Discrete Gambling And Stochastic Games

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Discrete Gambling And Stochastic Games

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Author : Ashok P. Maitra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Discrete Gambling And Stochastic Games written by Ashok P. Maitra and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Approximation Theorems For Gambling Problems And Stochastic Games

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Author : A. Maitra
language : en
Publisher:
Release Date : 1991

Approximation Theorems For Gambling Problems And Stochastic Games written by A. Maitra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.

Noncooperative And Dominant Player Solutions In Discrete Dynamic Stochastic Games

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Author : Finn Kydland
language : en
Publisher:
Release Date : 1974

Noncooperative And Dominant Player Solutions In Discrete Dynamic Stochastic Games written by Finn Kydland and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.

Probability Guide To Gambling

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Author : Catalin Barboianu
language : en
Publisher: INFAROM Publishing
Release Date : 2006

Probability Guide To Gambling written by Catalin Barboianu and has been published by INFAROM Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Games & Activities categories.

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability (definitions, properties, theorems and calculus formulas), combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the "Guide to Numerical Results" to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled "The Mathematics of Games of Chance" presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game's section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold'em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one (like many other titles published on this subject), but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.

Problems In Two Person Zero Sum Stochastic Games

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Author : Piercesare Secchi
language : en
Publisher:
Release Date : 1995

Problems In Two Person Zero Sum Stochastic Games written by Piercesare Secchi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.

How To Gamble If You Must

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Author : Lester E. Dubins
language : en
Publisher: Courier Corporation
Release Date : 2014-08-20

How To Gamble If You Must written by Lester E. Dubins and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-20 with Mathematics categories.

This classic of advanced statistics is geared toward graduate-level readers and uses the concepts of gambling to develop important ideas in probability theory. The authors have distilled the essence of many years' research into a dozen concise chapters. "Strongly recommended" by the Journal of the American Statistical Association upon its initial publication, this revised and updated edition features contributions from two well-known statisticians that include a new Preface, updated references, and findings from recent research. Following an introductory chapter, the book formulates the gambler's problem and discusses gambling strategies. Succeeding chapters explore the properties associated with casinos and certain measures of subfairness. Concluding chapters relate the scope of the gambler's problems to more general mathematical ideas, including dynamic programming, Bayesian statistics, and stochastic processes. Dover (2014) revised and updated republication of the 1976 Dover edition entitled Inequalities for Stochastic Processes. See every Dover book in print at www.doverpublications.com

Handbook Of Markov Decision Processes

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Author : Eugene A. Feinberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Handbook Of Markov Decision Processes written by Eugene A. Feinberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.

Eugene A. Feinberg Adam Shwartz This volume deals with the theory of Markov Decision Processes (MDPs) and their applications. Each chapter was written by a leading expert in the re spective area. The papers cover major research areas and methodologies, and discuss open questions and future research directions. The papers can be read independently, with the basic notation and concepts ofSection 1.2. Most chap ters should be accessible by graduate or advanced undergraduate students in fields of operations research, electrical engineering, and computer science. 1.1 AN OVERVIEW OF MARKOV DECISION PROCESSES The theory of Markov Decision Processes-also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming-studiessequential optimization ofdiscrete time stochastic systems. The basic object is a discrete-time stochas tic system whose transition mechanism can be controlled over time. Each control policy defines the stochastic process and values of objective functions associated with this process. The goal is to select a "good" control policy. In real life, decisions that humans and computers make on all levels usually have two types ofimpacts: (i) they cost orsavetime, money, or other resources, or they bring revenues, as well as (ii) they have an impact on the future, by influencing the dynamics. In many situations, decisions with the largest immediate profit may not be good in view offuture events. MDPs model this paradigm and provide results on the structure and existence of good policies and on methods for their calculation.

Two Scale Stochastic Systems

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Author : Yuri Kabanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Two Scale Stochastic Systems written by Yuri Kabanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.

Stochastic Networks And Queues

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Author : Philippe Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Stochastic Networks And Queues written by Philippe Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks. In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.

Stochastic Simulation Algorithms And Analysis

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Author : Søren Asmussen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-14

Stochastic Simulation Algorithms And Analysis written by Søren Asmussen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-14 with Mathematics categories.

Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods; the second half discusses model-specific algorithms. Exercises and illustrations are included.