Probability, Decisions and Games

ABEL RODRÍGUEZ, PHD, is Professor in the Department of Applied Mathematics and Statistics at the University of California, Santa Cruz (UCSC), CA, USA. 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, CA, USA.

• Preface xiAcknowledgments xvAbout the Companion Website xvii1 An Introduction to Probability 11.1 Whati s Probability? 11.2 Odds and Probabilities 51.3 Equiprobable Outcome Spaces and De Méré’s Problem 61.4 Probabilities for Compound Events 91.5 Exercises 122 Expectations and Fair Values 152.1 Random Variables 152.2 Expected Values 162.3 Fair Value of a Bet 192.4 Comparing Wagers 192.5 Utility Functions and Rational Choice Theory 232.6 Limitations of Rational Choice Theory 242.7 Exercises 263 Roulette 313.1 Rules and Bets 313.2 Combining Bets 373.3 Biased Wheels 383.4 Exercises 424 Lotto and Combinatorial Numbers 454.1 Rules and Bets 454.1.1 The Colorado Lotto 454.1.2 The California Superlotto 514.2 Sharing Profits: De Méré’s Second Problem 524.3 Exercises 555 The Monty Hall Paradox and Conditional Probabilities 595.1 The Monty Hall Paradox 595.2 Conditional Probabilities 625.3 Independent Events 655.4 Bayes Theorem 665.5 Exercises 706 Craps 756.1 Rules and Bets 756.1.1 The Pass Line Bet 756.1.2 The Don’t Pass Line Bet 846.1.3 The Come and Don’t Come Bets 856.1.4 Side Bets 856.2 Exercises 867 Roulette Revisited 897.1 Gambling Systems 897.1.1 Martingale Doubling Systems 897.1.2 The Labouchère System 927.1.3 D’Alembert Systems 947.2 You are a Big Winner! 967.3 How Long will My Money Last? 977.4 Is This Wheel Biased? 1017.5 Bernoulli Trials 1027.6 Exercises 1038 Blackjack 1078.1 Rules and Bets 1078.2 Basic Strategy in Blackjack 1098.3 A Gambling System that Works: Card Counting 1148.4 Exercises 1179 Poker 1219.1 Basic Rules 1219.2 Variants of Poker 1239.3 Additional Rules 1249.4 Probabilities of Hands in Draw Poker 1249.4.1 The Effect of Card Substitutions 1279.5 Probabilities of Hands in Texas Hold’em 1289.6 Exercises 13210 Strategic Zero-Sum Games with Perfect Information 13510.1 Games with Dominant Strategies 13510.2 Solving Games with Dominant and Dominated Strategies 13910.3 General Solutions for Two Person Zero-Sum Games 14310.4 Exercises 14411 Rock–Paper–Scissors: Mixed Strategies in Zero-Sum Games 14711.1 Finding Mixed-Strategy Equilibria 14811.2 Mixed Strategy Equilibria in Sports 15211.3 Bluffing as a Strategic Game with a Mixed-Strategy Equilibrium 15311.4 Exercises 15912 The Prisoner’s Dilemma and Other Strategic Non-zero-sum Games 16112.1 The Prisoner’s Dilemma 16112.2 The Impact of Communication and Agreements 16212.3 Which Equilibrium? 16412.4 Asymmetric Games 16812.5 Exercises 17113 Tic-Tac-Toe and Other Sequential Games of Perfect Information 17513.1 The Centipede Game 17513.2 Tic-Tac-Toe 17813.3 The Game of Nim and the First- and Second-Mover Advantages 18113.4 Can Sequential Games be Fun? 18413.5 The Diplomacy Game 18413.6 Exercises 187A A Brief Introduction to R 191A. 1 Installing R 191A. 2 Simple Arithmetic 192A. 3 Variables 194A. 4 Vectors 195A. 5 Matrices 199A. 6 Logical Objects and Operations 201A. 7 Character Objects 204A. 8 Plots 205A.9 Iterators 208A.10 Selection and Forking 211A.11 Other Things to Keep in Mind 211Index 213

Select Guide Rating