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When the amount of money in the booster fund is sufficient, it is withdrawn and used for a Super Draw.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

Probability of a Mega Millions rollover or having a single winner decrease as sales approach 600M

As 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 $540M $640M, we now believe that up to 600 million tickets may be sold.

Thus, we asked ourselves two questions:

1. What is the probability that there will be no winner in tonight's drawing?
2. What is the probability that there will only be one sole winner?

Using our brute force duplicate ticket estimator, we have produced two tables for your reference.

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.

	Table 1: Probability of Mega Millions Winning Tickets
Winning Tickets	300M Sold	400M Sold	500M Sold	600M Sold
None, No winner	18.1%	10.3%	5.8%	3.3%
1 Winner Only	39.3%	35.4%	31.2%	27.4%
2 Winner Only	28.2%	29.5%	28.2%	25.9%
3 Winner	12.4%	18.4%	21.5%	22.2%
4 Winner	1.9%	5.9%	11.0%	14.9%
5 Winner		0.5%	2.3%	5.6%
6 Winner			0.1%	0.6%
7 Winner
8 Winner
Total Probability	100.0%	100.0%	100.0%	100.0%

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.

	Table 2: Distribution of Mega Millions Tickets Sold
Numbers	300M Sold	400M Sold	500M Sold	600M Sold
All Combinations	175,711,536	175,711,536	175,711,536	175,711,536
Unsold	31,864,733	18,036,279	10,209,010	5,778,566
1 Only (Singles)	143,846,803	157,675,257	165,502,526	169,932,970
2  (Doubles)	103,460,042	131,466,722	149,526,982	160,511,932
3 (Triples)	45,526,185	82,214,057	114,388,867	137,818,542
4 (Quadruples)	7,022,773	26,431,098	58,127,495	92,689,034
5 (Quintuples)	144,138	2,198,990	12,023,012	35,013,149
6 (Sextuplets)	59	13,876	430,590	3,988,410
7 (Septuplets)	0	0	528	45,963
8 (Octuplets)				0
Sum	300,000,000	400,000,000	500,000,000	600,000,000

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.

Cheers,

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.

Multiple Lottery Ticket Odds Calculator Released

With 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.

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.

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.

Let us know what you think. 

Thanks, JL ......

Powerball's 2012 Powerplay buying guideline

Introduction
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.

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).

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.

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.

Is the Powerplay Option worth the extra cost?

Still, the correct answer remains both Yes and No!
But, it depends on the size of the Jackpot.

How would you know when to buy it?
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.

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.

For the 2012 Powerball game, the Breakeven is now $112.5 million: Buy the Powerplay Option whenever the Jackpot is below this value. Never above this. Put the extra dollar towards an extra ticket instead.

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.

Learn More
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:

• 2012 Powerball Power Play Recommendation Analysis

Which 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:

Which Game Should I Play?

Given that jackpots and combinations vary so much, it is often difficult to make a choice. 

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.

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.

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.

You can access this page at: Which Game Should You Play?

Cheers and Merry Christmas!

JL ...........

Expected Powerball 2012 jackpot levels and growth - Part 2: Analysis of the new 2012 Powerball game changes

Powerball recently announced that it will modify the format of the Powerball game in January of 2012. You should expect to see:

• Average jackpots of $115 to $145 million;
• A high jackpot of $700 to $800 million;
• Average jackpot growth of $15 to $20 million.

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:

• Part 1: Evaluate the prize structure in comparison to Mega Millions (published October 2011),
• Part 2: Examine the average Powerball jackpots and anticipated increases (this post), and
• Part 3: Compare the new Powerball return to Mega Millions and other lottery games (to be published).

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.

To begin, we summarize the two most significant changes that affect the annuity jackpot offerings. These are:

1. Minimum jackpot is set at $40 million
2. Cost of each ticket is $2 each.

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.

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:

How quickly will Powerball jackpots grow?

What will be the average size of Powerball jackpots?

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Historical Jackpot Distributions

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:

1. The complete range from minimum to maximum.
2. The 84% range (shown by the thick white portion)
3. The average (horizontal black line)
4. The median (both the orange horizontal line and the purple square
5. The 97% marker (orange square)

This data is a graphic visualization of the table immediately below.

	PB all	PB after Jan 09	MM all	MM after Jun 05
Average	66.6	74.2	56.3	65.0
Median	49.0	59.0	37.0	44.0
Mode	20.0	20.0	12.0	12.0
Maximum	365.0	260.0	370.0	370.0
Minimum	10.0	20.0	5.0	12.0

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.

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.

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).

Thus, we can conclude that the mode of Powerball after 2012 will later become $40 million.

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Historical Jackpot Changes

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).

	Avg JP	Avg Chg	GT 100M	40-100M	LT 40M
PB All	66.6	12.4	25.4	12.1	7.1
PB After 2009	74.2	15.0	25.7	15.0	8.7
MM All	56.3	11.5	30.4	11.9	6.4
MM After Jun 05	65.0	13.4	29.5	12.5	7.9

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.

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).

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.

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Expected Distribution

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.

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Estimating Future Powerball Jackpots after 2012

Utilizing all of the above information, we have prepared the table below indicating our estimates of future Powerball Jackpots. These are shown in Yellow. Next to our estimates are Mega Millions and the existing Powerball game.

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.

Chg	PB 2012+ Projected Jackpots	Dwg #		Chg	Current MM Jackpots	Dwg #		Chg	Current PB Jackpots	Dwg #
15	40	1		8	12	1		9	20	1
	55	2			20	2			29	2
	70	3			28	3			38	3
	85	4			36	4			47	4
	100	5		13	44	5		15	56	5
30	115	6			57	6			71	6
	145	7			70	7			86	7
	175	8			83	8			101	8
	205	9			96	9			116	9
60	235	10		30	109	10		25	131	10
	295	11			139	11			156	11
	355	12			169	12			181	12
100	415	13			199	13			206	13
	515	14		60	229	14		60	231	14
	615	15			289	15			291	15
	715	16			319	16			316	16

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).

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Conclusion: Summary of Powerball 2012 Jackpots

Based on the above information, we can answer our initial questions and summarize our findings as follows:

• Expect average jackpots to grow by $15 to $20 million.
• Expect average jackpots of $115 to $145 million;
• Look for jackpots to reach $700 to $800 million.

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Word of Caution

Initially, we believed these estimates to be too low. But then we realized the conflict that the new Powerball 2012 game posed.

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.

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.

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).

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.

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.