The new edition of a favourite which introduces and develops some of the important and beautiful elementary mathematics needed for rational analysis of various gambling and game activities. Most of the standard casino games (roulette, craps, blackjack, keno), some social games (backgammon, poker, bridge) and various other activities (state lotteries, horse racing) are treated in ways that bring out their mathematical aspects. The mathematics developed ranges from the predictable concepts of probability, expectation, and binomial coefficients to some less well-known ideas of elementary game theory. The second edition includes new material on: • Sports betting and the mathematics behind it • Game theory applied to bluffing in poker and related to the 'Texas Holdem phenomenon' • The Nash equilibrium concept and its emergence in popular culture • Internet links to games and Java applets for practice and classroom use. Game-related exercises are included and solutions to some appear at the end of the book.
Author(s): Edward W. Packel
Series: Anneli Lax New Mathematical Library 28
Edition: 2
Publisher: Mathematical Association of America
Year: 2006
Language: English
Pages: 189
title page
Contents
Preface to the First Edition
Preface to the Second Edition
Acknowledgements and Dedication
1 The Phenomenon of Gambling
1.1 A selective history
1.2 The gambler in 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
References from the text
Other relevant works not referenced directly in the text
Selected references and web links on specific games and activities
Index
About the Author
