Probability, Decisions and Games: A Gentle Introduction using R
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 well-known casino games. The authors cover zero-sum games, non-zero-sum 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 class-tested 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 well-known simple games, such as casino games, zero-sum games, non-zero-sum 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.
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
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
Chapter 3: Roulette
3.1 Rules and bets
3.2 Combining bets
3.3 Biased wheels
Chapter 4: Lotto and combinatorial numbers
4.1 Rules and bets
4.2 Sharing profits: De Mere's second problem
Chapter 5: Conditional probabilities
5.1 The Monty Hall paradox
5.2 Conditional probabilities
5.3 Independent events
5.4 Bayes Theorem
Chapter 6: Craps
6.1 Rules and bets
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
Chapter 8: Blackjack
8.1 Rules and bets
8.2 Basic strategy in Blackjack
8.3 A gambling system that works: card counting
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
Chapter 10: Strategic zero-sum games
10.1 Games with dominant strategies
10.2 Dominant and dominating strategies
10.3 General solutions for two person zero-sum games
Chapter 11: Mixed strategies in zero-sum games
11.1 Finding mixed-strategy equilibria
11.2 Mixed strategy equilibria in sports
11.3 Bluffing as a strategic game
Chapter 12: Non-zero-sum games
12.1 The prisoner's dilemma
12.2 The impact of communication and agreements
12.3 Which equilibrium?
12.4 Asymmetric games
Chapter 13: Sequential games
13.1 The centipede game
13.3 The game of Nim
13.4 Can sequential games be fun?
13.5 The diplomacy game
Appendix: A brief introduction to R
A.1 Installing R
A.2 Simple arithmetic
A.6 Logical objects and operations
A.7 Character objects
A.10 Selection and forking
A.11 Other things to keep in mind
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.