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 developed 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 shastic control and shastic 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 Shastic Processes by Dubins and Savage (1965) uses gambling terminology and examples to develop an elegant, deep, and quite general theory of discrete-time shastic control. A gambler "controls" the shastic process of his or her successive fortunes by choosing which games to play and what bets to make.
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 developed 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 shastic control and shastic 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 Shastic Processes by Dubins and Savage (1965) uses gambling terminology and examples to develop an elegant, deep, and quite general theory of discrete-time shastic control. A gambler "controls" the shastic process of his or her successive fortunes by choosing which games to play and what bets to make.
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