GAMBLING: An interesting problem

Penney’s Game
6 March 2010
By Donald Catlin

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Every now and then in this column I like to look at so-called proposition bets (for example see my archived article An Earful of Cider that appeared in December of 1999). These are wagers that sound like either a sure thing, or at worst a fair bet, and are anything but. A dandy example of this is Penney’s Game named after its inventor Walter Penney (Journal of Recreational Mathematics, October 1969, p. 241). I wish to thank my friend The Midnight Skulker for bringing this game to my attention.

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I don’t know how this applies to gambling in that I don’t know where you can get such a bet in a casino.

That being said, the article’s findings (i.e., Player B has an advantage) were surprising.

Given that playing slots is like being Player B (I.e., the Casino is Player A and sets the terms of the wager), I’d like an advantage.

Last time I heard of a player getting an advantage was when the Canadian casino kept turning off the Keno machine allowing the same results to come day after day. Wonder if that smart fellow, who won a lot of money, was allowed to keep his “winnings”. (Hope so!)

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