The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of change. 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 optimal strategies are at the heart of the modern theory of stochastic control and stochastic games. This monograph provides an introduction to the ideas of gambling theory and stochastic games. The first chapters introduce the ideas and notation of gambling theory. Chapters 3 and 4 consider "leavable" and "nonleavable" problems which form the core theory of this subject. Chapters 5, 6, and 7 cover stationary strategies, approximate gambling problems, and two-person zero-sum stochastic games respectively. Throughout, the authors have included examples and there are problem sets at the end of each chapter.
Discrete Gambling and Stochastic Games
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2 of 2 people found the following review helpful:
3.0 out of 5 stars
not the best book, I ever read...,
By PST "A Reader from Germany" (Eislingen Deutschland) - See all my reviews
This review is from: Discrete Gambling and Stochastic Games (Stochastic Modelling and Applied Probability) (Hardcover)
Unfortunately, stochastic games constitute only one chapter out of seven.The mathematical prerequisites are modest for the most part, except for chapter 6, and for the use of transfinite induction throughout the book. Chapter 6 somehow seems out of the mainstream of the book, I never fully understood, why it was included (it is also the longest chapter). The numerous examples mostly show, why some technical prerequisite in a theorem is necessary, by providing an artifical counterexample. They almost never give "practical" aplications of the subject matter. There are a few ( I counted about 20) typos, mostly harmless. Overall, I expected a bit more out of this book.
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Inside This Book
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First Sentence:
The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
optimal stationary family, stop rule induction, nonleavable gambling problem, optimal stationary families, capacitability theorem, saturated house, optimal return function, stationary plans, randomized action, optimal stopping theory, equalizing strategies, uncountable state spaces, timid play, optional sampling theorem, gambling theory, optimality equation, stochastic games, composition closure, initial gamble, history trick, conditioning formula, measurable problems, stop rules, matrix game, stationary strategy Key Phrases - Capitalized Phrases (CAPs): (learn more)
König's Lemma, Choquet's Capacitability Theorem, Good Strategies New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The theory of probability began in the seventeenth century with attempts to calculate the odds of winning in certain games of chance. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
optimal stationary family, stop rule induction, nonleavable gambling problem, optimal stationary families, capacitability theorem, saturated house, optimal return function, stationary plans, randomized action, optimal stopping theory, equalizing strategies, uncountable state spaces, timid play, optional sampling theorem, gambling theory, optimality equation, stochastic games, composition closure, initial gamble, history trick, conditioning formula, measurable problems, stop rules, matrix game, stationary strategy Key Phrases - Capitalized Phrases (CAPs): (learn more)
König's Lemma, Choquet's Capacitability Theorem, Good Strategies New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 53
books:
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42
books
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- Contributions to the Theory of Games, Vol. III (Annals of Mathematics Studies) by Melvin Dresher in Back Matter (1), Back Matter (2), and Back Matter (3)
- Stochastic Integration and Differential Equations by Philip E. Protter in Front Matter
- Provability, Computability and Reflection, Volume 100 (Studies in Logic and the Foundations of Mathematics) by Lev D. Beklemishev in Back Matter
- Deterministic and Stochastic Optimal Control (Stochastic Modelling and Applied Probability) (v. 1) by Wendell H. Fleming in Front Matter
- Difference Methods and Their Extrapolations (Stochastic Modelling and Applied Probability) by G.I. Marchuk in Front Matter
See all 53 books this book cites
- Stochastic Games and Applications (NATO Science Series C: (closed)) by Abraham Neyman on page 35, page 91, and page 365
- A First Course on Zero Sum Repeated Games by Sylvain Sorin in Front Matter, and Back Matter
- Advances in Dynamic Games and Applications (Annals of the International Society of Dynamic Games) by Jerzy A. Filar on page 300, and page 322
- Stochastic and Differential Games: Theory and Numerical Methods (Annals of the International Society of Dynamic Games) by Martino Bardi on page 269, and page 340
- Stochastic Networks and Queues (Stochastic Modelling and Applied Probability) by Philippe Robert in Front Matter
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