Discrete Gambling and Stochastic Games

1. Front Matter

   Pages i-xi

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2. Introduction

   • Ashok P. Maitra, William D. Sudderth

   Pages 1-3

3. Gambling Houses and the Conservation of Fairness

   • Ashok P. Maitra, William D. Sudderth

   Pages 5-22

4. Leavable Gambling Problems

   • Ashok P. Maitra, William D. Sudderth

   Pages 23-57

5. Nonleavable Gambling Problems

   • Ashok P. Maitra, William D. Sudderth

   Pages 59-88

6. Stationary Families of Strategies

   • Ashok P. Maitra, William D. Sudderth

   Pages 89-111

7. Approximation Theorems

   • Ashok P. Maitra, William D. Sudderth

   Pages 113-170

8. Stochastic Games

   • Ashok P. Maitra, William D. Sudderth

   Pages 171-225

9. Back Matter

   Pages 227-244

   PDF

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.

• Martingal
• Martingale
• Odds
• Optional Sampling Theorem
• probability

• College of Liberal Arts School of Statistics, University of Minnesota, Minneapolis, USA

  Ashok P. Maitra, William D. Sudderth

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