Thursday, June 24, 2010

LottoMAX Lottery Update: Random Number Theory


I posted earlier about duplicate numbers on this LottoMAX quick-pick ticket:



Full disclosure: I'm actually a member of Mensa Canada and I fully understand random number generation and lottery systems. But when I saw the numbers on that ticket I couldn't help writing a campy blog entry about the coincidence.

LottoMAX headquarters responded graciously:
...Quick Pick selections are chosen by a random generator inside the retail terminal, which mixes the numbers available for the game and prints the selections required. With random generation it is not possible to eliminate the numbers previously printed, as this would diminish the randomness of the selections. It is important to remember that every combination of numbers has the exact same chance of being drawn.

I hope this information is helpful. If you have any further questions, please e-mail us again or call our OLG Support Centre toll-free at 1-800-387-0098.

Regards,

Kestine
Kestine is 100% correct. Every combination of numbers has the exact same chance of being drawn. Or quick-picked by the random number engine inside every lottery terminal.

The odds of any 7 number (1-49) set appearing randomly are generated thus:

1/49 × 1/48 × 1/47 × 1/46 × 1/45 × 1/44 × 1/43 = 1/432938943360

But hold on! Since the numbers are generated in any order, the 7! factorial comes into play, reducing the odds of any possible LottoMAX number set to 1/85900584.

The real chances of winning with any one number set are 1 in 8.6 million.

However, because LottoMAX tickets sell for three plays for $5, each player's chances of winning are actually closer to 1 in 2.86 million for every $5 played.

Good luck!

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