks. It began with the announcement that Powerball was going to change its format. With that, we wrote an analysis of the new format and projected anticipated jackpot growth. Along with that, we added a "Which Game Should You Play" page, and provided our users with a new 2012 Powerball playing guide (all of these are available on this blog).<br /><br />Our overall suite of products (website and blogs) has consistently maintained a level of 5,000 page views a day throughout the year. However, when the Mega Millions jackpot reached the $400 million level, we found that search traffic jumped dramatically. Our daily traffic at the peak for: the Lottery Power Picks website had a record level of 8,137 visits; our news blog had 265 visits; and this blog received 2,470 visits.<br /><br />During that period, we realized a few important things about lottery related sites. First, we learned that when jackpots are low, consumer interest is also low. People only become fanatics when the jackpot levels reach the $200 million level. Second, we learned that all the information that we provide is sought after during high times. Third, although daily visitor levels are relatively low most of the time, it is important to be positioned for the extraordinary times. Lastly, we learned that our information is valuable.<br /><br />This had brought new enthusiasm to us. And, we responded by re-writing our Lottery Power Picks website. Although this is not fully complete yet, we have released it beta. We expect this to be fully functional in the upcoming months and will cut it over to our live site by the end of 2012.<br /><br />Additionally, we have been working on a Pick 4 strategy that we believe will help you win those prizes. It differs from our Pick 3 strategy because the cost of playing too many combinations is not cost effective. We will release our Pick 4 pages and write a blog entry about this by Thanksgiving.<br /><br />Lastly, our web hosting company moved our site to a new server last Spring. Since then, our up-time has been nearly 100%, and more importantly, hacking attempts have dropped to a minimum. This allowed us to spend less time monitoring the traffic and more time developing our lottery brand.<br /><br />We wish to thank all of our users who visit us on a regular basis and have taken the time to write us and give us feedback. Additionally, we thank Google for providing us with a wide range of development and monitoring tools, and helping us appear in search results.<br /><br />We look forward to releasing our new website and analytical lottery coverage articles during the next year. Hopefully, one or more of us will win a jackpot prize as well!<br /><br />JL ............<br /><br /><br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-54731269712353126732012-04-30T12:45:00.001-07:002012-04-30T12:45:24.534-07:00Is is Time for a Euro Millions Super Draw?<div style="color: blue; text-align: center;">
<span style="font-size: large;"><b>Expect to see a Euro Millions Super Draw during May 2012</b></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.townhousecomms.co.uk/wp-content/uploads/2011/10/EUROMILLIONS-20.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="http://www.townhousecomms.co.uk/wp-content/uploads/2011/10/EUROMILLIONS-20.jpg" width="320" /></a></div>
One of the special features of the Euro Millions lottery is the Super Draw. These are named "Super" because the minimum jackpot prize is typically set at €100 million, regardless the level of the previous jackpot.<br />
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In these drawings, only the Jackpot prize amount is increased.<br />
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<b style="color: blue;">What if there is no winner?</b><br />
What happens to the Super Draw Jackpot prize it there is no jackpot winner depends on the Super Draw designation:<br />
<ul>
<li><b>Super Draw One</b> means that the jackpot will roll forward to the following drawing; and</li>
<li><b>Super Draw Two</b> means the jackpot prize will be allocated to the winners of the next lowest tier in which there is a winner.</li>
</ul>
<b style="color: blue;">How are these funded?</b><br />
After every Euro Millions drawing, 50% of the gross ticket revenue is allocated to the Common Prize Fund. Of this, 8.6% is placed in the EuroMillions Reserve Fund (also called the Booster Fund). <br />
<br />
When the amount of money in the booster fund is sufficient, it is withdrawn and used for a Super Draw.<br />
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On the average, approximately €1million are added to the booster fund after each drawing. This means, it will take about a year for €100 million to accumulate.<br />
<br />
To make Super Draws more frequent, the Super Draws are typically designated after the anticipated jackpot reaches €40M to €50M and the booster fund contains the remainder.<br />
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<b style="color: blue;">Why now?</b><br />
The last Super Draw was held on October 4, 2011, approximately 6 months ago.<br />
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<div style="color: blue;">
<b>At present, we have calculate the value of the Reserve Fund to be around €57 million, which means that we would expect to see a new Euro Millions Super Draw sometime soon in the month of May 2012 (or whenever the jackpot nears </b><b>€50 million).</b></div>
<br />
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com3tag:blogger.com,1999:blog-60725341237976466.post-30623395160550505242012-03-30T09:45:00.001-07:002012-03-30T10:49:00.990-07:00Probability of a Mega Millions rollover or having a single winner decrease as sales approach 600MAs tonight's record Mega Millions drawing approaches, ticket sales are going off the charts. We originally expected that 400 million tickets would be sold, but with the recent increases in the jackpot prize from $476M to <strike>$540M</strike> $640M, we now believe that up to 600 million tickets may be sold.<br />
<br />
Thus, we asked ourselves two questions:<br />
<ol>
<li>What is the probability that there will be no winner in tonight's drawing? </li>
<li>What is the probability that there will only be one sole winner?</li>
</ol>
Using our brute force duplicate ticket estimator, we have produced two tables for your reference.<br />
<br />
The first summarizes the probabilities of: 0 to 8 individual winning tickets. As shown, the probability of not having a winner tonight and rolling over again drops from 18% to 3% as ticket sales increase from 300 million to 600 million. Similarly, we can see that the probability of having a single winner decreases from 39% to 27%, while that of two winners decreases slightly from 28% to 26%. Interestingly, we find the probabilities of 3 to 5 winners rapidly increase as sales approach 600 million. We believe the likelihood that 6 or more winning combinations will be sold is rather slim.<br />
<br />
<br />
<br />
<br />
<center><table border="1" cellpadding="0" cellspacing="0" style="width: 482px;"><colgroup><col style="mso-width-alt: 4022; mso-width-source: userset; width: 83pt;" width="110"></col>
<col span="4" style="mso-width-alt: 3401; mso-width-source: userset; width: 70pt;" width="93"></col>
</colgroup><tbody>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="background-color: red; color: white; height: 15pt; text-align: center; width: 83pt;" width="110"><b><br /></b></td>
<td colspan="5" style="background-color: red; color: white; text-align: center; width: 70pt;" width="93"><b>Table 1: Probability of Mega Millions Winning Tickets</b></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="background-color: red; color: white; height: 15pt; text-align: center;"><b>Winning Tickets</b></td>
<td class="xl63" style="background-color: red; color: white; text-align: center;"><b>300M Sold </b></td>
<td class="xl63" style="background-color: red; color: white; text-align: center;"><b>400M Sold</b></td>
<td class="xl63" style="background-color: red; color: white; text-align: center;"><b>500M Sold</b></td>
<td class="xl63" style="background-color: red; color: white; text-align: center;"><b>600M Sold</b></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">None, No winner</td>
<td class="xl64" style="text-align: center;">18.1%</td>
<td class="xl64" style="text-align: center;">10.3%</td>
<td class="xl64" style="text-align: center;">5.8%</td>
<td class="xl64" style="text-align: center;">3.3%</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">1 Winner Only</td>
<td class="xl64" style="text-align: center;">39.3%</td>
<td class="xl64" style="text-align: center;">35.4%</td>
<td class="xl64" style="text-align: center;">31.2%</td>
<td class="xl64" style="text-align: center;">27.4%</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">2 Winner Only</td>
<td class="xl64" style="text-align: center;">28.2%</td>
<td class="xl64" style="text-align: center;">29.5%</td>
<td class="xl64" style="text-align: center;">28.2%</td>
<td class="xl64" style="text-align: center;">25.9%</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">3 Winner </td>
<td class="xl64" style="text-align: center;">12.4%</td>
<td class="xl64" style="text-align: center;">18.4%</td>
<td class="xl64" style="text-align: center;">21.5%</td>
<td class="xl64" style="text-align: center;">22.2%</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">4 Winner </td>
<td class="xl64" style="text-align: center;">1.9%</td>
<td class="xl64" style="text-align: center;">5.9%</td>
<td class="xl64" style="text-align: center;">11.0%</td>
<td class="xl64" style="text-align: center;">14.9%</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">5 Winner </td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;">0.5%</td>
<td class="xl64" style="text-align: center;">2.3%</td>
<td class="xl64" style="text-align: center;">5.6%</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">6 Winner </td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;">0.1%</td>
<td class="xl64" style="text-align: center;">0.6%</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">7 Winner </td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;"><br /></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">8 Winner </td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;"><br /></td>
<td class="xl64" style="text-align: center;"><br /></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">Total Probability</td>
<td class="xl65" style="text-align: center;">100.0%</td>
<td class="xl65" style="text-align: center;">100.0%</td>
<td class="xl65" style="text-align: center;">100.0%</td>
<td class="xl65" style="text-align: center;">100.0%</td>
</tr>
</tbody></table>
</center>
<br />
<br />
The second table summarizes the distribution of the tickets sold. It estimates the absolute number of tickets in each
category. Here we find that approximately 31.9 million combinations will not be generated when sales are at the 300M level, but only 5.8 million combinations will be unsold when 600M tickets are printed. In all other cases, the absolute number of tickets per category increase as sales increase. Interestingly enough, we can see how the size of the 6 and 7 tuplets begins to grow.<br />
<br />
<br />
<br />
<br />
<center><table border="1" cellpadding="0" cellspacing="0" style="width: 482px;"><colgroup><col style="mso-width-alt: 4022; mso-width-source: userset; width: 83pt;" width="110"></col>
<col span="4" style="mso-width-alt: 3401; mso-width-source: userset; width: 70pt;" width="93"></col>
</colgroup><tbody>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="background-color: red; color: white; height: 15pt; text-align: center; width: 83pt;" width="110"><b><br /></b></td>
<td colspan="4" style="background-color: red; color: white; text-align: center; width: 70pt;" width="93"><b>Table 2: Distribution of Mega Millions Tickets Sold</b></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="background-color: red; color: white; height: 15pt; text-align: center;"><b>Numbers</b></td>
<td class="xl63" style="background-color: red; color: white; text-align: center;"><b>300M Sold </b></td><td class="xl63" style="background-color: red; color: white; text-align: center;"><b>400M Sold</b></td><td class="xl63" style="background-color: red; color: white; text-align: center;"><b>500M Sold</b></td><td class="xl63" style="background-color: red; color: white; text-align: center;"><b>600M Sold</b></td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">All Combinations</td>
<td class="xl66" style="text-align: center;">175,711,536</td>
<td class="xl66" style="text-align: center;">175,711,536</td>
<td class="xl66" style="text-align: center;">175,711,536</td>
<td class="xl66" style="text-align: center;">175,711,536</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">Unsold</td>
<td class="xl66" style="text-align: center;">31,864,733</td>
<td class="xl66" style="text-align: center;">18,036,279</td>
<td class="xl66" style="text-align: center;">10,209,010</td>
<td class="xl66" style="text-align: center;">5,778,566</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">1 Only (Singles)</td>
<td class="xl66" style="text-align: center;">143,846,803</td>
<td class="xl66" style="text-align: center;">157,675,257</td>
<td class="xl66" style="text-align: center;">165,502,526</td>
<td class="xl66" style="text-align: center;">169,932,970</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">2 (Doubles)</td>
<td class="xl66" style="text-align: center;">103,460,042</td>
<td class="xl66" style="text-align: center;">131,466,722</td>
<td class="xl66" style="text-align: center;">149,526,982</td>
<td class="xl66" style="text-align: center;">160,511,932</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">3 (Triples)</td>
<td class="xl66" style="text-align: center;">45,526,185</td>
<td class="xl66" style="text-align: center;">82,214,057</td>
<td class="xl66" style="text-align: center;">114,388,867</td>
<td class="xl66" style="text-align: center;">137,818,542</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">4 (Quadruples)</td>
<td class="xl66" style="text-align: center;">7,022,773</td>
<td class="xl66" style="text-align: center;">26,431,098</td>
<td class="xl66" style="text-align: center;">58,127,495</td>
<td class="xl66" style="text-align: center;">92,689,034</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">5 (Quintuples)</td>
<td class="xl66" style="text-align: center;">144,138</td>
<td class="xl66" style="text-align: center;">2,198,990</td>
<td class="xl66" style="text-align: center;">12,023,012</td>
<td class="xl66" style="text-align: center;">35,013,149</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">6 (Sextuplets)</td>
<td class="xl66" style="text-align: center;">59</td>
<td class="xl66" style="text-align: center;">13,876</td>
<td class="xl66" style="text-align: center;">430,590</td>
<td class="xl66" style="text-align: center;">3,988,410</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">7 (Septuplets)</td>
<td class="xl66" style="text-align: center;">0</td>
<td class="xl66" style="text-align: center;">0</td>
<td class="xl66" style="text-align: center;">528</td>
<td class="xl66" style="text-align: center;">45,963</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">8 (Octuplets)</td>
<td class="xl66" style="text-align: center;"><br /></td>
<td class="xl66" style="text-align: center;"><br /></td>
<td class="xl66" style="text-align: center;"><br /></td>
<td class="xl66" style="text-align: center;">0</td>
</tr>
<tr height="20" style="height: 15.0pt;">
<td height="20" style="height: 15pt; text-align: center;">Sum</td>
<td class="xl66" style="text-align: center;">300,000,000</td>
<td class="xl66" style="text-align: center;">400,000,000</td>
<td class="xl66" style="text-align: center;">500,000,000</td>
<td class="xl66" style="text-align: center;">600,000,000</td>
</tr>
</tbody></table>
</center>
<br />
<br />
We wish everyone the best of luck tonight and hope your dreams come true. But, as we can see from the above, remember to set your expectations according to the probability that you may have to share the jackpot prize with somebody else.<br />
<br />
Cheers,<br />
<br />
JL...............<br />
<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com1tag:blogger.com,1999:blog-60725341237976466.post-46038053997406333942012-03-28T13:15:00.000-07:002012-03-29T06:52:17.215-07:00Should I buy all the 175.7M Mega Millions combinations?In the Tuesday night Mega Millions lottery drawing on March 27, 2012, an estimated 170 to 240 million tickets were sold. We obtain these numbers by doubling the increase in the cash (from $255M to $341M) and annuity (from $356M to $240M) prizes from the 27th to the Friday March 30th drawing. (<i>Note that while the Mega Millions annuity has been increased to $500M and cash to $359.4, we have chosen to use the original prize levels to estimate ticket sales</i>).<br />
<br />
However, for purposes of this discussion, we will assume that 200 million Mega Million tickets were sold for that drawing.<br />
<br />
Since our ticket sale estimate is well above the total number of allowable Mega Millions combinations (175.7 million), one can logically ask:<br />
<br />
<div style="color: orange; text-align: center;">
<span style="font-size: large;"><b>Why was there no Mega Millions Jackpot winner? </b></span></div>
<br />
The answer is: <span style="color: blue; font-size: large;"><b>Duplicates!</b></span><br />
<br />
Because of randomness, the percent of duplicate tickets increases rapidly as the number of tickets are sold. In Mega Millions, this increase begins to level off after sales exceed 400 million. As the illustration below shows, approximately 40% of the combinations printed are duplicates when 200 million individual tickets are sold. <br />
<br />
<div style="text-align: center;">
<b style="color: blue;">Graph 1: Percent of Mega Millions Duplicates per Million Tickets Sold</b></div>
<div style="text-align: center;">
<img alt="" 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" /></div>
<div style="text-align: center;">
<br /></div>
This means that of the 200 million sold, 80 million are duplicates, and only 120 million are unique. If we divide the 120 million by the 175 million Mega Millions combinations, we find that approximately 68.6% of the combinations were generated. Subtracting 68.6% from 100%, we learn that there is a 31.4% chance that the number picked in the drawing will be a loser.<br />
<br />
<div style="text-align: center;">
<b style="color: blue;">Graph 2: </b><b style="color: blue;">Chance of Losing Mega Millions per Million Tickets Sold</b></div>
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<img alt="" 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" /></div>
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Given the fact that the new Mega Millions annuity jackpot is set at $476 million for Friday night, we can expect ticket sales to potentially reach or exceed 300 million. At this level, about 52% of these tickets will be duplicate combinations, and there will be an 18% chance that there will be no Jackpot winner at all.<br />
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So, getting to our title question:<br />
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<div style="text-align: center;">
<span style="color: orange; font-size: large;"><b>Should I buy all the 175.7M Mega Millions combinations?</b></span></div>
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<b>The answer depends on how you purchase them</b>. If you purchase every single unique combination, then Yes, you are guaranteed to win the Jackpot. In this case, there will be no losing tickets. However, you have to worry about sharing the jackpot prize with others. Using Graph 1 above, we can say that at the 300 million ticket sales level, you have 50 - 50 chance of winning it alone or sharing it with one or more others.<br />
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If you take the Cash Option, you will lose money if you have to share it with 1 other person.<br />
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And, if you take the Annuity, you lose money if you share it with 2 others.<br />
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<b>However, if you are lazy and just buy 175.7 million Quick Picks, you are not guaranteed to win the jackpot.</b> As stated above, approximately 40% of these will be duplicates and you will have a 31.4% chance of losing.<br />
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The last thing to remember is that you will have to pay taxes on the money you receive. If you win the jackpot, you will be in the highest tax bracket possible, which means that you will be paying 28% to the federal government.Then, depending on the State where you purchased your winning ticket and live, you may have to pay state taxes as well.<br />
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<div style="color: blue;">
<b>So in summary, our advice is NO. You should not purchase the 175.7million Mega Millions combinations unless the jackpot becomes substantially higher to cover your taxes and the possible loss of sharing it with others.</b></div>
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<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com1tag:blogger.com,1999:blog-60725341237976466.post-22774787402882382372012-03-21T08:04:00.000-07:002012-03-21T08:04:19.787-07:00Multiple Lottery Ticket Odds Calculator ReleasedWith all the excitement of winning the large Mega Millions and Powerball jackpots recently, we realized that many players were searching for a calculator that would show the odds (or chances) of winning when multiple tickets are purchased.<br />
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In response, we created and released a new Multi-Ticket Lottery Odds Calculator gadget which can be found on the right hand sidebar of this blog (about 1/4 down the page), on our Lottery Power Picks News blog, and in the Google gadgets directory. To use this calculator, simply enter the number of tickets that you purchased and press the enter (or return) key. The odds of winning the top 2 prizes will automatically be displayed. In our rush to release this gadget, we sacrificed making this a "pretty" display.<br />
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You can either use the calculator directly on this blog, or you can add it to your own iGoogle home page by clicking on the "+ Google" button directly under the calculator.<br />
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Let us know what you think. <br />
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Thanks, JL ......John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-4770169137337522572012-01-09T11:47:00.000-08:002012-01-09T11:47:13.171-08:00Powerball's 2012 Powerplay buying guideline<a href="http://lotterypowerpicks.com/"><img alt="" border="0" src="http://lotterypowerpicks.com/images/lpp_logo.gif" style="cursor: pointer; float: left; height: 58px; margin: 0pt 10px 10px 0pt; width: 293px;" /></a><span style="color: #000099; font-weight: bold;">Introduction</span><br />
Powerball is changing. And, one of the important changes is the Powerplay option. No longer will players wonder what prizes they will win when they purchase Powerplay. Now, beginning after January 15, 2012, all Powerplay prizes will be fixed.<br />
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Like before, the Powerplay option will cost players $1 more. But the new Powerbal ticket with Powerplay will cost a total of $3 (rather than $2).<br />
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For this cost, all players matching the 5 white balls but not the Powerball will receive $2 million before taxes, which is a two times multiple. Those matching 4 white plus Powerball will receive $40,000, a 4 times multiple.<br />
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The lesser prizes for matching 4 white only, and 3 white with or without Powerball get double the standard prize. Matching 1 white with the Powerball will net a 3 times multiple, while the Poweball only prize payout will be a 4 times multiple.<br />
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<div style="font-weight: bold; text-align: center;">
<span style="color: #3366ff;">Is the Powerplay Option worth the extra cost?<br />
</span><span style="color: #ff9900;"><span style="color: #ff9900;"></span></span><br />
<div style="color: #a64d79;">
Still, the correct answer remains both Yes and No!<br />
But, it depends on the size of the Jackpot.</div>
</div>
<br />
<span style="color: #000099; font-weight: bold;">How would you know when to buy it?</span><br />
If your lottery playing strategy is to win the Jackpot only, we advise
that you never buy the Powerball option because paying $3 for a single ticket is a lot of money. If you buy 5 straight Powerball tickets, your cost will be $10. But, it you opt for the Powerplay, you will spent $9 for only 3 tickets. This means that your chance of winning the Jackpot jackpot with 3 Powerplay tickets increases to 1 in 58+ million, compared to about 1 in 35 million when buying 5 regular tickets.<br />
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However, if your lottery playing strategy is to win the $2 million second place prize, then we recommend that you only purchase the Powerplay option when the jackpot is below the breakeven level.<br />
<br />
For the <span style="color: red; font-weight: bold;">2012 Powerball game, the Breakeven is now $112.5 million:</span> <span style="font-weight: bold;">Buy </span>the Powerplay Option whenever the <span style="font-weight: bold;">Jackpot is below </span><span style="font-weight: bold;">this value</span>. <span style="font-weight: bold;">Never</span> <span style="font-weight: bold;">above this</span>. Put the extra dollar towards an extra ticket instead.<br />
<ul>
</ul>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.lotterypowerpicks.com/pb_powerplayAnalysis-Jan12.htm" imageanchor="1" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" src="http://3.bp.blogspot.com/-wDh8aFAkbEQ/TwswA2pkT4I/AAAAAAAAAIA/IZG3KODvIew/s1600/pplay1.bmp" /></a></div>
<br />
The illustration above compares the overall returns of a single 2012 Powerball game ticket verses its Powerplay ticket. As shown, the Powerplay tickets return more to the players when the annuity jackpot is in the range of $40 million to $112.5 million. After that, the single ticket prize payouts always return more money. This is because the jackpot itself is always fixed. Thus, as it increases above $112.5 million, the jackpot value far out weights the lower tier prizes.<br />
<br />
<span style="color: #000099; font-weight: bold;">Learn More </span><br />
To help you assess the value of the Powerplay option, we have constructed a page that will always illustrate the current jackpot level and tell you if you should buy this option. You can see this by clicking on the image above or the following link:<br />
<ul style="font-weight: bold;">
<li><a href="http://www.lotterypowerpicks.com/pb_powerplayAnalysis-Jan12.htm" target="_blank">2012 Powerball Power Play Recommendation Analysis</a></li>
</ul>
<span style="color: #000099; font-weight: bold;"><br />
<a href="http://www.stumbleupon.com/submit?url=http://jlotterysbimonthlyarticles.blogspot.com//&title=Should%20You%20Buy%20the%20Power%20Play,%20Sizzler,%20or%20Megaplier?"></a></span>John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-48758200947518595452011-12-20T13:33:00.000-08:002011-12-20T13:33:43.122-08:00Which Lottery Game Should You Play?If you are like many people, you may be on a limited budget. You want to play the lottery, but given so many choices of games, you may wonder:<br />
<br />
<div style="text-align: center;">
<span style="font-size: large;"><b><a href="http://www.lotterypowerpicks.com/what-game-to-play.htm" target="_blank">Which Game Should I Play?</a></b></span></div>
<br />
Given that jackpots and combinations vary so much, it is often difficult to make a choice. <br />
<br />
So, we decided to build a useful tool that allows you to compare two different lottery games and find out which offers the best return for your dollars.<br />
<br />
Our page currently lets you compare: Mega Millions, Powerball, Powerball 2012, Hot Lotto, Super Lotto Plus, Lotto Max, Lotto 649, Euro Millions, Irish Lotto, UK Lotto, and Thunderball.<br />
<br />
Simply select the games you wish to compare using a pull-down menu, and the results are automatically displayed. By using the current jackpot levels, the lottery with the highest overall return is recommended.<br />
<br />
You can access this page at: <b><a href="http://www.lotterypowerpicks.com/what-game-to-play.htm" target="_blank">Which Game Should You Play?</a></b><br />
<br />
Cheers and Merry Christmas!<br />
<br />
JL ...........John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-77418343697995203172011-11-22T06:22:00.001-08:002011-11-22T06:30:25.929-08:00Expected Powerball 2012 jackpot levels and growth - Part 2: Analysis of the new 2012 Powerball game changes<b style="color: blue;">Powerball recently announced that it will modify the format of the Powerball game in January of 2012</b>. You should expect to see:<br />
<ul style="color: red; font-family: inherit;">
<li><span style="font-size: large;"><b>Average jackpots of $115 to $145 million;</b></span></li>
<li><span style="font-size: large;"><b>A high jackpot of $700 to $800 million;</b></span></li>
<li><span style="font-size: large;"><b>Average jackpot growth of $15 to $20 million.</b></span></li>
</ul>
<br />
To help players understand the implications of these changes and
whether they should continue to play the new Powerball game, we are
writing a 3 part series of posts:<br />
<ul>
<li> <b><a href="http://jlotterysbimonthlyarticles.blogspot.com/2011/10/analysis-of-new-2012-powerball-game.html">Part 1: Evaluate the prize structure in comparison to Mega Millions (published October 2011),</a></b></li>
<li>Part 2: Examine the average Powerball jackpots and anticipated increases (this post), and</li>
<li>Part 3: Compare the new Powerball return to Mega Millions and other lottery games (to be published).</li>
</ul>
<div style="color: blue;">
<b>This post is Part 2 of our series. It addresses the potential impact of the new changes on the Jackpot offerings and projects the the anticipated jackpot offerings.</b></div>
<br />
<b>To begin, we summarize the two most significant changes that affect the annuity jackpot offerings. These are:</b><br />
<ol>
<li><b>Minimum jackpot is set at $40 million</b></li>
<li><b>Cost of each ticket is $2 each.</b></li>
</ol>
<b>Powerball's goal of offering larger jackpots will be achieved by doubling the ticket price to $2. Having twice the amount of money, they will be able to double the minimum jackpot from $20 million to $40 million.</b><br />
<br />
Since jackpot levels will be higher, they believe that the players "buy" level will be reached more rapidly and that players will eagerly purchase tickets at the inflated costs. So, the questions arise:<br />
<br />
<div style="color: #b45f06; font-family: inherit; text-align: center;">
<b><span style="font-size: large;">How quickly will Powerball jackpots grow?</span></b></div>
<div style="color: #b45f06; font-family: inherit; text-align: center;">
<b><span style="font-size: large;">What will be the average size of Powerball jackpots?</span></b></div>
<br />
<br />
<hr />
<div style="color: blue;">
<b>Historical Jackpot Distributions</b></div>
To begin, we review the range of winning Powerball and Mega Millions jackpots since 2001. In the graph below, we observe 4 historical jackpot ranges. The first two on the left illustrate Powerball, and the two on the right represent Mega Millions. Each range graph identifies 5 pieces of information:<br />
<ol>
<li>The complete range from minimum to maximum.</li>
<li>The 84% range (shown by the thick white portion)</li>
<li>The average (horizontal black line)</li>
<li>The median (both the orange horizontal line and the purple square</li>
<li>The 97% marker (orange square)</li>
</ol>
<img alt="Current Powerball / Mega Millions Jackpot Ranges" border="1" src="http://chart.googleapis.com/chart?chf=c,s,BBCCED&chs=360x280&cht=lc&chd=t0:-1,2,5,1,3,-1%7C-1,2,5,1,3,-1%7C-1,31,33,28,30,-1%7C-1,91,65,93,93,-1%7C-1,17,19,14,16,-1%7C-1,45,46,41,46,-1%7C-1,12,15,9,11,-1%7C-1,7,10,5,7,-1&chxt=y,x&chxr=0,0,400,50&chm=F,0000FF,0,1:2,20%7CF,FF0000,0,3:4,20%7CH,000000,4,1:4,1:20%7Ce,ff7700,5,-1,7%7Ce,9900ee,7,-1,14%7CH,FF7700,6,1:4,1:20%7CH,777777,3,1:4,1:10&chxl=1:%7C%7CPB+all%7CJan09%5E%7CMM+all%7CJun05%5E%7C&chtt=Current+Powerball+/+Mega+Millions%7CJackpot+Ranges&chdl=PB+84%+Range%7CMM+84%+Range++++%7CAverage%7C97.7%%7CMedian+%2850%%29&chco=0000FF,FF0000,000000,ff7700,9900ee&chdlp=r" />
<br />
<br />
This data is a graphic visualization of the table immediately below.<br />
<br />
<table border="2" style="width: 320px;">
<tbody>
<tr>
<td style="text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">PB</span><br />
<span style="font-size: x-small;">all</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">PB</span><br />
<span style="font-size: x-small;">after</span><br />
<span style="font-size: x-small;">Jan 09</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">MM</span><br />
<span style="font-size: x-small;">all</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">MM</span><br />
<span style="font-size: x-small;">after</span><br />
<span style="font-size: x-small;">Jun 05</span></td>
</tr>
<tr>
<td><span style="font-size: x-small;">Average</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">66.6</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">74.2</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">56.3</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">65.0</span></td>
</tr>
<tr>
<td><span style="font-size: x-small;">Median</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">49.0</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">59.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">37.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">44.0</span></td>
</tr>
<tr>
<td><span style="font-size: x-small;">Mode</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">20.0</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">20.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">12.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">12.0</span></td>
</tr>
<tr>
<td><span style="font-size: x-small;">Maximum</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">365.0</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">260.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">370.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">370.0</span></td>
</tr>
<tr>
<td><span style="font-size: x-small;">Minimum</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">10.0</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">20.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">5.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">12.0</span></td>
</tr>
</tbody></table>
<br />
<br />
Since the format of both games changed, we wanted to see the impact of the most recent. Thus, we break apart the Powerball jackpots after January 2009 and the Mega Millions after its June 2005 changes.<br />
<br />
Since the minimum jackpot offerings grew for both these games, we see that the average jackpot won increased as well. For Powerball, it increased from $66.6M to $74.2M; and Mega Millions increased from $56.3M to $65M. Interestingly, the median value (the 50% level) increased by the amount equal to the increase in jackpots. So, as the Powerball minimum moved from $10M to $20M, its median moved by $10M as well, from $49M to $59M. And, the Mega Millions median increased $7M (from $37.0M to $44.0M) after the minimum jackpot increased from $5M to $12M.<br />
<br />
Additionally, the mode (the most frequent jackpot level) for both games is calculated to be the same as the minimum jackpot after the changes (i.e. $20M for Powerball, and $12M for Mega Millions).<br />
<br />
<div style="color: blue;">
<b>Thus, we can conclude that the mode of Powerball after 2012 will later become $40 million.</b></div>
<br />
<hr />
<div style="color: blue;">
<b>Historical Jackpot Changes</b></div>
To help estimate how the new 2012 Powerball jackpots will grow, we first examine the historical changes in jackpot growth as shown in the table below. Here we see the complete growth of all drawings, compared to growth when jackpots are below $40M (LT 40M), between $40M-$100M (40-100M), and above $100M (GT 100M).<br />
<br />
<table border="1" style="width: 411px;">
<tbody>
<tr>
<td><span style="font-size: x-small;"><br /></span></td>
<td><span style="font-size: x-small;">Avg JP</span></td>
<td><span style="font-size: x-small;">Avg Chg</span></td>
<td><span style="font-size: x-small;">GT 100M</span></td>
<td><span style="font-size: x-small;">40-100M</span></td>
<td><span style="font-size: x-small;">LT 40M</span></td>
</tr>
<tr>
<td style="background-color: #9fc5e8;"><span style="font-size: x-small;">PB All</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">66.6</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">12.4</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">25.4</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">12.1</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">7.1</span></td>
</tr>
<tr>
<td style="background-color: #9fc5e8;"><span style="font-size: x-small;">PB After 2009</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">74.2</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">15.0</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">25.7</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">15.0</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">8.7</span></td>
</tr>
<tr>
<td style="background-color: #ea9999;"><span style="font-size: x-small;">MM All</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">56.3</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">11.5</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">30.4</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">11.9</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">6.4</span></td>
</tr>
<tr>
<td style="background-color: #ea9999;"><span style="font-size: x-small;">MM After Jun 05</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">65.0</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">13.4</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">29.5</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">12.5</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">7.9</span></td>
</tr>
</tbody></table>
<br />
Since the minimum Mega Millions jackpot is $12M and Powerball is $20M, we find that Powerball jackpots increase at a faster rate than Mega Millions when the jackpot is $100 million or less. However, the differences are not as great as we would expect.<br />
<br />
Once the jackpot (in either game) reaches $100M, we find that Mega Millions jackpots increase faster. We attribute this to the fact that the chances of winning Mega Millions (1 in 175 million) is less than Powerball (1 in 195 million).<br />
<br />
However since the overall odds of the new 2012 Powerball game will be the same as the current Mega Millions game, we expect Powerball accretion to equal that of Mega Millions once the jackpot reaches and exceeds $100 million.<br />
<br />
<hr />
<div style="color: blue;">
<b>Expected Distribution</b></div>
Looking at the distribution of the actual jackpots won, we see that the Mega Millions and Powerball jackpots are rather similar. Certainly, Mega Millions peaks around $50 million, whereas Powerball peaks at $80 million. Beyond that, we find that Mega Millions players have won more jackpots over $200M than those of Powerball. <br />
<br />
<img alt="Cumulative Winning Jackpot Distribution (Pct)" border="1" height="245" src="http://chart.apis.google.com/chart?chf=c,s,BBCCED&chxl=1:%7C20%7C30%7C40%7C50%7C60%7C70%7C80%7C90%7C100%7C150%7C200%7C250%7C300&chxr=0,0,50&chxt=y,x&chbh=8,2&chs=360x245&cht=bvg&chco=0000FF,FF0000&chds=5,55,0,55&chd=t:23,29,33,36,42,46,47,39,29,18,7,-1,-1%7C27,36,43,49,48,43,42,39,20,13,9,5,1&chdl=Powerball%7CMega+Millions&chdlp=t&chma=%7C50,30&chtt=Cumulative+Winning+Jackpot+Distribution+%28Pct%29&chts=000000,14" width="360" />
<br />
<br />
<hr />
<div style="color: blue;">
<b>Estimating Future Powerball Jackpots after 2012</b></div>
<span style="background-color: yellow;">Utilizing all of the above information, we have prepared the table below indicating our estimates of future Powerball Jackpots. These are shown in Yellow.</span> Next to our estimates are Mega Millions and the existing Powerball game.<br />
<br />
Each game begins a sequence set to the the minimum Jackpot. Since the Powerball begins at $40 million, we expect each jackpot from $40M to $100M to increase by $15M. Once the $100 million level is reached, new Powerball will increase by $30M until the 10th drawing. At that point, it will double to $60M. When the jackpot reaches $400 million, subsequent jackpots will increase by $100 million each.<br />
<br />
<table border="2" style="width: 450px;">
<tbody>
<tr>
<td style="background-color: blue; color: white; text-align: center;"><span style="font-size: x-small;"><b> Chg </b></span></td>
<td style="background-color: blue; color: white; text-align: center;"><span style="font-size: x-small;"><b>PB 2012+ Projected Jackpots </b></span></td>
<td style="background-color: blue; color: white; text-align: center;"><span style="font-size: x-small;"><b>Dwg</b></span><br />
<span style="font-size: x-small;"><b>#</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><b> </b></span></td>
<td style="background-color: #e06666; text-align: center;"><span style="font-size: x-small;"><b> Chg </b></span></td>
<td style="background-color: #e06666; text-align: center;"><span style="font-size: x-small;"><b>Current MM</b></span><br />
<span style="font-size: x-small;"><b>Jackpots</b></span><br />
<span style="font-size: x-small;"><b> </b></span></td>
<td style="background-color: #e06666; text-align: center;"><span style="font-size: x-small;"><b>Dwg</b></span><br />
<span style="font-size: x-small;"><b>#</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><b> </b></span></td>
<td style="background-color: #6fa8dc; text-align: center;"><span style="font-size: x-small;"><b> Chg </b></span></td>
<td style="background-color: #6fa8dc; text-align: center;"><span style="font-size: x-small;"><b>Current</b></span><br />
<span style="font-size: x-small;"><b>PB</b></span><br />
<span style="font-size: x-small;"><b>Jackpots</b></span><br />
<span style="font-size: x-small;"><br /></span><br />
<span style="font-size: x-small;"><b> </b></span></td>
<td style="background-color: #6fa8dc; text-align: center;"><span style="font-size: x-small;"><b>Dwg</b></span><br />
<span style="font-size: x-small;"><b>#</b></span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>15</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>40</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>1</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">8</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">12</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">1</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">9</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">20</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">1</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>55</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>2</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">20</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">2</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">29</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">2</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>70</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>3</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">28</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">3</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">38</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">3</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>85</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>4</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">36</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">4</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">47</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">4</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>100</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>5</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">13</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">44</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">5</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">15</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">56</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">5</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>30</b></span></td>
<td style="background-color: #f6b26b; color: blue; text-align: center;"><span style="font-size: x-small;"><b>115</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>6</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #f6b26b; text-align: center;"><span style="font-size: x-small;">57</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">6</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #f6b26b; text-align: center;"><span style="font-size: x-small;">71</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">6</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: #f6b26b; color: blue; text-align: center;"><span style="font-size: x-small;"><b>145</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>7</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #f6b26b; text-align: center;"><span style="font-size: x-small;">70</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">7</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #f6b26b; text-align: center;"><span style="font-size: x-small;">86</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">7</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>175</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>8</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">83</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">8</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">101</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">8</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>205</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>9</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">96</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">9</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">116</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">9</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>60</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>235</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>10</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">30</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">109</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">10</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">25</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">131</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">10</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>295</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>11</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">139</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">11</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">156</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">11</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>355</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>12</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">169</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">12</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">181</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">12</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>100</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>415</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>13</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">199</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">13</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">206</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">13</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>515</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>14</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">60</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">229</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">14</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">60</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">231</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">14</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>615</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>15</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">289</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">15</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">291</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">15</span></td>
</tr>
<tr>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b><br /></b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>715</b></span></td>
<td style="background-color: yellow; color: blue; text-align: center;"><span style="font-size: x-small;"><b>16</b></span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">319</span></td>
<td style="background-color: #ea9999; text-align: center;"><span style="font-size: x-small;">16</span></td>
<td style="background-color: #666666; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;"><br /></span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">316</span></td>
<td style="background-color: #9fc5e8; text-align: center;"><span style="font-size: x-small;">16</span></td>
</tr>
</tbody></table>
<br />
Regarding the potentially largest jackpots, it is reasonable to expect to see a jackpot of $700 to $800 million. This would be reached after the 16th or 17 consecutive drawing without a winner. This amount would be in line with those previously reached by Mega Millions and Powerball (approximately $370 million).<br />
<br />
<hr />
<div style="color: blue;">
<b>Conclusion: Summary of Powerball 2012 Jackpots</b></div>
Based on the above information, we can answer our initial questions and summarize our findings as follows:<br />
<span style="font-size: large;"><b></b></span><br />
<ul style="color: #b45f06; font-family: inherit;">
<li><span style="font-size: large;"><b>Expect average jackpots to grow by $15 to $20 million.</b></span></li>
<li><span style="font-size: large;"><b>Expect average jackpots of $115 to $145 million;</b></span></li>
<li><span style="font-size: large;"><b>Look for jackpots to reach $700 to $800 million.</b></span></li>
</ul>
<br />
<hr />
<div style="color: blue;">
<b>Word of Caution</b></div>
Initially, we believed these estimates to be too low. But then we realized the conflict that the new Powerball 2012 game posed.<br />
<br />
Although the new game offers jackpots twice the size of the existing game, players are expected to purchase tickets that cost twice as much. We believe the lure of the new jackpot level of $40 million will attract players to purchase the same dollar amount as they would currently spend. This means that jackpots will increase at the same rate of $15 million when levels are at or above $40M. This level of increase will be sustainable because Powerball will be paying out the same amount of money in the new game as they would in the old game.<br />
<br />
But, the difference is only half the amount of tickets will be sold. Thus, on the average, it will still take 6 to 7 drawings before a jackpot is won. By then, the jackpot will be $115M to $145M.<br />
<br />
Powerball 2012 will have the same winning frequency as the Mega Millions game which will continue to have jackpots of half the size (because tickets cost half as well).<br />
<br />
Two factors pose risks for Powerball. If the expected jackpot levels are not reached and maintained, then players will become frustrated and reluctant to spend twice the money for a ticket. Further, if mega jackpot levels of $250 or more are not reached quickly, players will become more convinced that Mega Millions and other State lotteries offer better opportunities. If this happens, then the new 2012 Powerball will fail to succeed.<br />
<br />
On the other hand, if these levels are reached quickly, players will eagerly flock to the new game regardless of cost. Thus, we have to wait and see.John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com2tag:blogger.com,1999:blog-60725341237976466.post-61278365238117269672011-10-18T08:34:00.000-07:002011-11-22T06:37:12.424-08:00Analysis of the new 2012 Powerball game changes. Part 1: Game summary & prize evaluationIn late June, the MUSL announced that it was going to change the format of Powerball. Since most available literature simply reiterates the notice of changes, we believe that players are wondering whether: these new changes are good for them, and if they should be eager to purchase tickets at the increased costs.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://t1.gstatic.com/images?q=tbn:ANd9GcTXissiIewCZVEg62Pox9VwZKP9c6xE7DcG1yCWrv0i2WKrwWzovdd6aWuB" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="120" id=":current_picnik_image" src="http://2.bp.blogspot.com/-gwTSCaHyeOM/Tpx18UauAxI/AAAAAAAAAHA/erwqybBr5Vk/s400/16872058263_jm65v.jpg" width="400" /></a></div>
<br />
To help players understand the implications of these changes and whether they should continue to play the new Powerball game, we are writing a 3 part series of posts that:<br />
<ul>
<li> Part 1: Evaluate the prize structure in comparison to Mega Millions (this post),</li>
<li><a href="http://jlotterysbimonthlyarticles.blogspot.com/2011/11/expected-powerball-2012-jackpot-levels.html">Part 2: Examine the average Powerball jackpots and anticipated increases</a> (published November 2011), and</li>
<li>Part 3: Compare the new Powerball return to Mega Millions and other lottery games (to be published).</li>
</ul>
Originally, we intended to include all of these topics in one post. But, we quickly realized that the length of the post was too long, thus we are breaking the analysis into these 3 parts.<br />
<br />
This is Part 1. Its purpose is to explain what the new changes are, and what they will mean to lottery players with regard to prizes that the new Powerball game offers.<br />
<br />
<div style="color: blue;">
<b>The 2012 Powerball Changes <br />
</b></div>
The table below summarizes the array of the Powerball changes. Most notably, players will find that the cost of tickets will increase
from $1 to $2 each and that the minimum jackpot will increase to $40
million.<br />
<br />
<table border="1">
<tbody>
<tr>
<td style="background-color: blue; color: white; text-align: center;"><b>Summary of 2012 Powerball Changes
</b></td><td style="background-color: blue; color: white; text-align: center;"><b>Power Play Prizes Fixed
</b></td></tr>
<tr>
<td valign="top">Starting jackpot at $40 million (up from $20 million)<br />
Match 5 prize fixed at $1 million (up from $200,000)<br />
Matching Powerball Only prize at $4 (up from $3)<br />
White Ball Remains at 1 to 59 (no change) <br />
Powerballs 1 to 35 (down from 39)<br />
Regular Ticket Costs $2 (up from $1)<br />
Powerplay Ticket Costs $3 (up from $2)<br />
Power Play Prize Amounts Now Fixed (no multiples)</td><td style="text-align: center;" valign="top">$1M Prize to $2M (2x)<br />
$10,000 Prize to $40,000 (4x)<br />
$100 Prizes to $200 (2x)<br />
$7 Prize to $14 (2x)<br />
$4 Prize to $12 (3x)</td></tr>
</tbody></table>
<br />
Because the number of white balls remains the same, the chances of winning the 2nd tier prize of 5+0 remains the same at 1 in 5,153,632.65. However, since the number of Powerballs decreases by 4 to 35, the overall chance of winning the Powerball jackpot will decrease by approximately 20 million to 1 in 175,223,510.<br />
<br />
<div style="color: blue;">
<b>Implementation Date<br />
</b></div>
Implementation of the new game format will coincide with the Powerball's 20th anniversary. The expected sales date for the new Powerball format is January 15, 2012 and the first drawing will be January 18, 2012.<br />
<br />
<div style="color: blue;">
<b>Why the Changes? Powerball's Reasoning.</b></div>
On its FAQ page, Powerball identified 9 reasons for modifying the game. The first eight provide their rationale why players will continue to purchase tickets at the increased ticket cost. Each of these addresses the players' psychology and takes advantage of their vulnerability. The last reason, "Game variety" is something that must be questioned.<br />
<ol>
<li>Scratch tickets costing $2, $3, $5, $10, $20 and $50 all sell</li>
<li>Powerball price was fixed for 20 years </li>
<li>Ticket sales increase more rapidly when jackpot is higher</li>
<li>Jackpots should increase by $10M each drawing, reaching players "buy" level more quickly </li>
<li>Average jackpot of new format will be $255 million (was $141 million)</li>
<li>There will be more millionaires since all match 5+0 winners will receive $1M.</li>
<li>A fixed Power Play takes uncertainty out of winning. Those matching 5+0 will get $2M, enough to pay taxes and still keep $1M</li>
<li>There will be more winners. </li>
<li>Game variety.</li>
</ol>
<div style="color: blue;">
<b>Game Variety?</b></div>
With the new Powerball odds reduced to 1 in 175+ million, it is easy to conclude that the overall game format is very similar to Mega Millions which also boasts a 1 in 175+ million chance of winning. The major difference between the games will be: the ticket price; and the prizes for the top two prizes.<br />
<br />
The table below summarizes the differences between the two games in a side by side manner. Powerball is shown in the light blue columns, and Mega Millions is shown in the pink columns.<br />
<br />
<table border="1" cellpadding="0" cellspacing="0" style="width: 100%;"><colgroup><col style="width: 74pt;" width="99"></col>
<col span="2" style="width: 74pt;" width="98"></col>
<col style="width: 63pt;" width="84"></col>
<col style="width: 48pt;" width="64"></col>
<col style="width: 62pt;" width="83"></col>
<col style="width: 63pt;" width="84"></col>
<col style="width: 62pt;" width="83"></col>
<col style="width: 63pt;" width="84"></col>
</colgroup><tbody>
<tr height="17" style="height: 12.75pt;">
<td class="xl73" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">Match</span></td>
<td class="xl73" style="background-color: #f4cccc; text-align: center; width: 74pt;" width="98"><span style="font-size: x-small;">MM 5/56+1/46</span><br />
<span style="font-size: x-small;">Odds</span></td>
<td class="xl74" style="background-color: #9fc5e8; text-align: center; width: 74pt;" width="98"><span style="font-size: x-small;">PB 5/59+1/35</span><br />
<span style="font-size: x-small;">Odds</span></td>
<td class="xl73" style="background-color: #f4cccc; text-align: center; width: 63pt;" width="84"><span style="font-size: x-small;">Winners</span><br />
<span style="font-size: x-small;">MM </span></td>
<td class="xl74" style="background-color: #9fc5e8; text-align: center; width: 48pt;" width="64"><span style="font-size: x-small;">Winners</span><br />
<span style="font-size: x-small;">PB </span></td>
<td class="xl73" style="background-color: #f4cccc; text-align: center; width: 62pt;" width="83"><span style="font-size: x-small;">Prize $</span><br />
<span style="font-size: x-small;">MM </span></td>
<td class="xl74" style="background-color: #9fc5e8; text-align: center; width: 63pt;" width="84"><span style="font-size: x-small;">Prize $</span><br />
<span style="font-size: x-small;">PB </span></td>
<td class="xl73" style="background-color: #f4cccc; text-align: center; width: 62pt;" width="83"><span style="font-size: x-small;">Prize $</span><br />
<span style="font-size: x-small;">Megaplier</span></td>
<td class="xl74" style="background-color: #9fc5e8; text-align: center; width: 63pt;" width="84"><span style="font-size: x-small;">Prize $</span><br />
<span style="font-size: x-small;">Power Play</span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">5+1</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">175,711,536.00</span></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">175,223,510.00</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">1</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">1</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$12,000,000 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$40,000,000 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$12,000,000 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$40,000,000 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">5+0</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">3,904,700.80</span></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">5,153,632.65</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">45</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">34</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$250,000 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$1,000,000 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$1,000,000 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$2,000,000 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">4+1</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">689,064.85</span></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">648,975.96</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">255</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">270</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$10,000 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$10,000 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$34,762 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$40,000 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">4+0</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">15,312.55</span></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">19,087.53</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">11,475</span></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">9,180</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$150 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$100 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$521 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$200 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">3+1</span></td>
<td align="right" class="xl66" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">13,781.30</span></td>
<td align="right" class="xl70" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">12,244.83</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">12,750</span></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">14,310</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$150 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$100 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$521 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$200 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">3+0</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">306.25</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">360.14</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">573,750</span></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">486,540</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$7 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$7 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$24 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$14 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">2+1</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">843.75</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">706.43</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">208,250</span></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">248,040</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$10 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$7 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$35 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$14 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">2+0</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">18.75</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">20.78</span></td>
<td class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;"><br /></span></td>
<td class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;"><br /></span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;"> </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;"> </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;"> </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;"> </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">1+1</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">140.63</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">110.81</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">1,249,500</span></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">1,581,255</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$3 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$4 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$10 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$12 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">1+0</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">3.13</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">3.26</span></td>
<td class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;"><br /></span></td>
<td class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;"><br /></span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;"> </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><br /></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;"> </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;"> </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">0+1</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">74.8</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">55.41</span></td>
<td align="right" class="xl68" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;">2,349,060</span></td>
<td align="right" class="xl72" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;">3,162,510</span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$2 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$4 </span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;">$7 </span></td>
<td align="right" class="xl71" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;">$12 </span></td>
</tr>
<tr height="17" style="height: 12.75pt;">
<td class="xl65" height="17" style="background-color: #9fc5e8; height: 12.75pt; text-align: center; width: 74pt;" width="99"><span style="font-size: x-small;">0+0</span></td>
<td align="right" class="xl65" style="background-color: #f4cccc; width: 74pt;" width="98"><span style="font-size: x-small;">1.66</span></td>
<td align="right" class="xl69" style="background-color: #9fc5e8; width: 74pt;" width="98"><span style="font-size: x-small;">1.63</span></td>
<td class="xl65" style="background-color: #f4cccc; width: 63pt;" width="84"><span style="font-size: x-small;"><br /></span></td>
<td class="xl69" style="background-color: #9fc5e8; width: 48pt;" width="64"><span style="font-size: x-small;"><br /></span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;"> </span></td>
<td class="xl69" style="background-color: #9fc5e8; width: 63pt;" width="84"><span style="font-size: x-small;"><br /></span></td>
<td align="right" class="xl67" style="background-color: #f4cccc; width: 62pt;" width="83"><span style="font-size: x-small;"> </span></td>
<td style="background-color: #9fc5e8;"><span style="font-size: x-small;"><br /></span></td>
</tr>
</tbody></table>
<br />
Illustrated are the odds (or chances), number of winners, prize payout for normal tickets, and prize payout for the multiplier (Megaplier and Power Play) tickets of both games.<br />
<br />
The six graphs below illustrate various portions of this table, showing the Powerball players percent gain or loss in each of these pairs of information. The percentages are calculated by: dividing the Powerball values by the associated Mega Millions values; subtracting 1; and then multiplying by 100. <br />
<br />
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<a href="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=FF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7CFF0000&chxr=1%2C-40%2C40&chbh=a&chd=t%3A-0.3%2C32%2C-5.8%2C24.7%2C-11.1%2C17.6%2C-16.3%2C10.8%2C-21.2%2C4.2%2C-25.9%2C-1.8&chtt=P1%3A%20PB%20to%20MM%20Odds%20Comparison%20%28%25%29&chxp=2%2C50&chds=-40%2C40&chp=0.5&chg=100%2C25&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.5%2C1%2C0" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=FF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7CFF0000&chxr=1%2C-40%2C40&chbh=a&chd=t%3A-0.3%2C32%2C-5.8%2C24.7%2C-11.1%2C17.6%2C-16.3%2C10.8%2C-21.2%2C4.2%2C-25.9%2C-1.8&chtt=P1%3A%20PB%20to%20MM%20Odds%20Comparison%20%28%25%29&chxp=2%2C50&chds=-40%2C40&chp=0.5&chg=100%2C25&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.5%2C1%2C0" /></a></div>
<span style="color: #000099; font-weight: bold;">1. Compare Overall Odds of both Games</span><br />
Chart P1 shows the differences between the odds of both games. As shown, the chance of winning the Powerball jackpot is only 0.3% less than winning the Mega Million jackpot (so they are about the same). However, odds of matching anywhere from 5 to 1 of the white balls and not the Powerball are much more difficult in Powerball. It is 32% harder to win the 2nd tier prize of 5+0, 24.7% harder to match 4+0, and 17.6% harder to obtain a 3+0 winner in Powerball.<br />
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But when a Powerball is matched, it is easier to win a prize. That is because there are less Powerballs than Megaballs. As shown in red, it is 5.8% easier to match a Powerball 4+1, 11.1% to easier for 3+1, and so on. Matching the Powerball only is 25.9% easier in Powerball.<br />
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If you are one of the typical 96.9% of players, you will probably not win anything at all. In Powerball, you are 1.8% more likely not to match any balls in Powerball than in Mega Millions. But, on the overall, there will be 0.6% more winners in Powerball.<br />
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<a href="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7C0000FF%7C0000FF%7C0000FF%7C0000FF%7C0000FF&chxr=1%2C-40%2C40&chbh=a&chd=t%3A0%2C-24.4%2C5.9%2C-20%2C12.2%2C-15.2%2C19.1%2C0%2C26.6%2C0%2C34.6%2C0&chtt=P2%3A%20PB%20to%20MM%20Winners%20Comparison%20%28%25%29&chxp=2%2C50&chds=-40%2C40&chp=0.5&chg=100%2C25&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.5%2C1%2C0" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7C0000FF%7C0000FF%7C0000FF%7C0000FF%7C0000FF&chxr=1%2C-40%2C40&chbh=a&chd=t%3A0%2C-24.4%2C5.9%2C-20%2C12.2%2C-15.2%2C19.1%2C0%2C26.6%2C0%2C34.6%2C0&chtt=P2%3A%20PB%20to%20MM%20Winners%20Comparison%20%28%25%29&chxp=2%2C50&chds=-40%2C40&chp=0.5&chg=100%2C25&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.5%2C1%2C0" /></a></div>
<span style="color: #000099; font-weight: bold;">2. Compare Total Winners in both Games</span><br />
Chart P2 illustrates the differences between the numbers of winners in each category. In effect, it is the mirror image of the above odds comparison. In both games, there is only 1 jackpot winner, and no winners for matching 0, 1, or 2 white balls and not the bonus ball. This means players are indifferent to those categories.<br />
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Excluding the jackpot, Powerball offers more opportunities to win a prize whenever the Powerball bonus is matched. In these cases, the Powerball advantage ranges from 5.9% to 34.6%.<br />
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When the player does not match the bonus Powerball, Mega Millions outperforms (in red). There will be 24.4% more 2nd tier Mega Millions winners than Powerball. Similarly, those matching 4+0 or 3+0 are 20% and 15.2% more likely to win a prize in Mega Millions than in Powerball.<br />
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These differences are all explained by the fact that there are less white balls in Mega Millions and less bonus balls in Powerball.<br />
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<a href="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7C0000FF%7C0000FF%7CFF0000%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7C0000FF%7C0000FF%7C0000FF%7C0000FF&chxr=1%2C-50%2C350&chbh=a&chd=t%3A233.3%2C300%2C0%2C-33.3%2C-33.3%2C0%2C-30%2C0%2C33.3%2C0%2C100%2C0&chtt=P3%3A%20PB%20to%20MM%20Prize%20per%20Ticket%20Bought%20%28%25%29&chxp=2%2C50&chds=-50%2C350&chp=0.5&chg=100%2C25&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.125%2C1%2C0" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="228" src="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7C0000FF%7C0000FF%7CFF0000%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7C0000FF%7C0000FF%7C0000FF%7C0000FF&chxr=1%2C-50%2C350&chbh=a&chd=t%3A233.3%2C300%2C0%2C-33.3%2C-33.3%2C0%2C-30%2C0%2C33.3%2C0%2C100%2C0&chtt=P3%3A%20PB%20to%20MM%20Prize%20per%20Ticket%20Bought%20%28%25%29&chxp=2%2C50&chds=-50%2C350&chp=0.5&chg=100%2C25&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.125%2C1%2C0" width="320" /></a><span style="color: #000099; font-weight: bold;">3. Compare PB to MM Prizes per Ticket</span><br />
Chart P3 summarizes the difference in prize winnings per ticket between the two games.<br />
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This verifies Powerball's goal of offering higher jackpot and 2nd tier prizes when the jackpot is set to minimum. Those who win a Powerball jackpot will collect 233.3% more than the Mega Millions winner, and will get 300% more when matching 5 white only.<br />
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The Powerball winning ticket also has the advantage for those matching the Powerball and 1 or 0 white balls which will pay out more than its rival game.<br />
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Those in the middle are better off with Mega Millions as players matching 4+0, 3+1, or 2+1 balls will receive approximately 1/3 larger prizes.<br />
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There is no difference in winnings for players matching 4+1 or 3+0 in either game. And, of course, all losing tickets will collect an even $0.<br />
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<a href="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7C0000FF%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7C0000FF%7C0000FF&chxr=1%2C-80%2C120&chbh=a&chd=t%3A66.7%2C100%2C-50%2C-66.7%2C-66.7%2C-50%2C-65%2C0%2C-33.3%2C0%2C0%2C0&chtt=P4%3A%20PB%20to%20MM%20Prize%20per%20Dollar%20Spent%20%28%25%29&chxp=2%2C50&chds=-80%2C120&chp=0.4&chg=100%2C20&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.4%2C1%2C0" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="228" src="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7C0000FF%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7C0000FF%7C0000FF&chxr=1%2C-80%2C120&chbh=a&chd=t%3A66.7%2C100%2C-50%2C-66.7%2C-66.7%2C-50%2C-65%2C0%2C-33.3%2C0%2C0%2C0&chtt=P4%3A%20PB%20to%20MM%20Prize%20per%20Dollar%20Spent%20%28%25%29&chxp=2%2C50&chds=-80%2C120&chp=0.4&chg=100%2C20&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.4%2C1%2C0" width="320" /></a></div>
<span style="color: #000099; font-weight: bold;">4. Compare PB to MM Prizes by Dollar Spent</span><br />
Since Powerball tickets will cost $2 each and Mega Millions only $1, it is necessary to normalize the prize winnings to dollar spent.<br />
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Chart P4 illustrates this difference. Here we see that Powerball only pays out more for the jackpot and 2nd tier winners.<br />
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All other lower tier Powerball prizes pay substantially less than or equal to their associated Mega Millions counterparts.<br />
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<a href="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7C0000FF%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF&chxr=1%2C-100%2C250&chbh=a&chd=t%3A233.3%2C0%2C-71.2%2C-80.8%2C-80.8%2C-71.2%2C-79.9%2C0%2C-61.6%2C0%2C-42.5%2C0&chtt=P5%3A%20PB%20to%20MM%20Megaplier%20Prize%20per%20Ticket%20%28%25%29&chxp=2%2C50&chds=-100%2C250&chp=0.2857&chg=100%2C14.2857&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.2857%2C1%2C0" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="228" src="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7C0000FF%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7C0000FF%7CFF0000%7C0000FF%7CFF0000%7C0000FF&chxr=1%2C-100%2C250&chbh=a&chd=t%3A233.3%2C0%2C-71.2%2C-80.8%2C-80.8%2C-71.2%2C-79.9%2C0%2C-61.6%2C0%2C-42.5%2C0&chtt=P5%3A%20PB%20to%20MM%20Megaplier%20Prize%20per%20Ticket%20%28%25%29&chxp=2%2C50&chds=-100%2C250&chp=0.2857&chg=100%2C14.2857&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.2857%2C1%2C0" width="320" /></a><span style="color: #000099; font-weight: bold;">5. Compare PB Ticket to MM Megaplier Ticket</span><br />
So what happens if a player buys a $2 Megaplier ticket in comparison to the $2 Powerball ticket?<br />
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In each case, the player pays $2 either way. But, except for the 1st prize, Powerball players receive lesser prize amounts. Depending on their winning, a player will receive 42.5% to 80.8% less than a Mega Millions winner.<br />
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If the player is lucky enough to claim the winning jackpot ticket, the Powerball winner will be paid 233.3% more. Whereas, it you match all 5 white balls and not the bonus ball, you will win the same amount of money in both games. <br />
<span style="font-size: 78%;"><br /></span><br />
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<a href="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7C0000FF%7C0000FF%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7C0000FF%7C0000FF%7C0000FF%7C0000FF%7C0000FF&chxr=1%2C-100%2C250&chbh=a&chd=t%3A233.3%2C100%2C15.1%2C-61.6%2C-61.6%2C-42.5%2C-59.7%2C0%2C15.1%2C0%2C72.6%2C0&chtt=P6%3A%20Powerplay%20to%20Megaplier%20Prize%20per%20Ticket%20%28%25%29&chxp=2%2C50&chds=-100%2C250&chp=0.2857&chg=100%2C14.2857&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.2857%2C1%2C0" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="228" src="http://chart.googleapis.com/chart?cht=bvg&chs=350x250&chxt=x%2Cy%2Cx&chxl=0%3A%7C5%2B1%7C5%2B0%7C4%2B1%7C4%2B0%7C3%2B1%7C3%2B0%7C2%2B1%7C2%2B0%7C1%2B1%7C1%2B0%7C0%2B1%7C0%2B0%7C2%3A%7CBalls%20Matched%20%28White%20%2B%20Bonus%29%7C&chdlp=t&chco=0000FF%7C0000FF%7C0000FF%7CFF0000%7CFF0000%7CFF0000%7CFF0000%7C0000FF%7C0000FF%7C0000FF%7C0000FF%7C0000FF&chxr=1%2C-100%2C250&chbh=a&chd=t%3A233.3%2C100%2C15.1%2C-61.6%2C-61.6%2C-42.5%2C-59.7%2C0%2C15.1%2C0%2C72.6%2C0&chtt=P6%3A%20Powerplay%20to%20Megaplier%20Prize%20per%20Ticket%20%28%25%29&chxp=2%2C50&chds=-100%2C250&chp=0.2857&chg=100%2C14.2857&chm=N**%2C000000%2C0%2C-1%2C10%2C%7Ch%2C000000%2C0%2C0.2857%2C1%2C0" width="320" /></a><span style="color: #000099; font-weight: bold;">6. Compare PB Powerplay to MM Megaplier </span><br />
Lastly, a player may wish to buy the multiplier options in both games, which means he will spend $3 for a Powerball Powerplay ticket, and $2 for a Mega Millions Megaplier ticket.<br />
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Here we see a pattern similar to that of buying a single Powerball and Mega Millions ticket.<br />
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In this case, Chart P6 summarizes the winning payouts. Here, the Powerball player will win more if they win any of the first 3 prizes or the bottom two.<br />
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Those whose tickets fall in the middle will receive smaller Powerball prizes compared to Mega Millions.<br />
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<hr style="height: 1px;" />
<span style="color: #000099; font-weight: bold;">Summary</span><br />
In summary, we can agree that the Powerball game will pay out higher jackpot prizes. However, we do not believe the extra cost enhances the desirability of the prize.<br />
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Players have to remember that approximately 97% of all tickets sold will be losers. This means that only 3% will win something.<br />
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Since the chances of winning the jackpot is about the same in both Mega Millions and Powerball, we believe that it is more beneficial for players to buy 2 individual Mega Millions tickets instead of 1 Powerball ticket. By doing this, the Mega Millions player will have twice as many chances of winning a prize compared to the Powerball player. On a per dollar basis, the prize structure for Mega Millions is more attractive as well.<br />
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However, if your goal is to win a prize of at least $1 million, then it is better to buy 1 Mega Millions ticket with the Megaplier option. Except for the jackpot, these players lucky enough to have a winning ticket will always win more than the Powerball ticket holder. <br />
<span style="font-size: 78%;"><br /></span><br />
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<span style="color: #000099; font-weight: bold;">Sources:</span><br />
<a href="http://www.nelottery.com/article.xsp?aid=2537">Powerball® Enhancements Start January 2012 (Nebraska Lottery)</a><br />
<a href="http://www.powerball.com/pb_contact.asp">Powerball FAQ/History/News (Official Site)</a><br />
<a href="http://jlotterysbimonthlyarticles.blogspot.com/2008/12/how-2009-powerball-changes-effect-you.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+PowerballResearchArticles+%28Powerball+Research+Articles%29&utm_content=Google+Feedfetcher">How 2009 Powerball Changes Effect You</a>John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-10304813374445024832011-09-06T10:14:00.000-07:002011-09-06T10:14:09.534-07:00Our 5th Year (Wooden) Anniversary (2006-2011)The month of September marks the 5th year anniversary of our website: <a href="http://www.lotterypowerpicks.com/">Lottery Power Picks</a>.<br />
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<a href="http://sandrarosedesigns.com/media/catalog/product/cache/1/image/9df78eab33525d08d6e5fb8d27136e95/g/c/gcu_5-year-anniversary-road-sign.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="142" id=":current_picnik_image" src="http://4.bp.blogspot.com/-yupIF511G-w/TmZTnrJ1ruI/AAAAAAAAAGc/M7abdvBTMgQ/s200/16217216438_xs3BV.jpg" width="200" /></a>When we launched our site in 2006, we never imagined the difficulties we would face, nor the amount of time it would require. Like many others, we simply thought that when we launched, it would be an instant success. We aimed our focus at various forums and asked participants to visit us. However, we were quickly dismissed by many who noted that our site didn't even appear in a Google search.<br />
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Since then, we have learned to respect the hard work of others and ceased promoting our website within other lottery sites. Instead, we advertised a bit and remained focused on building a comprehensive set of analytical tools to help the general lottery playing population.<br />
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Now, five years later, we can boast of a registered membership that exceeds 3,400 players. And, during the past year, we've had over 50 Major Winners: (see our <a href="http://www.lotterypowerpicks.com/winners.htm">Lottery Power Picks Winners</a> page). The largest prizes that members won were during 2010 to 2011 were:<br />
<ul>
<li>$10,000 Mega Millions ( Oct 12 2010 )</li>
<li>C$5,373.70 Lotto Max ( Jan 14 2011 )</li>
<li>C$1,187.40 Lotto 649 ( Mar 19 2011 )</li>
<li>$500 Hot Lotto ( Oct 23 2010 )</li>
</ul>
Our development efforts during this past year were aimed at learning to utilize and incorporate Google Visualizations into our pages. We believe these tools assist in providing user interaction with both graphic and tabular data. One of the first development projects was to examine the rotation of the earth and moon around the sun:<br />
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<div style="text-align: center;">
<b><a href="http://www.lotterypowerpicks.com/earth-orbit-MotionChart.htm">Earth's Orbit about the Sun using the Google Visualization Motion Chart</a></b></div>
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While this type of work does not appear not to relate to lotteries, its information has helped us to formulate future analytic solutions for us to address.<br />
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This year we have concentrated on adding new functionality and analysis. For example, we have added a new navigation bar at the top of most pages for your use in locating our information. In addition, we have written a variety of full wheel calculators that lets you compare your expenditures versus you potential winnings. Our Pick 3 pages have gained momentum this past year, particularly after we added a number of other states. Of course, we have had to revise our previously released pages whenever a lottery modified their game format (Thunderball, Mega Million, and Euro Millions).<br />
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A subset of articles and pages we published this past year are listed below for your reference.<br />
<ul>
<li><a href="http://jlotterysbimonthlyarticles.blogspot.com/2011/02/revised-look-at-mega-millions-megaplier.html">A Revised Look at the Mega Millions Megaplier Option</a></li>
<li><a href="http://fortuna-lotterypowerpicks.blogspot.com/2011/04/introducing-our-new-navigation-menu.html">Introducing Our New Navigation Menu</a> </li>
<li><a href="http://fortuna-lotterypowerpicks.blogspot.com/2011/02/lotto-649-uk-lotto-and-irish-lotto-full.html">Lotto 649, UK Lotto, and Irish Lotto Full Wheel Calculators Now Released</a></li>
<li><a href="http://fortuna-lotterypowerpicks.blogspot.com/2011/01/thunderball-super-lotto-plus-texas-2.html">Thunderball, Super Lotto Plus & Texas 2 Step Full Wheel Calculators Now Available</a></li>
<li><a href="http://fortuna-lotterypowerpicks.blogspot.com/2011/04/two-new-pick-3-games-released.html">Two New Pick 3 Games Released</a> (Arizona and Iowa)</li>
<li><a href="http://fortuna-lotterypowerpicks.blogspot.com/2011/05/california-idaho-missouri-pick-3-pages.html">California, Idaho, & Missouri Pick 3 Pages Released</a></li>
</ul>
Examples of new functionality we are adding to existing pages can be found in:<br />
<ul>
<li><a href="http://www.lotterypowerpicks.com/pb_powerplayAnalysis.htm">Powerball Power Play Multiplier Breakeven Analysis</a> </li>
<li><a href="http://www.lotterypowerpicks.com/expandedOdds/EU_EM_expanded.htm">EuroMillions Lottery Complete Odds and Returns to Players</a></li>
</ul>
Unfortunately, these pages are best viewed in Firefox. We are aware that other browsers display differently and are trying to get these to work in all browsers.<br />
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We wish to thank all of you who have written to us during the past year and have: informed us of problems, told us of their winnings, and requested new functionality.<br />
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And most importantly, we wish to thank all of you for being loyal followers of our site and referencing our information daily. We will continue to improve our content and hope we bring you success in winning the lottery prizes!John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-56115162406131222702011-08-21T03:42:00.000-07:002011-08-21T07:27:31.067-07:00Same 5 lottery numbers are drawn on same night in two different lottery gamesAs we were entering the lottery numbers for Hot Lotto, we realized that the numbers looked familiar. So we reviewed our other results and saw that the UK Thunderball selected the same 5 white balls earlier that evening. <b>The numbers drawn for both <span style="color: red;">Hot Lotto</span> and <span style="color: purple;">Thunderball </span>on Saturday, August 20, 2011 were:</b><br />
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<center><div style="text-align: center;">
</div>
<table border="1" style="width: 400px;">
<tbody>
<tr><td style="background-color: #cccccc; text-align: center;"><b>Game</b></td><td style="background-color: #cccccc; text-align: center;"><b>White</b><br />
<b>Numbers Drawn</b></td><td style="background-color: #cccccc; text-align: center;"><b>Thunderball</b><br />
<b>Hot Ball</b>
</td></tr>
<tr><td style="text-align: center;"><b>Thunderball </b></td><td style="color: red; text-align: center;"><b>6 7 11 22 33</b></td><td style="text-align: center;"><b>10</b>
</td></tr>
<tr><td style="text-align: center;"><b>Hot Lotto</b></td><td style="color: red; text-align: center;"><b>6 7 11 22 33</b></td><td style="text-align: center;"><b>13</b>
</td></tr>
</tbody></table>
</center>
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<div style="color: red; text-align: center;">
<b>The white balls are the same!</b></div>
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The two games are identical in the white ball format because they both require players to select 5 of 39 white balls.<br />
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Only the bonus balls portion of the games are different. Thunderball contains 14 Thunderballs, whereas Hot Lotto contains 19 Hot balls.<br />
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On the white ball side, there are 575,757 unique combinations in each game. To select the same winning number more than once seems nearly impossible, but drawing it on the same night in two different lottery games across the pond is a miracle.<br />
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<br />John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-73602246695081593542011-06-27T09:13:00.000-07:002011-06-27T09:13:00.639-07:00How Irish Lottery Players Win Money Playing Lotto 5-4-3-2-1<a href="http://www.lottery.ie/images/results/logo-54321-Lotto-vert-small.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://www.lottery.ie/images/results/logo-54321-Lotto-vert-small.gif" /></a>One game that all Irish lottery players should be playing is <b style="font-family: "Trebuchet MS",sans-serif;"><a href="http://www.lottery.ie/en/Games/How-to-play/How-to-play-Lotto-5-4-3-2-1/"><span style="color: red;">Lotto 5</span>-<span style="color: lime;">4</span>-<span style="color: orange;">3</span><span style="color: cyan;">-2</span>-<span style="color: red;">1</span></a></b>. This is because the numbers utilized are based the Irish Lotto (Lotto Plus 1, and Lotto Plus 2) results and the winning payouts are substantially high.<br />
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To play <b style="font-family: "Trebuchet MS",sans-serif;"><span style="color: red;">Lotto 5</span>-<span style="color: lime;">4</span>-<span style="color: orange;">3</span><span style="color: cyan;">-2</span>-<span style="color: red;">1</span></b>, a player chooses five numbers and selects which game results they would like to match. We recommend that the Irish Lotto always be used because of the variety of analytical analysis available. To win a prize, the player must match one of more of the numbers selected in the Lotto drawing.<br />
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For this purpose, the player has the option to include or not include the bonus number. We recommend that the bonus number NOT be used because the payouts are higher. The table below illustrates the <b style="font-family: "Trebuchet MS",sans-serif;"><span style="color: red;">Lotto 5</span>-<span style="color: lime;">4</span>-<span style="color: orange;">3</span><span style="color: cyan;">-2</span>-<span style="color: red;">1</span></b> payouts for both the <b style="color: red;">6 Number Game</b> (<b style="color: red;">recommended</b>) and the 7 Number Game (not recommended)<br />
<h2 class="LotteryRegular"><b></b></h2><img alt="" id=":current_picnik_image" src="http://1.bp.blogspot.com/-LX0Lhxr5Upk/Tgilwa_NpRI/AAAAAAAAAGE/JtPh3daI9kE/s1600/14891055134_XFwF5.jpg" /><br />
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Next, using the results displayed in our <b style="color: #38761d;"><a href="http://www.lotterypowerpicks.com/IR6_hotcold.htm">Irish Lotto Hot Cold Number Analysis</a></b> page, we currently have identified 5 hot numbers. These are:<br />
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<div style="color: red; font-family: "Trebuchet MS",sans-serif; text-align: center;"><span style="font-size: large;"><b>02 04 06 12 38</b></span></div><br />
These are the numbers that you should play in the 6 Number <b style="font-family: "Trebuchet MS",sans-serif;"><span style="color: red;">Lotto 5</span>-<span style="color: lime;">4</span>-<span style="color: orange;">3</span><span style="color: cyan;">-2</span>-<span style="color: red;">1</span></b> Lottery Game. Based on our results analysis, a player using this 5 number combination <b style="color: lime;">would have won €1,482 in the last 3 month</b> (26 week) period. Your cash outlay would have been €26, and you would have earned a €1,456 profit. The breakdown of winnings would have been<br />
<ul><li>Match 1: Seven times (7 * €6 = €42)</li>
<li>Match 2; Nine times ( 9 * €40 = €360), and</li>
<li>Match 3: Two times ( 2 * €540 = €1,080).</li>
</ul>So, if you live in Ireland and play the Irish Lotto, we highly recommend you play the above numbers in the <b style="font-family: "Trebuchet MS",sans-serif;"><span style="color: red;">Lotto 5</span>-<span style="color: lime;">4</span>-<span style="color: orange;">3</span><span style="color: cyan;">-2</span>-<span style="color: red;">1</span></b> Game.John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-75369660743085482172011-05-24T06:54:00.000-07:002011-07-11T06:24:56.464-07:00Mega Millions Picks All Hot Numbers AgainFor the second time in less than 6 months, the Mega Millions lottery has drawn all Hot white ball numbers. In the May 24, 2011 Friday night drawing, the 5 hot white balls: <b style="color: red;">10 17 19 45 48</b> were picked. That night, the annuity jackpot was $16 million.<br />
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<center><table border="1"><tbody>
<tr> <td><img alt="MM HC Results 20110520" src="http://www.lotterypowerpicks.com/images/mm_hcResults20110520.jpg" /></td><td><img alt="MM HC Numbers 20110520" src="http://www.lotterypowerpicks.com/images/mm_hcNums20110520.jpg" /></td></tr>
</tbody></table></center><br />
Prior to that drawing, we classified 11 white balls as being hot. If a full wheel of these numbers was played, there would have been 462 unique combinations. If all these were purchased, the cost would have been $462 and the winner would have earned $250,000. However, if the player purchased the Megaplier as well, a cool $1 million would have won for a mere $924 investment. Unfortunately, the Mega Ball that night was the number 30, which was classified as a neutral number.<br />
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The last time all hot balls were drawn in the Mega Millions was Tuesday, December 17, 2010. In that drawing, the annuity prize offered was $133M, but it was not won. You can read our previous article <b><a href="http://jlotterysbimonthlyarticles.blogspot.com/2010/12/all-hot-numbers-picked-in-last-mega.html">All Hot Numbers Picked in Last Mega Millions Drawing</a></b> for reference.John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0tag:blogger.com,1999:blog-60725341237976466.post-89710251808236551742011-04-19T11:40:00.000-07:002011-04-19T11:40:23.710-07:00Investing or Gambling? Part 10: ConclusionDuring the past 9 weeks, we have presented a series of articles questioning whether investing and gambling are synonymous.<br />
<ul><li>Week 1, we provided an overview of the topic and laid out an outline of the posts to follow.</li>
<li>Week 2 we defined investing and gambling. We noted the three main distinctions that an investor has verses a gambler: ownership of an asset; value derived from market demands; and option to sell. We also summarized the two similarities: success is based on probabilities; and the future outcomes are unknown.</li>
<li>In Week 3, we discussed why this topic is important at this time. We pointed out that because of the weak U.S. economy, many people are desperate to earn a living and that temptation to invest and gamble is everywhere. </li>
<li>Week 4 concentrated on the differences between investing and gambling. Again, we reiterated that investing involves ownership but gambling does not. Also, we indicated that gambling infers fun while investing infers work.</li>
<li>Week 5's article focused on a few of the successful gamblers and investors or our time. Most of these individuals are currently earning substantial livings concentrating on both of these disciplines. We pointed out that most: were very highly educated and possessed a deep knowledge of mathematics; worked very hard to refine their skills; and dedicated many years of their lives to perfecting their livelihood.</li>
<li>In Week 6, we presented the various investment products that investors and gamblers have the options buy or play. Investors can be conservative and focus only on CDs or Bonds, or they can get excitement and thrills buying derivatives, commodities, collectibles, or other unique items. Gamblers can also vary their risk by buying lottery tickets, analyzing sporting events, playing board games or casino poker.</li>
<li>Week 7's discussion focused on the profile of typical investors and gamblers. We noted that successful gamblers were more: in control of their spending; optimistic about the future; and were more prepared for retirement. Both professionals were highly educated and made analytical decisions. Neither view their profession as gambling.</li>
<li>In Week 8, we indicated the two mathematical skills that both investors and gamblers possessed were the ability to mentally: construct complex decision trees; and know the probability of success of each outcome by heart.</li>
<li>Lastly, Week 9 presented the concept of manipulation in the two different industries. Our current belief is that the gambling industry is more regulated and less likely to be manipulated. Whereas, the investment industry is regulated only on a macro level, which leaves the doors to manipulation wide open.</li>
</ul>In our opinion, we believe that investing is much more risky than gambling is to the common man. Both professions are comprised of individuals whose sole purpose is to earn a substantial amount of money. Those who gamble usually understand their odds of winning and of losing. They typically wager small amounts of money and participate for the enjoyment or entertainment factor.<br />
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However, these same individuals invest comparatively large sums of money in the stock market and 401k accounts. Rarely do they understand the products they are buying or the potential risks of losing money. Far too many people have lost their children's educational funds during the collapse of the dot.com bubble, and are now underwater on their home's real estate investment.<br />
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Those who are against legalized gambling will point to the losses of the compulsive gambler, saying how those individuals are sick, irresponsible, and have lost everything.<br />
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Yet the losses of our entire population during the recent financial meltdown serve as a lesson in understanding risk. We truly believe that you should never buy anything that you do not understand, and more importantly, never invest with only the hope of attaining a win-fall, because this is when investing becomes simply another word for gambling.John Lotteryhttp://www.blogger.com/profile/00782386609012778100noreply@blogger.com0