02 February 2011

How to win the Ontario lottery's tic-tac-toe game

Jonah Lehrer writes for Wired on breaking a scratch-off game in the Ontario lottery. In 2003, Mohan Srivastava, a geostatistician, figured out a way to crack a tic-tac-toe game that the Ontario lottery was running at the time. In this game, you're given a set of eight three-by-three grids with numbers between one and thirty-nine on them (seventy-two numbers in total) -- these are visible to you when you buy the tickets. After buying the ticket, you then scratch off a set of "your numbers"; if three of these numbers appear in a row in one of the grids, in tic-tac-toe fashion, you win. Since there are 72 numbers on the ticket and they are between 1 and 39, there is much repetition. It turned out that if a ticket contained three non-repeated numbers in a row it was very likely to be a winner.

The article doesn't say how the tickets are turned out this way, though; what sort of algorithm could produce this behavior? But for Srivastava's purpose of demonstrating that it's possible to tell winning tickets from losing tickets with high probability, this was not necessary. Srivastava also points out that this isn't worth it as a way to make money, unless possibly if you could hypothetically get your hands on a pile of tickets, go through them at home, and return the losing ones to the store.

(I learned about this from metafilter. The commenters there, a usually reliable bunch, seem to be split on whether you could return the losing tickets or not.)

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