Jan

15

How to Gamble If You Must: Inequalities for Stochastic Processes

This classic of advanced statistics is geared toward graduate-level readers and uses the concepts of gambling to develop important ideas in probability theory…. Following an introductory chapter, the book formulates the gambler's problem and discusses gambling strategies. Succeeding chapters explore the properties associated with casinos and certain measures of subfairness. Concluding chapters relate the scope of the gambler's problems to more general mathematical ideas, including dynamic programming, Bayesian statistics, and stochastic processes.

And a more recent paper:

How to Gamble If You Must
Kyle Siegrist, Department of Mathematical Sciences, University of Alabama - Huntsville

In red and black, a player bets, at even stakes, on a sequence of independent games with success probability p, until she either reaches a fixed goal or is ruined. In this article we explore two strategies: timid play in which the gambler makes the minimum bet on each game, and bold play in which she bets, on each game, her entire fortune or the amount needed to reach the target (whichever is smaller). We study the success probability (the probability of reaching the target) and the expected number of games played, as functions of the initial fortune. The mathematical analysis of bold play leads to some exotic and beautiful results and unexpected connections with dynamical systems. Our exposition (and the title of the article) are based on the classic book Inequalities for Stochastic Processes; How to Gamble if You Must, by Lester E. Dubbins and Leonard J. Savage.

Jeff Watson comments:

Only play cards with suckers, and never try to fill an inside straight. Never sit in a poker game with a guy named Doc. Never lay the points, stay away from sports betting altogether, never be the bank in a casino baccarat style game. Stay away from slots, casino pit games, you will get ground down by the vig.

There are only two bets I can afford in a casino. One is betting the pass/no pass line in craps, the vig on the pass is 1.414% and 1.36% on the no pass. Plus you can get bets behind the line. The other is the banker bet in baccarat where the house has a 1.06% edge. Even with the commission, it’s a good bet. Still, no matter what, play the game long enough and the vig will kill you.

The banker bet can be real good. Playing for an entire session as banker can cause one the embarrassment of losing everything then having the game boss ask very politely, “How do you plan to settle the commission?”


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