游戏和博彩中的数学

Preface to the First Edition Preface to the Second Edition 1 The Phenomenon of Gambling 1．1 A selective history 1．2 The gamblerin fact and fiction 2 Finite Probabilities and Great Expectations 2．1 The probability concept and its origins 2．2 Dice，cards，and probabilities 2．3 Roulette，probability and odds 2．4 Compound probabilities： The rules of the game 2．5 Mathematical expectation and its application 2．6 Exercises 3 Backgammon and Other Dice Diversions 3．1 Backgammon oversimplified 3．2 Rolling spots and hitting blots 3．3 Entering and bearing off 3．4 The doubling cube 3．5 Craps 3．6 Chuck-a-Luck 3．7 Exercises 4 Permutations，Combinations，and Applications 4．1 Careful counting： Is order important? 4．2 Factorials and other notation 4．3 Probabilities in poker 4．4 Betting in poker： A simple model 4．5 Distributions in bridge 4．6 Keno type games 4．7 Exercises 5 Play it Again Sam： The Binomial Distribution 5．1 Games and repeated trials 5．2 The binomial distribution 5．3 Beating the odds and the \"law\" of averages 5．4 Betting systems 5．5 A brief blackjack breakthrough 5．6 Exercises 6 Elementary Game Theory 6．1 What is game theory? 6．2 Games in extensive form 6．3 Two-person games in normal form 6．4 Zero-sum games 6．5 Nonzero-sum games，Nash equilibria and the prisoners' dilemma 6．6 Simple n-person games 6．7 Power indices 6．8 Games computers play 6．9 Exercises 7 Odds and Ends 7．1 The mathematics of bluffing and the Texas Holdem invasion 7．2 Off to the races 7．3 Lotteries and your expectation 7．4 The gambler's ruin Answers/Hints for Selected Exercises Bibliography Index About the Author