Friday, September 11, 2009

Lotto Max Analysis - When to Play Guide

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.

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.

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

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.

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)

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.

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.

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.


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,

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.

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  1. I recently came accross your blog and have been reading along. I thought I would leave my first comment. I dont know what to say except that I have enjoyed reading. Nice blog. I will keep visiting this blog very often.



  2. "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 Max."

    This paragraph needs changing ... it currently reads as a "heads I win, tails you lose" sentence. In both situations you've said to play Lotto Max.

    Also, the graph isn't the most intuitive.

    Look forward to the corrections.

  3. Hey Kevin,

    Thanks for spotting this TYPO, and letting us know. I have revised the text to be correct!


  4. I was searching for information on the new Lottomax on Google and did not expect to find this wealth of information from your site. It was definitely informative and a great read.



  5. Alan,

    Your comments and feedback are truly appreciated. Hope this site's information helps.

    And, please feel welcome to visit all of our sites often. Who knows, maybe one of us will win!


  6. Hi John,

    There’s a promo in March 2010 where if you buy five Lotto Max boards, you get five free Encore with it (so a $5 value) … just wondering if you could redo your “When to buy Lotto Max?” calculations taking this new set of circumstances into account.


  7. Just read your comment Richard regarding the promotion.

    I'll look into it the next couple of days & write a comment back.


  8. Richard,

    I took a look at the OLC offer to give 5 free Encore tickets if you buy 5 Lotto Max.

    Creating an analysis of this is too complicated for the short term, but my recommendations are:

    1. If you can afford to spend the C$25 for the 5 Lotto Max, then you should take advantage and do it, since its "Free Money".

    2. However, I wouldn't recommend spending the extra C$1 for Encore because the probability of winning is very slim.

    Remember, you have to buy Lotto Max on Thursdays during March 2010 to get this offer.

    I will write a more detailed analysis of Encore in the following months explaining why I would stay away from this game.


  9. Can you elaborate on how the odds in Maxmillions mode are calculated (or provide a link) The week there are 45 Maxmillions so intuitively the odds should increase reasonably if one ticket is good for 46 separate draws... certainly the public is in a lotto frenzie.

  10. Anonymous,

    Thanks for your comment. We've written a new post on this Blog indicating that this is the time to buy Lotto Max. (I hope this is what you're looking for).

    Note that adding 45 more winners to to total winning pool does not change the total overall statistics of winning any single prize.

    However, it is significant that 1 in every 1.5-2.0 million combinations has the chance to produce a new millionaire.

    More importantly, this means that one in 1/2 million Canadians may possibly become rich after the Friday night Lotto Max drawing.

    Good Luck,



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