Discrete Gambling And Stochastic Games

The theory of probability began in the seventeenth century with attempts tocalculate the odds of winning in certain games of change. However it was notuntil the... » 

The theory of probability began in the seventeenth century with attempts tocalculate the odds of winning in certain games of change. However it was notuntil the middle of the twentieth century that mathematicians developed generaltechniques for maximizing the chances of beating a casino or winning against anintelligent opponent. These methods of finding optimal strategies are at theheart of the modern theory of stochastic control and stochastic games. Thismonograph provides an introduction to the ideas of gambling theory andstochastic games. The first chapters introduce the ideas and notation ofgambling theory. Chapters 3 and 4 consider leavable and nonleavableproblems which form the core theory of this subject. Chapters 5 6 and 7 coverstationary strategies approximate gambling problems and twoperson zerosumstochastic games respectively. Throughout the authors have included examplesand there are problem sets at the end of each chapter. «