Reminder: Friday will be the last Super 7 drawing

The last Canadian Super 7 Lottery drawing will be held this coming Friday, September 18, 2009, and all outstanding prizes will be awarded. The current jackpot is C$21 million. If it is not won, the jackpot prize pool will roll down to the lower tier prizes. And, all Free tickets will be cashed out for C$2.00 each.

So make sure to play this final week, since higher prizes may be awarded to all lower tiers. You will have 1 year to redeem your prize winnings, so don't misplace your tickets.

Then, beginning Saturday, the 19th, tickets for the newly launched Lotto Max will go on sale.

Lottery Power Picks considers this Game to be "Super 7" format change, so we will maintain continuous coverage of this new Lottery including History, Hot/Cold Analysis, and more.

Cheers & Good Luck to All,

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

Lotto Max Analysis - When to Play Guide

Introduction
Lotto Max is a new Friday night Canadian lottery being launched on Saturday, September 19, 2009. The game offers players the chance to win a Jackpot prize ranging from C$10 to C$50 million. And, once the jackpot reaches and exceeds C$50M, additional MAXMILLIONS drawings will be conducted for every additional C$1 Million above the C$50M cap. The single prize of these additional MAXMILLIONS drawings will be fixed at C$1 million. Like all other lotteries, a player must correctly match each of the white balls to win the Lotto Max or MAXMILLIONS jackpot (bonus balls are excluded).

Lotto Max is essentially a Super 7 makeover with a slight format change.

• Player required to select and match 7 white balls.
  
• White balls increased from 47 to 49
• Bonus ball prizes still awarded when matching 6 white or 3 white balls plus bonus ball
  
• Minimum Jackpot C$10 million
• Maximum Jackpot C$50 million
• When Jackpot pool exceeds C$50M, additional MAXMILLIONS drawings will be conducted
• Prize winning award structure same as Super 7
• Most lower tier prizes are doubled in size.

Wow, sounds Great! So what's the catch?

The cost! Lotto Max tickets cost C$5 each for 3 combinations, This is 2 1/2 times more than Super 7. But, the Lotto Max organizers will argue, the minimum jackpot of C$10M is 4 times larger than the old Super 7 minimum.

Considering the fact that the Jackpot and prizes increased, players must question:

Should I really spend C$5 for 3 combinations?
Or, should I stick with 649 or the regional lotteries?

We found that the Correct Answer is:
You Should Do Both
depending on
the sizes of the Lotto Max and competing jackpots.

The following explains our advice.

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Lotto Max Basic Returns
In Lotto Max, a player is required to pick 7 numbers from a set of 49 white balls. There are 85,900,584 combinations. The tickets are packaged as 3 selections for C$5, meaning a single combination costs C$1.666 each. Assuming a that all combinations are sold and there are no duplicates, a total of C$143,167,640 will be received. When the Jackpot is set at the advertised C$10 million minimum, Lotto Max will pay out C$49,723,431 back to the players. By dividing the the C$49.7M by C$143.2 received, we obtain a return of C$0.3473 per C$1 spent.

When the Jackpot increases by C$1 million, the return to players will increase by C$0.00698. For example: when the jackpot is C$20M, the return is C$0.4172; and, when the jackpot is C$50M, the return is $0.6267.

Even when Lotto Max goes into MAXMILLIONS mode, the return to the players remains linear. This is because return only compares money paid verses money received. Accordingly: when the jackpot is C$60M, the return is C$0.6966; and, when the jackpot is C$100M, the return is $0.9759.

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Visualizing Return
It is often helpful to visualize the returns of various lotteries. The Graph LM-GR01 below illustrates the implied returns of Lotto Max, Lotto 649, and the Old Super 7.




There are a few things to note from this graph:

• the old Super 7 format always returned more money than the newly created Lotto Max
• the increase in Lotto Max return is vary flat
• the Lotto Max return intersects Lotto 649 at approximately C$2.5M
  

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Utilizing Return
By understanding the implied return of various lotteries, we are able to utilize this linear function to compare different lotteries with varying formats. This can be done because return is always stated in a per $ basis.

Lottery players in Canada who wish to win C$1 million or more have three choices. They can play:

1. Lotto Max, with a minimum jackpot of C$10M
2. Lotto 649, with a minimum jackpot of C$3M
3. Provincial lottery, with a fixed jackpot of C$1M or C$2M depending on where they live

Those who on limited budgets, or who wish to acheive the greatest possibility of winning should know which lottery offers the best return for their playing dollars.

The illustrations below tell you when you should buy Lotto Max, Lotto 649, or the Regionals.

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Buy Lotto Max or Lotto 649?
There are two difficulties when deciding whether to buy Lotto Max or Lotto 649 tickets

1. The Jackpots sizes are vastly different magnitudes ( C$2.5M vs C$10.0M )
2. The Jackpots of each vary
   

The graph below identifies when you are better off buying Lotto Max or 649 tickets.



Graph LM-GR02 shows Lotto Max (LM) jackpots ranging from C$10M to C$100M. Beneath these, are corresponding Lotto 649 (L649) jackpot levels. These thresholds should be used to determine which game to play.

For example, assume that the Lotto Max jackpot is C$10M. If the Lotto 649 jackpot is below C$3.8M, then you should play Lotto Max; if 649 is above C$3.8M then play Lotto 649. (corrected)

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Buy Lotto Max or Regionals?
A second choice Canadian lottery players have is whether it is better to buy Lotto Max tickets or their regional provincial game. In the Atlantic, Ontario, and Western 49 games, tickets only cost C$0.50 each but the jackpot is fixed at C$1 million. In British Columbia and Quebec, tickets sell for C$1.00 and the jackpots are fixed at C$2 million.

However, because the populations are limited, the Canadian Lottery is more liberal with its income, and returns more of its intake back to the players.

Compared to Lotto Max, the regionals are more attractive in all cases.




For each of these, Graph LM-GR03 above illustrates the Jackpot level that Lotto Max must reach for the player to be indifferent to either game.

As shown, players should purchase:

• Atl 49 whenever Lotto Max is below $40.2M
• BC49 whenever Lotto Max is below $31.8M
• LQ49 whenever Lotto Max is below $31.8M
• Ont49 whenever Lotto Max is below $28.6M
• Wst49 whenever Lotto Max is below $53.9M

We believe these these breakeven jackpot levels are sufficiently large enough for wise players to generally favor and play the regional game rather than Lotto Max.

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Buy Lotto 649 or Regionals?
By comparison, Lotto 649 is a nationwide game whose format is nearly identical to the regionals. In all, the number of combinations are identical, fixed at 13,983,816.

The main difference is that Lotto 649 jackpots can grow. By calculating the implied breakeven returns, we identify much lower Lotto 649 thresholds.



The above Graph LM-GR04 shows the Jackpot level that Lotto 649 must reach for a player to be indifferent to either game.

As shown, players should purchase:

• Atl 49 whenever Lotto 649 is below $9.7M
• BC49 whenever Lotto 649 is below $8.1M
• LQ49 whenever Lotto 649 is below $8.1M
• Ont49 whenever Lotto 649 is below $7.5M
• Wst49 whenever Lotto 649 is below $12.4M

We believe these these breakeven jackpot levels are sufficiently low enough for players to be continually interested in both games.

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What about the MAXMILLIONS Mode?
One of the unique features of Lotto Max is its MAXMILLIONS mode. This kicks in whenever the Jackpot pool exceeds C$50M. When in effect, the Lotto Max jackpot becomes capped at $50M, and numerous MAXMILLIONS drawings will be conducted for a single prize of C$1 million each. This means that if the pool is C$60M, there will be 10 MAXMILLIONS drawings. If the pool is C$100M, there will be 50 MAXMILLIONS drawings.

The advertised importance of this mode is that whenever the jackpot pool exceeds C$50M, there is a possibility of having many C$1 million winners and a large Lotto Max jackpot winner all at once.

But as noted earlier, having more winners does not affect our return calculations.

It does, however, lower the Odds or Changes of winning. But, this change in odds is so small, it can effectively be ignored :

• Jackpot C$10-C$60M: Odds are 19.8031
• Jackpot C$70-C$90M: Odds are 19.8030
• Jackpot C$100-C$110M: Odds are 19.8029

Notice that only the 4th decimal place varies, and that from C$10M to C$100M, your chances of winning any prize increase by only 2/10,000.

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Conclusion

Whether you should buy and play the new Lotto Max lottery depends on your budget and willingness to play.

Since the chances of winning any jackpot prize is extremely small, we believe players should always play the game that promises to offer the fairest return for your hard earned dollar.

The above information provides you with the educational knowledge of making a sound decision. From this, we conclude that:

Canadian Provincial Lotteries offer the best per dollar return,
and
Buy Lotto Max only when jackpots are high!

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

• Canadian Lottery Comparison
• Lotto Max - Complete Odds & Return
• Introducing LOTTO MAX Announcement

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Stay Tuned - Our Lotto Max Analysis to be Published Next Week

Tickets for the new Canadian Lotto Max lottery will go on sale beginning Saturday, September 19th 2009 and the first drawing will be held the following Friday (September 25th).

This new lottery replaces Super 7 which will be retired after the Friday Sept 18 drawing.

Essentially, Lotto Max is a weekly game nearly identical to Super 7. To win, the player must successfully match 7 balls. However, the major differences are that: the number of white balls increased to 49; jackpots begin at C$10 million; tickets cost C$5 for three; the jackpot is capped at C$50M; and above $C50M, additional MAXMILLION C$1 million drawings will be conducted for each million above the C$50M threshold.

In the spirit of offering our players the most comprehensive information, we are preparing a new Blog Post comparing Lotto Max to the old Super 7 and Lotto 649. We believe this is important because the cost of tickets and the chances of actually winning have substantially increased.

While many news releases are currently circulating about this new game, we have found little definitive opinions about whether you should or should not purchase tickets and play it.

We anticipate publishing our analysis by the end of next week so stay tuned!

JL........

Goodbye Super 7, Hello LOTTO MAX

Beginning Saturday, September 19 2009, tickets for the new Canadian multi-provincial game LOTTO MAX will go on sale. The first drawing for this new weekly game will be on Friday, September 25th. And, the minimum jackpot prize is C$10 million, but is capped at C$50 million. Above C$50M, seperate drawings for a single C$1 million prize will be conducted. This feature is called MAXMILLONS, and for every C$1M over C$50M, a seperate drawing will be held. That could be a lot of drawings!

This new game replaces the existing Super 7 game held every Friday night, and it promises to payout bigger prizes.

LOTTO MAX is very similar to Super 7 in that a player must correctly pick 7 white balls to win the jackpot. An eighth bonus ball is also drawn, and used for awarding 2nd (6 white+bonus) and 6th place (3 white+bonus) prizes.

However, bigger prizes come with a price. In LOTTO MAX's case, its C$5 minimum per play. Yes, each player must purchase 3 combinations for C$5 each (which is 2 1/2 times the cost of the Super 7 tickets).

Also, the number of white balls increases from 47 to 49, thus making it a bit harder to win.

As for us, we are busy creating our statistical pages for this new lottery, and beginning to construct histories of the smaller and more affordable individual provincial lotteries (BC 49, Atlantic 49, etc)

Since it is nearly identical to Super 7, we are simply considering it to be a Super 7 format and name changes for analytical purposes.

JL..........

How Lottery Odds Change When Buying Multiple Tickets

Introduction
Over the past several years, I have read many posts on the internet from people who have wondered how their odds of winning the large lottery jackpots improve when they purchase multiple tickets. Most often, the replies stated that you should simply:

Divide the
Number of tickets you purchased for that drawing.
by the
Total number of combinations

Is this correct?
The answer is: Absolutely yes. This is the basic formula for computing the probability.

For example:
If you play Powerball, the chances of your tickets matching the winning Jackpot combination when you buy:

• 1 Ticket, will be: 1 in 146,107,962 or 1 in 146,107,962
• 2 Tickets, will be: 2 in 146,107,962 or 1 in 73,053,981
• 3 Tickets, will be: 3 in 146,107,962 or 1 in 48,702,654
• 4 Tickets, will be: 4 in 146,107,962 or 1 in 36,526,990.5
• 5 Tickets, will be: 5 in 146,107,962 or 1 in 29,221,592.4
• and so on.
  

Similarily, if you play Mega Millions, the chances of your tickets matching the winning Jackpot combination when you buy:

• 1 Ticket, will be: 1 in 175,711,536 or 1 in 175,711,536
• 2 Tickets, will be: 2 in 175,711,536 or 1 in 87,855,768
• 3 Tickets, will be: 3 in 175,711,536 or 1 in 58,570,512
• 4 Tickets, will be: 4 in 175,711,536 or 1 in 43,927,884
• 5 Tickets, will be: 5 in 175,711,536 or 1 in 35,142,307.2
• and so on.
  

Note that because this is a simple division formula, it is mathematically correct to reduce the numerator and denominator to the lowest terms. Whether the terms are reduced or not, the resulting probability value will be identical.

If this is so simple, why do people argue about it?
Because of the definition of the word "Odds". If you visit the AllExperts.com post: Probability & Statistics, you will read that we are in agreement. However, you will note that the article speaks in terms of "Chances" and "Probability", but not "Odds".

The question by Daren Henning in Dr. Math's Powerball Odds When Buying More Tickets, also alludes to this confusion, but the answer is not clarified.

Mr. Henning says that he and his friend are arguing about the odds when buying 10 tickets in a hypothetical 80,000,000 Powerball lottery. The friend says the odds are 10/80,000,000 or 1 in 8,000,000. However, Henning thinks the odds are to 79,999,990 to 1. Dr. Math agrees with the friend and explains why.

To be correct, Henning should have stated that he believed the odds were 10 to 79,999,990. In this case, he too would be correct.

How can they both be correct?
Once again, because of the definition of the word "Odds"
It is context dependent.

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Statistical Definitions
When you buy a Lottery Ticket, you are buying a "chance" to win the jackpot.

In Dictionary.com, chance is defined as:

1. the absence of any cause of events that can be predicted, understood, or controlled: often personified or treated as a positive agency: Chance governs all
2. luck or fortune: a game of chance
3. possibility or probability of anything happening: a fifty-percent chance of success

Measuring Chance
"Chance is measured using either probabilities (a ratio of occurrence to the whole) or odds (a ratio of occurrence to nonoccurrence, or for and against)."

• Probability = events/(events+non-events) values range from 0 to 1
  
• Odds = events/non-events values range from 0 to infinity
  

From sources: Measuring chance and Primer on Probability, Odds and Interpreting their Ratios

Example
As an example, assume that we are rolling a single 6 sided dice.

We wish to measure the chance that a "5" will appear. The probability that a 5 will appear is 1/6, or 0.1666667. Whereas, the odds that a 5 will appear are 1/5, meaning one change for, and 5 against.

Next, let us measure the chance that an even number will appear. The probability that an even number will appear is 3/6, or 0.50. Whereas, the odds that an even number will appear are 3/3 or 1/1 meaning one change for and one against.

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Confusion Abounds
Just looking at the numbers above, one cannot tell if we are viewing an expression of probability or odds. While all these numbers are correct, we need more information in order to interpret their meanings properly.

Returning to Mr. Henning's question about the lottery odds above, both the friend and Dr. Math are asserting the correctness of the probability definition. In this, they are correct, but should have clearly stated that they are speaking of Probability, not Odds.

Whereas, according to the above definitions, Mr. Henning is correct in asserting the odds, because he is referring to the occurrences for verses occurrences against.

---

Resolving the Ambiguity of the Word Odds
We cannot change City Hall. In the Lottery World, the use of the word Odds is often synonymous with Probability or Chances.

If you visit the Minnesota Lottery Figuring the Odds or the Powerball - Prizes and Odds pages, you will see that they incorrectly define your odds in terms of Probability.

Conversely, when you read the Mega Millions How to Play and BCLC How play Lotto 6/49 pages, you will learn that they are correctly presenting your Chances.

In order to resolve the ambiguity of the word Odds, we believe the meaning is "sub-language" dependent.

• Within the Lottery Context, we suggest that Odds be interpreted as Lottery Odds (which is the same as Probability)
• Within the Gambling Context, such as horse racing, we suggest that Odds be interpreted as the defined Odds (Chances For verses Chances Against).
  

The easiest and least confusing thing to remember about Lottery Odds is to:

Always think in terms of Chances.
That way, you can't go wrong!

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To learn more about the Odds / Chances discussions, you can read the following:

• Lottery Post Discussion Thread
• Odds and Probability - Brian Alspach
• Odds Slang for Probability? - Dr Math
• Lottery - Odds of winning (1 ticket and 2 tickets)- Ricci rec.gambling.lottery
• Lottery - Odds of winning (1 ticket and 2 tickets) - Perkis rec.gambling.lottery
• Lotteries: What are the odds?

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Focus for June : Analysis of the Powerball Cash verses Annuity Options

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Analysis of the Canadian Lotteries

Introduction
I have received many e-mails from players in Canada asking if we would offer Lottery Power Picks for the smaller Jackpot Provincial lotteries: Atlantic 49, BC 49, Quebec 49, Ontario 49, Quebec 49, and Western 649. Initially, we felt that these games were insignificant, but after reading one person's comments, we realized that we needed to take a closer look. He had said that even though the Ontario 49 Jackpot was fixed at C$1.0 million, he preferred to play Ontario 49 because it only cost C$0.50.

This made us think. Were these provincial lotteries with smaller jackpots a better or worse value than Lotto 649 and Super 7?

One would normally think that bigger is better. But after conducting this research, we have changed our thinking to:

Bigger is better ONLY WHEN the Jackpots are High.

How would you know which to buy?
If you have an unlimited amount of money and want to win a lottery jackpot, you should buy tickets for every lottery available to you.

But, if you're like most folks on a budget, you'll want to spend your lottery dollars wisely. For this purpose, we have prepared the breakeven return table below to help you decide. Each row indicates when you should buy the provincial lottery instead of Lotto 649 or Super 7.

Table 1: Provincial vs Multi-State Breakeven
Buy		When Lotto 649 is below	When Super 7 is below
	Atlantic 49	C$9.7 M	C$8.4 M
	BC 49	C$8.1 M	C$5.9 M
	Loto-Quebec 49	C$8.1 M	C$5.9 M
	Ontario 49	C$7.5 M	C$5.0 M
	Western 649	C$12.4 M	C$12.4 M

• Buy Atlantic 49:
• When Lotto 649 is below C$9.7 M
• When Super 7 is below C$8.4 M
• Buy BC 49:
• When Lotto 649 is below C$8.1 M
• When Super 7 is below C$5.9 M
• Buy Quebec 49:
• When Lotto 649 is below C$8.1 M
• When Super 7 is below C$5.9 M
• Buy Ontario 49:
• When Lotto 649 is below C$7.5 M
• When Super 7 is below C$5.0 M
• Buy Western 649:
• When Lotto 649 is below C$12.4 M
• When Super 7 is below C$12.4 M

Why is that?
To make the smaller Provincial lotteries attractive to the players, they typically return more of the money received back to players. Thus, when the Lotto 649 and Super 7 jackpots are low, you get more for your money from the provincials.

However, as the Lotto 649 and Super 7 jackpots grow, the money returned back to players also grows. When their returns exceed the fixed returns of the provincials, you should buy the larger mult-states.

Why is it difficult to know which to buy?
It is difficult to know which lottery to buy because everything varies: the ticket price, the odds, the payout, etc. In order to give you an indication of the variety in each of the Canadian lotteries, we have graphed 6 aspects of the games. Looking at these, you can quickly see that without some strict measure, it is difficult to determine which game to play.

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1. Minimum Jackpot Size
Graph CS1 illustrates the minimum jackpots for each of the 7 Canadian lotteries. For Super 7, C$2.5 M is the fixed minimum, while C$3.0 M is the Lotto 649 minimum. Since both of the lotteries are nationwide, their jackpots will grow each time a drawing fails to produce a jackpot winner. Whereas, the provincial lottery jackpots are fixed at: C$1.0 M for the Atlantic 49, Ontario 49, and Western 649; and at C$2.0 M for BC 49 and Quebec 49.

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2. Price per Ticket C$
Ticket prices for each of the lotteries also vary. The most expensive is Lotto 649, which costs C$2.0 per ticket. Next are BC 49 and Quebec 49, at C$1.0 per entry. While Super 7 sells 3 plays for C$2.00, the individual ticket costs C$0.67 each. Lastly, Atlantic 49, Ontario 49, and Western 649 tickets only cost C$0.50 each. Note however that Western 649 requires players to buy 2 games at once.

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3. Number of Tickets for C$2.00
To make these purchases equivalent, let's assume that a player will purchase C$2.00 worth of tickets. For this amount: Lotto 649 players will have 1 chance to win the C$3.0M jackpot; the BC and Quebec 49 players will receive 2 chances to win C$2.0 M; Super 7 players will have 3 chances to win C$2.5 M; and the Atlantic 49, Ontario 49, and Western 649 players will have 4 chances to win C$1.0 M.

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4. Overall Odds of Winning
The overall odds of winning any prize also vary. Super 7 offers the best chances, giving players a 1:17.66 to win something. Super 7 odds are 1.8 times better than Lotto 469, BC 49 and Quebec 49 whose odds are 1:32.31. Further, Super 7 odds are 3.0 times better than the Atlantic, Ontario and Western 49 odds of 53.66.

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5. Average Ticket Payout
Although Super 7 contains more winning tickets, the average ticket payout is C$4.92. Whereas, Lotto 649 tickets average the highest payout of C$20.54 (4.2 times better than Super 7). As for the provincials: Ontario 49 pays C$12.81 per ticket ( 2.6 times Super 7); Atlantic 49 pays C$14.97 (3.0 times); BC and Quebec 49 pay C$16.14 (3.3 times); and Western 649 pays out C$17.54 per ticket (3.6 times more than Super 7).

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6. Total C$ Returned to Players
The total dollars returned to players is displayed as cents per dollar. These indicator is important because it allow us to compare value on an equivalent basis. As shown, Lotto 649 returns the least back to the players, at only C$0.32 per every dollar received. Next comes Super 7 at C$0.42 per dollar, and Ontario 49 at C$0.48/dollar. Both the BC and Quebec 49 give back 1/2 of their take. Atlantic 49 returns C$0.56 to players. And, Western 649 pays out a whopping C$0.65 per dollar received, mor than twice as much as Lotto 649.

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What about Lotto 649 verses Super 7?
Table 2 below provides you with a guideline as to when you should buy Super 7 of Lotto 649. To utilize this information, find out what the current Super 7 jackpot is. Then, look down the left column for this number. When found (or interpreted), read the right most column. If the Lotto 649 jackpot is below the number shown, then buy Super 7 tickets. If it is equal to or greater, then buy Lotto 640 tickets.

Table 2: Super 7 vs Lotto 649 Breakeven
If Super 7 Jackpot is		Then Buy Super 7 whenLotto 649 is below
	C$2.5 M	C$5.8 M
	C$5.0 M	C$7.5 M
	C$10.0 M	C$10.8 M
	C$15.0 M	C$14.1 M
	C$17.0 M	C$15.5 M
	C$20.0 M	C$17.5 M
	C$25.0 M	C$20.8 M
	C$30.0 M	C$24.1 M
	C$40.0 M	C$30.8 M
	C$50.0 M	C$37.5 M

• When the Super 7 Jackpot is C$12.0 million or lower, you should buy Super 7 unless Lotto 649 is greater than shown
• Above the C$12.0 million breakeven cross-over point, buy Super 7 only when its jackpot is higher than the Lotto 649 levels shown.

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Conclusion
As you can see, the decision to buy the Provincial lotteries or the larger multi-territorial national lotteries depends on the current jackpot size and how much money you wish to spend. If you are not on a budget, buy every available lottery. But, if your funds are limited, consult Tables 1 and 2 above to determine which lottery will give you the most for your money.

Don't ignore the Canadian Provincial Lotteries just because the jackpots are low!
They are often a very good value to play.

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

• Canadian Lottery Comparison
• Atlantic 49
• BC 49
• Ontario 49
• Quebec 49
• Western 649

Focus for April: How Your Probability of Winning Changes when you buy Multiple Tickets

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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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