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Discrete Gambling and Stochastic Games

Discrete Gambling and Stochastic Games (Stochastic Modelling and Applied Probability) by Ashok P. Maitra
English | Sep 17, 2011 | ISBN: 1461284678 | 244 Pages | PDF | 16 MB

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 deВ­ veloped general techniques for maximizing the chances of beating a casino or winning against an intelligent opponent. These methods of finding opВ­ 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 termiВ­ nology and examples to develop an elegant, deep, and quite general theory of discrete-time stochastic control. A gambler "controls" the stochastic proВ­ cess of his or her successive fortunes by choosing which games to play and what bets to make.