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Chance: The Life of Games and The Game of Life

J. P. Marques de Sá
Publication Date: 
Number of Pages: 
[Reviewed by
Barbara E. Reynolds
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This book gives a delightful overview of Probability, that is, Chance, as a phenomenon in both games and life. The writing style is clear and engaging. Concepts of probability theory are presented in a way that helps the reader realize why we would want to understand these ideas. As a mathematician who teaches probability and statistics courses from time to time, I found this book to be filled with examples that I will use in class the next time I teach Probability. When the author uses the usual examples of flipping coins, rolling dice, and drawing balls from an urn, he makes it clear how these probability experiments can be used to model real life.

In ten chapters, this book presents an intuitive overview of the theory of probability, including both the classical notion of probability, and use of relative frequencies to estimate probabilities. There are chapters on conditional probability (Amazing Conditions), mathematical expectation (Expecting to Win), the normal and binomial distributions, and the law of large numbers (The Wonderful Curve), inference (Probable Inferences), chance and determinism (The Nature of Chance), and sequences and random processes (Noisy Irregularities). Games of chance that are played in casinos (roulette, craps, card games, slot machines) and state-sponsored lottery games are introduced early, and recur throughout the book as examples that bring light to concepts that can be difficult to explain. These games form the backdrop for explaining mathematical expectation; after all, a casino does not stay in business unless the House is winning in the long run. The author consistently connects these examples to probabilities that I care about in daily life, such as the probability of having cancer given the outcome of a screening test. My students are likely to enjoy the last chapter, Living with Chance, in which the author discusses Learning, in Spite of Chance, and proves that there are circumstances in which learning is impossible.

The author keeps the mathematical prerequisites to a minimum, so that this book would be accessible to an undergraduate who has completed Calculus. In fact, no calculus is used in this book, but an undergraduate who has completed calculus would have the mathematical maturity to read (and enjoy!) this book. The author provides appendices on Powers, the Exponential Function, the Logarithmic Function, the Factorial Function, Sinusoids, and the Binary Number System for those students who need a review (or even a basic introduction) to these topics. Although this is not a textbook (for one thing, there are no exercises), I would consider using it as a text for a student who wanted to do an independent study of probability theory.

Apparently this book was first written in Portuguese, but no translator is given. I surmise then that the author himself is the translator. The back cover note mentions that the author has written "four books in Portuguese and three in English." I mention this because this book does not read like a translation; the author-translator gives an excellent presentation of this material, and one is not distracted by awkward phrases that sometimes appear in material that has been translated from another language. This book reads as if it were originally written in English.

Sr. Barbara E. Reynolds, SDS, is Professor of Mathematics & Computer Science at Cardinal Stritch University, Milwaukee, WI.