Bollman M. Basic Gambling Mathematics. The Numbers Behind the Neon 2ed 2023

Textbook in PDF format

Basic Gambling Mathematics: The Numbers Behind the Neon, Second Edition explains the mathematics involved in analyzing games of chance, including casino games, horse racing and other sports, 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 mathematics behind games of chance is drawn from probability theory at various levels of complexity. This is appropriate, because the origins of this branch of mathematics lie with the analysis of simple games of chance. This began with a series of letters noted above, between Blaise Pascal and Pierre de Fermat in 1654, that raised and answered several questions at the foundation of probability theory while addressing questions that arose in resolving gambling games. Later mathematicians have developed and expanded this topic into a rigorous field of mathematics with many important applications unrelated to gambling.
In this section, we shall outline the fundamental ideas of probability that are essential for analyzing casino games. In so doing, we will have occasion to use some of the mathematical ideas of set theory, informally. A deck of playing cards is a good illustration of the concept of a set.
Preface
Fundamental Ideas
Combinatorics and Probability
Probability Distributions and Expectation
Modified Casino Games
Blackjack: The Mathematical Exception
Betting Strategies: Why They Don’t Work
Appendix A: House Advantages