Probability, Decisions and Games, First Edition, A Gentle Introduction using R by Rodr, Abel -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Dedication Table of Contents Preface

Why Gambling and Gaming? Using this Book

Acknowledgments About the Companion Website Chapter 1: An Introduction to Probability

1.1 What is Probability? 1.2 Odds and Probabilities 1.3 Equiprobable Outcome Spaces and De Méré's Problem 1.4 Probabilities for Compound Events 1.5 Exercises

Chapter 2: Expectations and Fair Values

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 Méré's Second Problem 4.3 Exercises

Chapter 5: The Monty Hall Paradox and 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 Zero-Sum Games with Perfect Information

10.1 Games with Dominant Strategies 10.2 Solving Games with Dominant and Dominated Strategies 10.3 General Solutions for Two Person Zero-Sum Games 10.4 Exercises

Chapter 11: Rock–Paper–Scissors: 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 with a Mixed-Strategy Equilibrium 11.4 Exercises

Chapter 12: The Prisoner's Dilemma and Other Strategic 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 12.5 Exercises

Chapter 13: Tic-Tac-Toe and Other Sequential Games of Perfect Information

13.1 The Centipede Game 13.2 Tic-Tac-Toe 13.3 The Game of Nim and the First- and Second-Mover Advantages 13.4 Can Sequential Games be Fun? 13.5 The Diplomacy Game 13.6 Exercises

Appendix A: 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

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