Understand the Math Underlying Some of Your Favorite Gambling Games
Basic Gambling Mathematics: The Numbers Behind the Neon explains the mathematics involved in analyzing games of chance, including casino games, horse racing, and lotteries. The book helps readers understand the mathematical reasons why some gambling games are better for the player than others. It is also suitable as a textbook for an introductory course on probability.
Along with discussing the mathematics of well-known casino games, the author examines game variations that have been proposed or used in actual casinos. Numerous examples illustrate the mathematical ideas in a range of casino games while end-of-chapter exercises go beyond routine calculations to give readers hands-on experience with casino-related computations.
The book begins with a brief historical introduction and mathematical preliminaries before developing the essential results and applications of elementary probability, including the important idea of mathematical expectation. The author then addresses probability questions arising from a variety of games, including roulette, craps, baccarat, blackjack, Caribbean stud poker, Royal Roulette, and sic bo. The final chapter explores the mathematics behind "get rich quick" schemes, such as the martingale and the Iron Cross, and shows how simple mathematics uncovers the flaws in these systems.
Table of Contents
WHAT DOES IT MEAN TO BE RANDOM?
AXIOMS OF PROBABILITY
ELEMENTARY COUNTING ARGUMENTS
ADVANCED COUNTING ARGUMENTS
THE ADDITION RULES
THE MULTIPLICATION RULES AND CONDITIONAL PROBABILITY
Probability Distributions and Expectation
THE BINOMIAL DISTRIBUTION
Modified Casino Games
Blackjack: The Mathematical Exception
RULES OF BLACKJACK
THE MATHEMATICS OF BLACKJACK
Betting Strategies: Why They Don't Work
SLOT MACHINE STRATEGIES
AND ONE THAT DOES: LOTTERY STRATEGIES
HOW TO DOUBLE YOUR MONEY
Appendix A: House Advantages
Appendix B: Mathematical Induction
Appendix C: Internet Resources
Answers to Odd-Numbered Exercises
Exercises appear at the end of each chapter.
"Basic Gambling Mathematics: The Numbers Behind the Neon focuses on applying introductory probability theory to a plethora of well-known card games, dice games, casino games, and lottery games, as well as to their many less famous variations. ... This book is appropriate for readers who wish to understand the basics of probability theory, educators who wish to incorporate more concrete and exciting examples into their courses, and garners who wish to understand the mathematics behind their favorite pastimes. With its clear mathematical descriptions and multitude of examples and exercises, this book would even make an excellent supplement to any introductory probability course."
—Kathleen Ryan, in Mathematical Reviews Clippings, July 2015
"… the author does an excellent job at contextualizing probabilities and combinatorial quantities … Too many times, introductory probability books leave readers with a feeling that probability should be useful in building strategies for game play, yet these books do not explicitly make this connection for its readers. However, Basic Gambling Mathematics: The Numbers Behind the Neon does indeed make this connection.
This book is appropriate for readers who wish to understand the basics of probability theory, educators who wish to incorporate more concrete and exciting examples into their courses, and garners who wish to understand the mathematics behind their favorite pastimes. With its clear mathematical descriptions and multitude of examples and exercises, this book would even make an excellent supplement to any introductory probability course. Moreover, by incorporating visuals, such as diagrams of casino tables and images of old-time punchboards, and by also providing historical background for games, commentary on state gambling laws, and insight into the inner workings of casinos, this book successfully transforms an already fun topic into an even more enjoyable read."
—Mathematical Reviews, July 2015
"… it offers advice, backed up by detailed calculations, on standard gambles found in casinos and on the variations used to spice up these games. Most of these ‘extras’ turn out to have a far larger house advantage, but in their zeal to hook in potential customers, casinos may offer bets that favour the punter, or even free bets. Savvy readers can discover here how best to exploit these baits. … Useful tables list the basic data for a variety of games … The final chapter runs through a plethora of general betting strategies that have been suggested and explains their deficiencies patiently. … Reading this book would be time well spent for anyone contemplating a vacation in Las Vegas."
—John Haigh, London Mathematical Society Newsletter, November 2014
"Mark Bollman has written a wonderfully illuminating and accessible survey of the mathematics behind gambling. Firmly grounding his analysis in the historical and social context of the games, Bollman is able to explain both the theory behind the games and the practical application of that theory in a range of games, including not only the casino standbys of roulette, craps, and blackjack, but also new variations on those games. The included exercises give readers a chance to work out problems for themselves, which will undoubtedly enhance the usefulness of this book. This is a fantastic guide to gambling math, both for the beginner and the experienced gambler (or mathematician). As Bollman’s math proves, there’s rarely a sure bet, but Basic Gambling Mathematics comes pretty close."
—David G. Schwartz, University of Nevada, Las Vegas
"Basic Gambling Mathematics: The Numbers Behind the Neon is a must-have book for anyone interested in gambling mathematics. It not only covers all of the most popular casino games (blackjack, craps, roulette, keno), but is also a treasure trove of fascinating variants and novel games from casinos all over the world. Professors, students, and general gambling enthusiasts will all find something to capture their attention."
—Mike Ferrara, Associate Professor and Graduate Program Director, Department of Mathematical and Statistical Sciences, University of Colorado Denver
"….the book presents the mathematical analysis of fortune games in an easy style. It is an advantage that the book is completely understandable even for readers being not familiar in probability theory. From this point of view, the book is recommended for everybody without limitations. However, if the reader is interested in deeper technical details on the subject then he or she must look for a more advanced source."
—Gábor Szűcs, Szeged, 2017