A Winning Strategy for Roulette

We examine the statistical problem of computing a favorable betting strategy for the game of roulette with an unbalanced wheel. Using negative average expected log capital after n plays for loss function, we show that the Bayes strategy for a Dirichlet prior is asymptotically optimal. We simulate to illustrate the behavior of the strategy for a biased favorable wheel and an unbiased unfavorable wheel. 1 Introduction and Notation. Consider the problem of betting on a roulette game with the possibility of an unknown favorable bet due to wheel imbalance. Wilson (1965), presents a nice discussion of the problem with anecdotes about groups exploiting such imbalance to make money and giving data on his own experiences. More recently, Barnhart (1992) gives interesting stories about large casino wins. Ethier (1982), considers the related problem of hypothesis testing for favorable numbers. Of more direct interest to the gambler, is the problem of determining an optimal betting strategy to max..