Abstract: |
It is widely assumed that the instant-scratch lottery games run by governments throughout the world are ?fair? in the sense that any person buying a ticket has the same odds of winning as any other person. Or, put differently, the public generally believes that there is no way to increase one?s chances of winning above the global winning probabilities for the entire population of tickets.
In 2003, having never played any instant scratch game before in my life, I was given an instant scratch ticket as a joke gift. It turned out to be a winner and that happy coincidence engaged my curiosity. Specifically, I wondered how one would write an algorithm for generating the tickets under the constraint that the prize payout must be exactly controlled. With my background in multi-point simulation, the problem was familiar and I quickly developed the outline of an algorithm, and then promptly forgot about the problem. But, later, I realized that my first attempt at an algorithm was flawed because it would leave on the face of each ticket a spatial pattern that could be used to separate winners from losers. After checking a few more tickets, I realized that the lottery corporation had used essentially the same algorithm and that I could separate winners from losers with a success rate exceeding 90%.
I reported the problem to the lottery corporation, who pulled that particular game off the market, the first time they have ever done so because of an identified flaw in the game. While the lottery corporation acknowledges the flaw in that one game, they continue to insist that it was a fluke and that there is no similar problem with other games. I take a different view; specifically, I feel that many instant scratch games still on the market can be exploited using spatial data analysis and prediction tools that are familiar to geostatisticians: conditional spatial probabilities, Bayes? Theorem and conditional simulation.
This paper presents the case study details of the procedure used to break the Ontario Lottery?s TicTacToe game in 2003, describes how Bayes? Theorem can be used to produce a general approach to a wide variety of instant scratch games, and shows how conditional simulation can be used as a supplementary tool for increasing one?s odds of winning in some instant scratch games. |
