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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