Is is Time for a Euro Millions Super Draw?

Expect to see a Euro Millions Super Draw during May 2012

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.

In these drawings, only the Jackpot prize amount is increased.

What if there is no winner?
What happens to the Super Draw Jackpot prize it there is no jackpot winner depends on the Super Draw designation:

• Super Draw One means that the jackpot will roll forward to the following drawing; and
• Super Draw Two means the jackpot prize will be allocated to the winners of the next lowest tier in which there is a winner.

How are these funded?
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).

When the amount of money in the booster fund is sufficient, it is withdrawn and used for a Super Draw.

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.

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.

Why now?
The last Super Draw was held on October 4, 2011, approximately 6 months ago.

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 €50 million).

Euro Millions Jackpot Set to €129 Million this Friday

Image by Ingvar_Sverrisson via Flickr

For the 7th time in its history, the EuroMillions Jackpot is above the €100 million level. However, this is not a record.

During 2006, the jackpot reached €180M twice before being won. These were the only times that the jackpot grew naturally from drawing to drawing. All others times the jackpot was artificially set as a bonus level amount.

Since '06, three €130 million jackpots were up for grabs. One was in September 2007 and shared by 3 winners. The other two were in 2008 and there were no winners of either of these.

The jackpot never reached €100M in 2009.

But this is the second time the jackpot was established at €129 million in 2010.

So, lets cross our fingers and hope that one of us wins the EuroMillions €129 Million jackpot this coming Friday.

Answer to Lottery Trivia Question #6: How Many EuroMillions Lucky Star Combos are There?

Last week's Lottery Trivia Question #6 was:

• In Euro Millions, a player must correctly pick two Lucky Stars, each numbered 1 to 9.
  
• How many unique Lucky Star combinations are possible?

The Correct Answers are:

• There are 36 unique Lucky Star combinations! 
  
• A EuroMillions player selects 2 Lucky Stars numbered 1 to 9, but the numbers can't be repeated (meaning there are no 1-1, 2-2, ... 9-9 conbinations). One would think, therefore, that there are 9 times 8, or 72, combinations. But since order doesn't matter, we need to eliminate duplicates. Thus, we divide the 72 combinations by 2 to obtain the correct 36 unique combinations!
  

Remember to check-in tomorrow to read our 7th Lottery Trivia Question posting!

Thanks,

JL.........

Lottery Trivia Question 6: How Many EuroMillions Lucky Star Combos?

This week's Lottery Trivia Question is about EuroMillions.

Our Trivia Question #6 is:

• In Euro Millions, a player must correctly pick two Lucky Stars, each numbered 1 to 9.
  
• How many unique Lucky Star combinations are possible?
  

Enter your answer by leaving a Comment to this post below. Leave your name, and if you have a website or blog, provide it's URL and name.

We will provide the correct answer next Monday, November 9th, and will post your name and a URL link back to your site.

Have Fun,

JL.........

Should You Buy the Power Play, Sizzler, or Megaplier?

Introduction
Very often, someone asks me whether they should buy the Powerball Power Play Option. Not knowing the mathematical answer, my gut feeling was to tell them No. However, since one popular website encourages players to sign a petition to add a Megaplier Option to the Mega Millions lottery, I had my doubts. At present, the State of Texas offers this option. More recently, I read that Hot Lotto would be adding a Sizzler Option beginning in January 2008.

Realizing the importance of this topic, it was time to conduct research on this topic. What I learned is that for each of these three lottery options, the answer to the question:

Should I Buy the Power Play, Sizzler, or Megaplier?

The correct answer is both Yes and No!
It depends on the size of the Jackpot.

How do you know when to buy it?
You should always buy the multiplier option whenever the current jackpot value is below its Jackpot Breakeven level.

• For Powerball, Breakeven is $43.2 million: Buy the Power Play Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.
• For Hot Lotto, Breakeven is $2.59 million: Buy the Sizzler Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.
• For Mega Millions, Breakeven is $47.2 million: Buy the Megaplier Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.

Why is that?
The reason is that the Jackpot prizes in each of these lotteries are not multiplied. So, as the Jackpot increases above its minimum, only the probability weighted amount of jackpot money returned to players increases. At some point, which we call Jackpot Breakeven, the jackpot returns outweigh the sum of the payouts of all the other prizes. Once this is reached, buying the multiplier option is not a good investment. Remember, because the multiplier option costs $1 more, it is necessary to divide these probability weighted returns by 2 before comparing them to single $1 tickets. When the jackpot is above the breakeven level, the per dollar return of multiplier tickets becomes less and less valuable compared to that of a regular ticket.

As lottery players, we want to play the option that returns the most money back to us, the players. As you will see below, your option changes depending on the jackpot level.

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Powerball Power Play
When a player buys the Power Play option, any prize that the player wins, except the Jackpot, will be multiplied by either 2, 3, 4 or 5. The odds that any one of these multipliers will occur is (typically) a constant 25%, which means that a player can expect an average 3.5 times multiplier on average.

Based on this assumption, the graph below illustrates both the expected Power Play return (in blue) against the expected return of a single Ticket without the Power Play (in red).

When the jackpot is set to the minimum $15 million, Power Play returns $0.396 of each dollar received, compared to $0.300 for those without the option.

When the jackpot level reaches $43.2 million, both tickets with and without the Power Play returns $0.493 for each dollar received. We refer to this $43.2 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Power Play return more to the players. When the jackpot grows to $90 million, $0.813 is returned to straight ticket holders compared to only $0.653 to those who bought the Power Play.


Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Powerball jackpot is below $43.2 million, the Power Play should be purchased. When the jackpot is above this level, never purchase the Power Play. Go for the Jackpot instead.

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Hot Lotto Sizzler
When a player buys the Sizzler option, any prize that the player wins, except the Jackpot, will be multiplied by a fixed 3 times.

Given this, the graph below illustrates both the expected Sizzler return (in blue) against the expected return of a single Ticket without the Sizzler (in red).

When the jackpot is set to the minimum $1 million, Sizzler returns $0.401 of each dollar received, compared to $0.329 for those without the option.

When the jackpot level reaches $2.59 million, both tickets with and without Sizzler returns $0.474 of each dollar received. We refer to this $2.59 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Sizzler return more to the players. When the jackpot grows to $5 million, $0.694 is returned to straight ticket holders compared to only $0.584 to those who bought the Sizzler.


Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Hot Lotto jackpot is below $2.59 million, the Sizzler should be purchased. When the jackpot is above this level, never purchase the Sizzler. Go for the Jackpot instead.

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Mega Millions Megaplier (available only in Texas)
When a player buys the Megaplier option, any prize that the player wins, except the Jackpot, will be multiplied by either 2, 3, or 4. The odds that any one of these multipliers will occur is not constant, but on the average, a player can expect an average 3.476 times multiplier.

Based on this assumption, the graph below illustrates both the expected Megaplier return (in blue) against the expected return of a single Ticket without the Megaplier (in red).

When the jackpot is set to the minimum $12 million, Megaplier returns $0.350 of each dollar received, compared to $0.250 for those without the option.

When the jackpot level reaches $47.2 million, both tickets with and without Megaplier returns $0.451 of each dollar received. We refer to this $47.2 million as the Jackpot Breakeven level.

Above this breakeven level, tickets purchased without Megaplier return more to the players. When the jackpot grows to $90 million, $0.694 is returned to straight ticket holders compared to only $0.523 to those who bought the Megaplier.



Players should purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Mega Millions jackpot is below $47.2 million, the Megaplier should be purchased. When the jackpot is above this level, never purchase the Megaplier. Go for the Jackpot instead.

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Conclusion
As you can see, the decision to buy the Power Play, Sizzler, or Megaplier multiplier option is dependent upon the jackpot size. When the jackpot is below its breakeven level, players are encouraged to buy the multiplier option. But, when the jackpot is above its breakeven level, players should forego this option, and buy 2 straight tickets instead.


Learn More
To learn more about this subject, visit our in-depth pages that provide the detailed numbers behind each of these options.

• Powerball Power Play Analysis
• Hot Lotto Sizzler Analysis
• Mega Millions Megaplier Analysis

Focus for February: The Canadian Territories

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Hot Lotto to Add Sizzler

We read on the Kansas Lottery website that beginning January 3, 2008:

Hot Lotto will be adding a Sizzler Option

This will be similar to the Powerball Power Play. You pay $1 more, and all prizes EXCEPT the Jackpot will be Tripled.

Is this a good option? We will analyze both the Sizzler and Powerplay options in our December 2007 BiMonthly Article. Don't miss it!

Also, note that beginning in January 2008, Lottery Power Picks will be adding 6 new lotteries for you to get your numbers:

• California Super Lotto Plus
• Hot Lotto
• EuroMillions
• Irish Lotto
• UK Lotto
• Thunderball

If you're not familiar with our site, now is the time to visit LotteryPowerPicks.com so that you will start off 2008 on a winning track.

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The 2007 LPP Lottery Value Rankings

Introduction
Both the Lottery Power Picks Home Page and its Gadget display a graph of the up-to-date jackpots from select worldwide lotteries. Visitors can instantly see which ones are high and which are low, giving them a sense of where the money is. However, this sampling contains a mix of mini, mid-size, and jumbo lotteries, making it difficult to identify their intrinsic value when choosing a game.

People tend to play the lottery with the highest jackpot and skip the low jackpots.

Are they making the right decision?

After reading the following article, the answer may surprise you because Lottery Power Picks has calculated and created a simplistic value ranking of its lotteries. Using this information, we believe that our: Canadian members can more confidently decide if they should play Lotto 649 or Super 7; Californians can choose to play Super Lotto Plus or Mega Millions; UK residents can select the best of EuroMillions, Lotto, or Thunderball; borderline state residents can pick either Powerball or Mega Millions; and more.

Because players have a diverse choice of lotteries to play, this post is intended to help them find the best place to invest their lottery dollars. It is not meant to hinder or solicit sales, but to simply help lottery players understand their favorite games a little better. We hope you enjoy it.

The 2007 LPP Worldwide Lottery Value Rankings
The following lists our 2007 Lottery Value Rankings of our 10 sample Worldwide Lotteries. These lotteries are ordered from the best (lowest number) to the worst value (highest number) for the players. Note that there are 3 ties. In these cases, the lotteries are simply listed in alphabetical order.

1. Canada Super 7
   EuroMillions
2. 
   
3. Thunderball
4. Powerball
   UK Lotto
5. 
   
6. California Super Lotto Plus
7. Canada Lotto 649
   Irish Lotto
8. 
   
9. Hot Lotto
10. Mega Millions

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Ranking Components
In order to calculate these rankings, five statistical components were individually ranked according to value, and their sum was equally averaged. These average values were then ranked from lowest to highest, and each lottery were was assigned that ranking. The final ranking was ordered from lowest to highest, where the lowest represents the best value for lottery players, and the highest represents the least valuable for players. In the case of ties, our ranked list presented the lotteries in alphabetical order, and was not meant to imply any empirical order. The following table summarizes the individual components and rankings we calculated for each lottery. These are discussed in more detail below.

Component	MM	PB	CDA 649	CDA S7	CAL SL	HL	UK 649	TB	EM	IRL 645
1. Overall Win Odds	8	7	6	2	4	1	10	3	5	9
2. ReturnOn$	10	9	8	1	6	7	2	1	4	5
3. AvgPayout/$	5	3	4	9	8	10	1	6	7	2
4. Jackpot/Odds	3	2	6	5	4	7	9	10	1	8
5. Cash or Annuity	2	2	1	1	2	2	1	1	1	1
Average	5.6	4.6	5	3.6	4.8	5.4	4.6	4.2	3.6	5
Rank	10	4	7	1	6	9	4	3	1	7

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Component 1: Overall Winning Odds (Overall Win Odds)
To calculate the Overall Winning Odds, we assumed that each combination was sold and that there were no duplications. Next we counted the total number of winning combinations. By dividing the total combinations by the winning combinations, we derived the Overall (Winning) Odds. For this statistic, the lower the Overall Odds number, the better for the player.

For each lottery, we have calculated these values, and matched those stated by each lottery. The chart below graphically displays these results. Note that UK Lotto towers over the others, giving those players the worst chances of winning. This is followed by the Irish Lotto, and Mega Millions. The lotteries giving players the three best chances to win are: Thunderball, Canada Super 7, and Hot Lotto.

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Component 2: Average $ Returned to Player on $ Spent (ReturnOn$)
Having calculated the complete set of winning combinations above, we next determined the total value of the prize money paid back to the players by multiplying the prize cash values paid times the the number of winning combinations. We summed the total money paid and divided it by the total number of combinations to determine the Return on $ invested. The chart below summarized our findings. When reading this, please note that the higher the value, the better the player ranking.

For each $ a play spent on the lottery, Thunderball offers the highest returns with 0.54 for each $ spent. The second and third best returns were the UK Lotto and the Canadian Super 7.
Mega Millions returns the least back to the players, returning only 0.25 of each $ spent. Next comes Powerball, and then Canadian 649.

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Component 3: Average Ticket Payout per $ Spent (AvgPayout/$)
The cost that each lottery charges for a single ticket varies. Many charge $1 for 1 ticket, and others charge $1 for 2 tickets, $2 for one ticket, and $2 for 3 tickets (ignoring the foreign exchange considerations). In order to compare the lotteries on a common basis, we have calculated the prize dollar return per winning ticket. Using this type of cost basis, players are neutral to the actual cost of a particular lottery ticket, and can concentrate on the average value of a winning ticket per dollar they spent. Thus, when viewing the graph below, the average payouts are consistently presented. Please note that when reading this graph, the higher the value, the better the player ranking.

The calculations used to determine this information was to total the total cash value all of a lottery's prizes, divide it by the number of winning tickets, and then dividing the result by the cost of a single ticket.

As we can see, the first place UK Lotto average winning ticket payout is nearly $10 higher than the second place Irish Lotto. Third is Powerball. The 10th place lowest paid winning ticket is that of Hot Lotto. The Canadian Super 7 is in 9th place, and the California Super Lotto Plus is eighth.

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Component 4: Jackpot $ per Odds (Jackpot/Odds)
Each lottery offers a minimum jackpot prize. These vary from as low as $0.25 million to $15 million. Additionally, the odds of winning any also prize also varies. For comparative purposes, the graph below illustrates the the ratio of the jackpot to odds. Thus, one's jackpot expectation per odd is similarly quantified. Again, the higher the value, the better for the player.

As shown, the three major jumbo lotteries lead this risk/reward measure. First comes Euro Millions; second is Powerball; and third is Mega Millions. On the low side are: Thunderball whose payoffs are extremely small; and followed by the UK Lotto and the Irish Lotto.

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Component 5: Cash or Annuity (Cash/Annuity)
Of the 10 lotteries being ranked, six pay the stated cash jackpot prize. The other four: Mega Millions, Powerball, California Super Lotto Plus, and Hot Lotto, each pay the stated prize as an annuity which is a heavily discounted cash prize. This means that the actual cash paid to a jackpot winner in each of these is considerably less than what is stated.

To adjust this discrepancy, we have assigned a value of 1 to all lotteries paying cash, and penalized those who pay annuities by assigning a value of 2 for this measure. Thus, for this measure, the lower the value assigned, the better for the players.

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Summary
After ranking our 10 lotteries by each of the above measures and then finding their average placement, we derive an unbiased overall ranking that we call the LPP Lottery Value Ranking. In 2007, we believe that our summary informs the players which lotteries offer the best value for their investments. The list below re-iterates our findings and presents our rankings from best to worst value for players.

1. Canada Super 7
1. EuroMillions

3. Thunderball
4. Powerball
4. UK Lotto

6. California Super Lotto Plus
7. Canada Lotto 649
7. Irish Lotto

9. Hot Lotto
10. Mega Millions

After reviewing this list again, it is clear that we can't judge a lottery by it's jackpot size. Tied for Number 1 are: Canadian Super 7, whose minimum jackpot is $2.5 million; and EuroMillions, with a starting jackpot of €15 million. In third place is Thunderball, with a fixed jackpot of only £0.25 million. At the end are the Hot Lotto jackpot of $1.0 million, and lastly Mega Millions, offering $12 million.

As we can see, when looking Lottery Value Rankings list, the jackpot sizes are mixed and appear in an almost random order.

In our introduction above, we posed a question:

Should people play the lotteries with the highest
jackpot and skip those with low jackpots?

Based on our study herein, our answer clearly is:

No! Never judge a lottery simply by its jackpot size!

If you wish to learn more details about any one of these lotteries, read our detailed pages by clicking the links above.


Focus for December: The Powerball Powerplay


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Not All Lottery Combinations are Equal

If you play the lottery, invest in stocks, begin a business, play bridge, poker, backgammon, or simply want to be successful in a random world, you need to understand the odds of an event occurring in your particular sub-world, rather than simply relying on luck. By knowing the probabilities, you can make sound judgments and take advantage of the principals of randomness instead of being subject to them. Successful people utilize probability theory to take a particular viewpoint and then make their financial investments accordingly. This post takes the controversial viewpoint that all lottery combinations are not equal, and examines the probabilities that certain types of combinations will be drawn sooner than others. Winning is not gambling, it is all about mathematics.

Introduction
For years, my friend Ron and I have argued about the best combinations for winning the Mega Millions and Powerball lotteries. I believe that the most likely numbers to be drawn are those which are spread across the range of numbers. Ron insists that all combos have an equal chance of occurring and always plays the classic: 1 2 3 4 5 and 6. Since neither of us has won the jackpot yet, we continue to have this debate. However, after launching Lottery Power Picks last year, I am more convinced than ever that playing the numbers 1-2-3-4-5-6 is a poor investment and not worth the risk. This article explores why:

• All combinations do NOT have an equal chance of occurring.
• The odds of the combination 1,2,3,4,5,6 being drawn is minimal.

Powerball Example
For purposes of this discussion, we will focus on the Powerball. In this lottery, a player selects 5 numbers from a pool of 55 numbered white balls, and one Powerball from a set of 42 red balls. When the drawing is later held on Wednesday or Friday night, there will be two drums, one containing the 55 white balls, and one with the 42 red balls. The five white balls will be drawn first, one at a time, without replacement, which means there will no duplicate white ball numbers. Immediately afterwards, the single Powerball will be drawn. These six numbers become the winning combination for that drawing (Understanding Powerball Chances). Since there are 3,478,761 unique white ball combinations and 42 red balls, there is a grand total of 146,107,962 six number combinations. Thus, the overall chances of any single combination occurring is 1 in 146.1 million.

So then all Combinations are Equal?
On the surface, the answer is yes, because when the final combination is drawn, it will truly be the only 1 of the 146.1 million combinations. Thus, it would appear that any other combination could have been equally selected. This is why the official lotteries, most casual players, and lottery skeptics, like Ron, argue that all combinations are equal.

Not So
Both mathematicians and seasoned, or regular, lottery players know that: based on probabilities, certain combinations are more likely to be drawn than others. This means that all combinations are NOT equal. The argument for this hypothesis is that lottery drawings are completely random. Remember: "random does not mean haphazard. Even though individual outcomes are uncertain, it is possible to predict distributions of random events if we know their probability" (Randomness). We shall use these principals as the basis for our argument.

But First, Forget the Powerball
The Powerball Lottery actually consists of two separate drawing in one. The first is the drawing of the 5 white balls, and the second is the drawing of the Powerball itself. Since there is only one Powerball drawn out of a set of 42, the likelihood of any one ball being picked is identical. Thus, it really doesn't matter what the Powerball is. A player can easily eliminate this Powerball risk by playing all 42 Powerballs with each 5 number combination. Therefore, the Powerball is not important to our discussion, and we shall ignore it.

Concentrate on Predicting the 5 White Ball Combination
The primary objective of the lottery player is to pick 5 numbers before the drawing which will match those numbers chosen in the actual drawing. Lets examine two possible 5 white ball combinations, 01 02 03 04 05 and 01 19 22 38 53 to see if they have an equal chance of winning. For these purposes, we will use the Lottery Power Picks Combination Distribution Tables as our reference guidelines in order to evaluate the likelihood that the combination will be picked.

First, let's review the scenario when the player selects the combination: 1, 2, 3, 4, 5. These numbers do not look random because have a pattern and a sequence. However, these traits are not important in the mathematics of randomness. A number sequence does not have to "look" random in order to be random. Instead, it must follow well established criteria.

1. First, from an even-odd viewpoint, we see that the sequence 1, 2, 3, 4, 5 contains 2 even numbers and 3 odd numbers. There are 1,149,876 of these combinations and have a 33.1% chance of being selected (Table PB-1a: Powerball Even/Odd Combination Distribution). This is the best even/odd choice. Good so far.
2. Second, we examine this combination's bucket distribution. Here we notice that all five numbers fall within the Bucket 1-9. From Table PB-2a: Powerball Bucket Distribution, we find that there are only 126 combinations in this bucket, meaning its probability of occurrence is 0.00362% (126/3,478,761). This means that we will have a 1 in 126 chance of winning once every 27,609 drawings or 265.5 years. Not good.
3. Third, we check the combination's hi-low distribution in Table PB-3a: Powerball Low-Hi Number Distribution. Reading across the table with a first ball of 1 and a last ball of 5, we learn that there is only 1 possible outcome in the set of 3,478,761 combinations. From this viewpoint, the probability of this sequence being drawn is even closer to 0%, only 1/3,478,761. However, in this case, we can expect to be 100% correct once every 3,478,761 drawings or 33,449.6 years.

Comparatively, let's review the scenario where the player selects the numbers 1, 19, 22, 38, 53 instead.

1. Since this combination also has 2 even numbers and 3 odd numbers, it too has a 33.1% chance of being selected. This is the same as the above sequence.
2. Looking at this number's bucket distribution, we find that there are 54,000 combinations that can be formed using the numbers in Buckets 1-9, 10-19, 20-29, 30-39, and 50-55. This set of numbers represents 1.55% of all combinations, meaning that we can expect this condition to occur approximately once every 65 drawings or 32.5 weeks. When this happens, our odds of winning will be improved to 1/54000.
3. Next, after checking the combination's hi-low distribution of 1-53, we discover that there are 20,825 possible combinations having a 0.59% probability of occurring. This means that once every 167.0 drawings or 1.6 years, we will have a 1 in 20825 chance of winning.

Probabilities Favor Certain Combinations
From this information, we have learned how to understand the Lottery Power Picks Probability Distribution tables. From them, we can argue that one combination is more likely to be drawn than another because of its probabilities. Further, we have observed that:

1. The combination 1 2 3 4 5 has an extremely low probability of occurring.
2. Other combinations, such as 1 19 22 38 53, have higher probabilities of occurring.

But, before we can say this definitively, we need to examine the past Powerball results to see if it really does follow the probabilities we have asserted.

Verify Probabilities using Historical Results
Using the above two numerical sequences, we have reviewed and calculated the actual distribution probabilities by summarizing the Lottery Power Picks Powerball Results from January 01, 2001 through August 11, 2007. During this period, there were 692 drawings. Of these, we observed that:

• 227 combinations contained 3 odd and 2 even balls which is 32.8%. Using this set's 33.1% probability, we expected to find 228.7 combinations. (both sequences)
  
• 0 combinations were all contained in bucket 0-9 which is 0%. Using this set's 0% probability, we expected to find 0 combinations. (1-2-3-4-5 only)
  
• 0 combinations had a high-low distribution of 1-5 which is 0%. Using this set's 0% probability, we expected to find 0 combinations. (1-2-3-4-5 only)
• 7 combinations had a bucket distribution of 0-9, 10-19, 20-29, 30-39, 50-55 which is 1.01%. Using this set's 1.55% probability, we expected to find 10.7 combinations. (1-19-22- 38-53 only)
• 4 combinations had a high-low distribution of 1-53 which is 0.58%. Using this set's 0.59% probability, we expected to find 4.1 combinations. (1-19-22- 38-53 only)

As expected, the actual combination frequencies are very similar to the expected frequencies, verifying our assumption that: we can reasonably predict the distribution of Powerball lottery outcomes based on various distribution probabilities.

Conclusion: Not All Lottery Combinations are Equal
Given the fact that the Powerball and other lottery drawings are truly random, we have illustrated that it is possible to predict certain lottery outcomes knowing the likelihood, or probability, of that particular subset. Having applied the mathematical principals of randomness to two different sets of lottery numbers, we have shown that one combination is more likely to be drawn than another.

Since we have demonstrated that two combinations have different likelihoods of occurring, we may confidently conclude that we have proven the statement that:

All lottery combinations do NOT have an equal chance of occurring.

Therefore:

Not All Lottery Combinations are Equal!

Done.

Special Note - Not True for Pick 3 and Pick 4
This proof does not apply to Pick 3 and Pick 4 lotteries. In these, all combinations are truly equal for two reasons. First, the final combination is order dependent. Second, the numbers are picked with replacement, meaning that duplicate digits can occur: 221, 999, 777, etc.

Learn More
You can learn more about this topic by reading the articles listed below.

• Randomness and Probability
• Chance and Randomness: From Probability Theory to Games
  
• Gail Howard's Three Methods to Win at Lotto
• Free Winning Lottery Strategies
• Lotto combination 1,2,3,4,5,6: Probable but not likely
• Optimal Strategy and the Spectacle of Poker: A Possible Tendency
• The Infamous Combination
• Google Answers: Statistics - Lottery like
• Yahoo Answers: The probability of these numbers coming out on lottery ?
• Better Lottery Number Selection… Or Not!
• Randomness and Mathematical Proof

Visit Us
To further help your chances of winning the large lottery Jackpots, get and play your free Lottery Power Picks . If you win, you'll be glad you did.

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Your Lottery Odds May be Better than You Think

Introduction
The Mega Millions, Powerball, and other"Megaball" type Lotteries inform you your odds of winning the Jackpot and other prizes. However, we at Lottery Power Picks believe that your odds of winning the 3, 4, and 5 of five white ball prizes are better than what has been provided. This article explains your odds, and why we believe your chances of winning these prizes are better than what is printed.

Mega Millions Example
The Mega Millions lottery consists of a pool of a set of 56 numbered white balls and a set of 46 megaballs. The odds of selecting the 5 winning white balls is 1 in 3,819,816 (using the Excel function =combin( 56, 5) ). Multiplying this number by the 46 megaballs gives us 175,711,536. When we compare both of these numbers to those indicated on the Mega Millions Game Instructions page, we find that we match the 175M chances of picking all six numbers, but differ substantially in the winning 5 white ball combinations: 3,819,816 (from Excel) vs 3,904,701 (MegaMillions).

Why the Discrepancy?
This discrepancy led us to ask ourselves the question: If the total odds of selecting 6 numbers is correct, and knowing that there are 46 megaballs, then by working backwards, the odds of selecting the 5 white balls should be 3,819,816 as calculated in excel. So, Why do we have a difference of 84,885 chances?

Answer
The explanation is that there are only 45 combinations that have the correct 5 winning white balls, and 1 that has the winning megaball as well. This means that the odds of getting all 5 numbers correct, but not the megaball is 3,819,816 times 1/45, which equals 3,904,701 as MegaMillions states. For correctness, it is necessary for MegaMillions to state these odds because the do not payout the $250,000 prize to the holder of the complete 6 number winning combination. In this case, they only payout the Jackpot prize, which is a minimum or $12 million. Thus, there is only 45 payouts, not 46.

Should we care?
The answer to this question depends on your point of view. The mathematical enthusiast would argue that the Mega Millions odds are correct and cannot be misinterpreted. From this strict viewpoint, they are correct.

However, the Lottery enthusiast plays against the odds, always hoping to win the big prize. Most players would be thrilled and pleased to have one of the 5 winning white ball combinations, netting them the 2nd prize of $250,000. From this vantage point, it is better to consider the Mega Millions lottery as 2 separate games: One in which they win the 2nd prize with 5 white balls; and the second where they win the Jackpot prize because they did have the megaball. By aiming for the 5 white ball prize of $250,000, their odds have improved by 84,885 and have become 1 in 3,819,816. Additionally, they also have a 1 in 46 chance of winning the entire jackpot. Think of this: with this strategy and these odds, you will always win the 2nd prize of $250K, plus, you could receive the additional Jackpot less $250,000.

Your Improved Odds and Expectations
As a Lottery Player, you now have the improved odds of winning the 3, 4, and 5 white ball combinations, as well as having a 1 in 46 chance of receiving the megaball bonus.

The following table summarizes the quoted odds, the Lottery Power Picks straight odds, and your improvement in the odds for the: Mega Millions, Powerball, California Super Lotto, Hot Lotto, Euro Millions, and Thunderball lotteries.

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Match...MegaMillions......LPP......Improve.....Win...+.Bonus
5 White...3,904,701...3,819,816.....84,855...250,000.+.JP-250K
4 White......15,313......14,980........333.......150.+.9,850
3 White.........306.........300..........6.........7.+.143

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Match.....Powerball.......LPP......Improve.....Win...+.Bonus
5 White...3,563,609...3,478,761.....84,848...200,000.+.JP-200K
4 White......14,254......13,915........339.......100.+.9,900
3 White.........290.........284..........6.........7.+.93

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Match....SuperLotto.......LPP......Improve.....Win...+.Bonus
5 White...1,592,937...1,533,939.....58,998....10,000.+.JP-10K
4 White.......7,585.......7,304........281........50.+.450
3 White.........185.........178..........7........40.+.46

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Match.....Hot Lotto.......LPP......Improve.....Win...+.Bonus
White..... .607,743.....575,757.....31,986.......Percentage
4 White.......3,575..... .3,387........188.......Percentage
3 White.........108.........103..........5.......Percentage

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Match...EuroMillions.......LPP.....Improve.....Win..+.Bonus
5 White...3,632,160...1,118,760..1,513,400......Percentage
4 White......16,143.......9,417......6,726......Percentage
3 White..,......367.........214........153......Percentage

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Match....Thunderball.......LPP.....Improve.....Win...+.Bonus
5 White.....299,661....278,256......21,405.....5,000.+.245K
4 White.......2,067......1,919.........148.......100.+.4,900
3 White..........74.........69...........5.........5.+.15

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Conclusion
As a dedicated Lottery Player, you now have the improved odds of winning the 3, 4, and 5 white ball combinations, as well as having a 1 in a XX chance of receiving the megaball bonus.

We believe these lower combinatorial odds are important for you to know because they represent the actual number of different combinations available in the multi-white ball pool. In future articles, we will be using these numbers to explain which combinations have a higher or lower probability of occurring, so this is important to understand this concept.

If you think of this as winning the lower prize PLUS a chance to win a Bonus amount, you will remain optimistic while controlling your expectations of winning at the same time. Remember, in the large jackpot games, every little bit helps.

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