Probability, Decisions and Games: A Gentle Introduction using RISBN: 9781119302605
240 pages
April 2018

Description
This book introduces the basic concepts of probability, statistics, decision theory, and game theory and presents interesting gaming examples to highlight the practical applications and methodologies. The author uniquely utilizes the mathematical analyses of games of chance to develop an understanding of probability and utility (rational thinking) theories. Based on six years of classtesting, the authors’ approach to games and gambling is accessible for readers with minimal experience. Ranging from simple games to strategic games, this book features a variety of gaming and gambling examples to build a better understanding of quantitative reasoning, and the authors establish fundamental concepts before moving on to more strategic games that illustrate how multiple concepts fit together. Organized into thirteen chapters, this book presents equal coverage on the general mathematical analysis concepts found in a wide variety of games as well as the specific theories and problems associated with wellknown casino games. Covering zerosum games, nonzerosum games, and sequential games, the authors introduce ideas such as mathematical expectation and variance, bias, combinatorial calculus, conditional probability and Bayes Theorem, Bernoulli trials, and the Binomial distribution. The first two chapters feature an introductory discussion of utility and probability theory in finite and discrete spaces. Subsequent chapters utilize popular casino games to illustrate the practical probabilistic methodologies: roulette, which is one of the simplest casino games to play and analyze, is used to illustrate basic concepts in probability such as expectations; lotto is used to motivate counting rules and the notions of permutations and combinatorial numbers that allow for probability computation in large equiprobable spaces; craps and blackjack are used to illustrate and develop conditional probabilities; and poker illustrates how a combination of theories and techniques can be used together. Finally, the book concludes with discussions on game theory and strategic games. This book also features computer simulations using Microsoft Office® Excel® spreadsheets throughout in order to illustrate complex concepts and help readers calculate presented problems.
Table of Contents
Preface
Dedication
Chapter 1: An introduction to probability
1.1 What is probability?
1.2 Odds and probabilities
1.3 Equiprobable outcome spaces and De Mere's problem
1.4 Probabilities for compound events
1.5 Exercises
Chapter 2: Expectations and fair values 15
2.1 Random variables
2.2 Expected values
2.3 Fair value of a bet
2.4 Comparing wagers
2.5 Utility functions and rational choice theory
2.6 Limitations of rational choice theory
2.7 Exercises
Chapter 3: Roulette
3.1 Rules and bets
3.2 Combining bets
3.3 Biased wheels
3.4 Exercises
Chapter 4: Lotto and combinatorial numbers
4.1 Rules and bets
4.2 Sharing profits: De Mere's second problem
4.3 Exercises
Chapter 5: Conditional probabilities
5.1 The Monty Hall paradox
5.2 Conditional probabilities
5.3 Independent events
5.4 Bayes Theorem
5.5 Exercises
Chapter 6: Craps
6.1 Rules and bets
6.2 Exercises
Chapter 7: Roulette revisited
7.1 Gambling systems
7.2 You are a big winner!
7.3 How long will my money last?
7.4 Is this wheel biased?
7.5 Bernoulli trials
7.6 Exercises
Chapter 8: Blackjack
8.1 Rules and bets
8.2 Basic strategy in Blackjack
8.3 A gambling system that works: card counting
8.4 Exercises
Chapter 9: Poker
9.1 Basic rules
9.2 Variants of poker
9.3 Additional rules
9.4 Probabilities of hands in draw poker
9.5 Probabilities of hands in Texas hold'em
9.6 Exercises
Chapter 10: Strategic zerosum games
10.1 Games with dominant strategies
10.2 Dominant and dominating strategies
10.3 General solutions for two person zerosum games
10.4 Exercises
Chapter 11: Mixed strategies in zerosum games
11.1 Finding mixedstrategy equilibria
11.2 Mixed strategy equilibria in sports
11.3 Bluffing as a strategic game
11.4 Exercises
Chapter 12: Nonzerosum games
12.1 The prisoner's dilemma
12.2 The impact of communication and agreements
12.3 Which equilibrium?
12.4 Asymmetric games
12.5 Exercises
Chapter 13: Sequential games
13.1 The centipede game
13.2 Tictactoe
13.3 The game of Nim
13.4 Can sequential games be fun?
13.5 The diplomacy game
13.6 Exercises
Appendix: A brief introduction to R
A.1 Installing R
A.2 Simple arithmetic
A.3 Variables
A.4 Vectors
A.5 Matrices
A.6 Logical objects and operations
A.7 Character objects
A.8 Plots
A.9 Iterators
A.10 Selection and forking
A.11 Other things to keep in mind
Index