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

Description
Introduces the fundamentals of probability, statistics, decision theory, and game theory, and features interesting examples of games of chance to illustrate the presented mathematical concepts
Ranging from simple games to strategic games, Probability, Decisions and Games features a variety of gaming and gambling examples to build a better understanding of quantitative reasoning. 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. The authors cover zerosum games, nonzerosum games, and sequential games in order to introduce ideas such as mathematical expectation and variance, bias, combinatorial calculus, conditional probability and Bayes Theorem, Bernoulli trials, and the Binomial distribution.
This book presents interesting gaming examples to highlight the practical applications and methodologies behind the basic concepts of probability, statistics, decision theory, and game theory. The first two chapters of Probability, Decisions and Games: A Gentle Introduction using R 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. Finally, the book concludes with discussions on game theory and strategic games.
 Features introductory coverage of probability, statistics, decision theory, game theory, and mathematical analysis and has been classtested at University of California, Santa Cruz for the past six years
 Illustrates mathematical concepts through interesting and fun examples using five popular casino games: roulette, lotto, craps, blackjack, and poker
 Provides a variety of gaming and gambling examples of wellknown simple games, such as casino games, zerosum games, nonzerosum games, and sequential games, in order to help readers better understand quantitative reasoning
 Features computer simulations using R throughout in order to illustrate complex concepts and help readers calculate the presented problems
 Contains exercises throughout and approaches games and gambling at a level that is accessible for readers with minimal experience
 Presents a unique approach by presenting simple games first to demonstrate individual concepts before moving on to more strategic games that illustrate how these concepts work together
Probability, Decisions and Games: A Gentle Introduction using R is a unique and helpful textbook for undergraduate courses on statistical reasoning, introduction to probability, statistical literacy, and quantitative reasoning for students from a variety of disciplines.
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
Author Information
Abel Rodriguez, PhD, is Professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (UCSC). The author of 40 journal articles, his research interests include Bayesian nonparametric methods, machine learning, spatial temporal models, network models, and extreme value theory.
Bruno Mendes, PhD, is Lecturer in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz.