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Discrete Gambling and Stochastic Games

By: Ashok P. Maitra,William D. Sudderth

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Discrete Gambling and Stochastic Games

By: Ashok P. Maitra,William D. Sudderth

The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. However, it was not until the middle of the twentieth century that mathematicians de veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding op timal strategies for a player are at the heart of the modern theories of stochastic control and stochastic games. There are numerous applications to engineering and the social sciences, but the liveliest intuition still comes from gambling. The now classic work How to Gamble If You Must: Inequalities for Stochastic Processes by Dubins and Savage (1965) uses gambling termi nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler "controls" the stochastic pro cess of his or her successive fortunes by choosing which games to play and what bets to make.

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Page Count

249

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461240026

ISBN 13

9781461240020

How to Gamble If You Must

Inequalities for Stochastic Processes

By: Lester E. Dubins,Leonard J. Savage,William Sudderth,David Gilat

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How to Gamble If You Must

Inequalities for Stochastic Processes

By: Lester E. Dubins,Leonard J. Savage,William Sudderth,David Gilat

This classic of advanced statistics is geared toward graduate-level readers and uses the concepts of gambling to develop important ideas in probability theory. The authors have distilled the essence of many years' research into a dozen concise chapters. "Strongly recommended" by the Journal of the American Statistical Association upon its initial publication, this revised and updated edition features contributions from two well-known statisticians that include a new Preface, updated references, and findings from recent research. 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. Dover (2014) revised and updated republication of the 1976 Dover edition entitled Inequalities for Stochastic Processes. See every Dover book in print at www.doverpublications.com

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Page Count

307

Publisher

Courier Corporation

Published Date

ISBN 10

0486780643

ISBN 13

9780486780641