New Lotto Texas 2013 - Review of the Game Changes

Revised: Friday, April 26, 2013

For the 4th time since the game began in 1992, the Texas Lottery Commission (TLC) will be making changes to Lotto Texas.

These changes will become effective beginning with the April 17 2013 drawing.

This is our summary of the changes and our evaluation of them.

The basic Lotto Texas format will remain the same. 
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.

What Changes
However, there will be 4 differences in the new Lotto Texas 2013 game.

• First, a "Extra!" 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 Extra! 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).
• Second, the minimum annuity jackpot prize will be increased to $5.0 million.
• Third, the annuity payout period will increase from 25 to 30 payments.
• Forth, the annuity jackpot will increase in increments of $250,000 rather than the current $1 million.

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.

To help players understand how these changes will affect them, we discuss each of these 4 changes below.

Summary of Lotto Texas 2013 Changes and Payout Structure
To begin, we have prepared the summary Table 1 below illustrating the prize payouts for a single $1 ticket and the new $2 Extra! ticket.

Table 1: New Lotto Texas 2013 Payout Structure
Match	Chances	Occurs	Probability	Single $1   Ticket	New $2 Extra!
6	25,827,165.00	1	0.000004%	Jackpot	Jackpot
5	89,677.66	288	0.001115%	$2,000	$12,000
4	1,526.43	16,920	0.065512%	$50	$150
3	74.66	345,920	1.339365%	$3	$13
2	8.85	2,918,700	11.300892%	-	$2
1	2.51	10,273,824	39.779140%	-	-
0	2.10	12,271,512	47.513972%	-	-
	Total	25,827,165	100.000000%	-	-

Here we can see that there is no change to the single $1 ticket set of prizes. However, the Extra! 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.

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 Extra! 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 Extra!. 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.

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 Extra! 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 Extra! ticket. Thus, we believe that the Extra! option is attractive and should be played.

The Breakeven: When to buy Extra! - Like all other multiplier games, the new Lotto Texas Extra! option has an implied breakeven value. This is the jackpot amount where the returns of a single ticket equals that of the Extra! ticket. For Lotto Texas, we calculate this value to be: $11.4 million. Thus:

Buy Extra! when the jackpot is less than or equal $11.4 million;

Do not buy Extra! when the jackpot is more than $11.4 million.

Minimum Jackpot Increases to $5 Million
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 Extra! 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.

Thus, it is noteworthy that the Texas Lottey Commission recognized the potential for increased profits and raised the minimum Jackpot accordingly.

Annuity Payout Period increases to 30 payments.
However, changing the annuity payout period from 25 to 30 payments only benefits the Texas Lottery Commission, not the players.

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.

Thus, even though we have a higher annuity value, the corresponding cash value payout will be proportionately lower than what currently exists.

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.

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.

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.

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.

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.

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.

Table 2: Annuity to Cash and Yearly Payouts Scenarios
Jackpot	Yield	Old  Cash	New  Cash	Cash   Diff	Old Yearly Payout	New Yearly Payout
$4M	2.8%	$2.93	$2.76	-$0.17	Old Yrly	- na -
$5M	2.8%	$3.66	$3.45	-$0.21	$0.200	$0.167
$5M	4.0%	$3.25	$3.00	-$0.25	$0.200	$0.167
$5M	6.0%	$2.71	$2.43	-$0.28	$0.200	$0.167
$10M	2.8%	$7.32	$6.89	-$0.43	$0.400	$0.333
$10M	4.0%	$6.50	$5.99	-$0.51	$0.400	$0.333
$10M	6.0%	$5.42	$4.86	-$0.58	$0.400	$0.333

Table 2 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.

Jackpot Increases by $0.250 million
The last major change with the new 2013 Lotto Texas will be the increments by which the annuity jackpot will grow.

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.

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.

The reason is that the annuity can be adjusted more proportionately to actual ticket sales.

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.

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.

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.

Summary
In summary, four new rules to Lotto Texas will go into effect beginning with the April 17, 2013 drawing.

These changes include: offering a new Extra! 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.

Overall, we believe these changes will be beneficial to lottery players in Texas, and to the Texas Lottery Commission as well. The Extra! 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.

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.

Sources:

• Lotto Texas Change Announcement
• The Lotto Report review of changes
• Lotto Texas 2013 Complete Odds and Return to Players
• When to buy Lotto Texas Extra - Recommendation Analysis
• Texas Two Step Jackpot Growth History

Should you buy all 175.2 million Powerball combinations?

Update 1: The Powerball annuity jackpot has been increased to $500 million, and the cash value is now $327 million. (Tuesday, Nov 27 3:31 PM)
 
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. 

However, before one recklessly spends this much money, there are several factors that that must be considered.

1. 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.
2. 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.
3. The cash value being offered today is $278.3 million. If you take the cash, you will immediately lose $72.1 million.
4. 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.
5. 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.

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:

No, You should NOT but all the Powerball combinations.

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?
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.

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.

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.

Thus, we continue to recommend that you should:

NEVER buy all the Powerball combinations!

Introducing the Lottery Probability Surface

In 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".

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).

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.

3-D Image of Pick 4 Lottery Probability Surface

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.

Texas 2 Step Lottery Probability Surface (3-D)

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.

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).

JL ..........

Should 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. (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).

However, for purposes of this discussion, we will assume that 200 million Mega Million tickets were sold for that drawing.

Since our ticket sale estimate is well above the total number of allowable Mega Millions combinations (175.7 million), one can logically ask:

Why was there no Mega Millions Jackpot winner?

The answer is: Duplicates!

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.

Graph 1: Percent of Mega Millions Duplicates per Million Tickets Sold

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.

Graph 2: Chance of Losing Mega Millions per Million Tickets Sold

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.

So, getting to our title question:

Should I buy all the 175.7M Mega Millions combinations?

The answer depends on how you purchase them. 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.

If you take the Cash Option, you will lose money if you have to share it with 1 other person.

And, if you take the Annuity, you lose money if you share it with 2 others.

However, if you are lazy and just buy 175.7 million Quick Picks, you are not guaranteed to win the jackpot. As stated above, approximately 40% of these will be duplicates and you will have a 31.4% chance of losing.

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.

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.

Same 5 lottery numbers are drawn on same night in two different lottery games

As 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. The numbers drawn for both Hot Lotto and Thunderball on Saturday, August 20, 2011 were:

Game	White Numbers Drawn	Thunderball Hot Ball
Thunderball	6 7 11 22 33	10
Hot Lotto	6 7 11 22 33	13

The white balls are the same!

The two games are identical in the white ball format because they both require players to select 5 of 39 white balls.

Only the bonus balls portion of the games are different. Thunderball contains 14 Thunderballs, whereas Hot Lotto contains 19 Hot balls.

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.