This book introduces the basic concepts of probability, statistics, decision theory, and game theory and presents interesting gaming examples to highlight the practical applications and methodologies. The author uniquely utilizes the mathematical analyses of games of chance to develop an understanding of probability and utility (rational thinking) theories. Based on six years of class-testing, the authors’ approach to games and gambling is accessible for readers with minimal experience. Ranging from simple games to strategic games, this book features a variety of gaming and gambling examples to build a better understanding of quantitative reasoning, and the authors establish fundamental concepts before moving on to more strategic games that illustrate how multiple concepts fit together. Organized into thirteen chapters, this book presents equal coverage on the general mathematical analysis concepts found in a wide variety of games as well as the specific theories and problems associated with well-known casino games. Covering zero-sum games, non-zero-sum games, and sequential games, the authors introduce ideas such as mathematical expectation and variance, bias, combinatorial calculus, conditional probability and Bayes Theorem, Bernoulli trials, and the Binomial distribution. The first two chapters feature an introductory discussion of utility and probability theory in finite and discrete spaces. Subsequent chapters utilize popular casino games to illustrate the practical probabilistic methodologies: roulette, which is one of the simplest casino games to play and analyze, is used to illustrate basic concepts in probability such as expectations; lotto is used to motivate counting rules and the notions of permutations and combinatorial numbers that allow for probability computation in large equiprobable spaces; craps and blackjack are used to illustrate and develop conditional probabilities; and poker illustrates how a combination of theories and techniques can be used together. Finally, the book concludes with discussions on game theory and strategic games. This book also features computer simulations using Microsoft Office® Excel® spreadsheets throughout in order to illustrate complex concepts and help readers calculate presented problems.
