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Discrete Gambling and Stochastic Games

  • Ashok P. Maitra
  • William D. Sudderth

Part of the Applications of Mathematics book series (SMAP, volume 32)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Ashok P. Maitra, William D. Sudderth
    Pages 1-3
  3. Ashok P. Maitra, William D. Sudderth
    Pages 5-22
  4. Ashok P. Maitra, William D. Sudderth
    Pages 23-57
  5. Ashok P. Maitra, William D. Sudderth
    Pages 59-88
  6. Ashok P. Maitra, William D. Sudderth
    Pages 89-111
  7. Ashok P. Maitra, William D. Sudderth
    Pages 113-170
  8. Ashok P. Maitra, William D. Sudderth
    Pages 171-225
  9. Back Matter
    Pages 227-244

About this book

Introduction

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.

Keywords

Martingal Martingale Odds Optional Sampling Theorem probability

Authors and affiliations

  • Ashok P. Maitra
    • 1
  • William D. Sudderth
    • 1
  1. 1.College of Liberal Arts School of StatisticsUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4002-0
  • Copyright Information Springer-Verlag New York 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8467-3
  • Online ISBN 978-1-4612-4002-0
  • Series Print ISSN 0172-4568
  • Buy this book on publisher's site