Well written, intuitive and enjoyable book

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	• Chance: The Life of Games & the Game of Life Joaquim P. Marques de Sá Springer, 2008 - 224 pages average customer review:based on 2 reviews view larger image
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Well written, intuitive and enjoyable book

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.

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chance and randomness

It starts off with a quite elementary discussion of probability and statistics. Where the author motivates the reader by invoking as much as possible examples drawn from real life situations. You should be aware that the book is not meant for the raw tyro to the subject. The narrative quickly goes into the subtleties of conditional probabilities, which can be very confusing the first time round. Actually, it can still be confusing several times round.

Plus, he gets into discussions about randomness and chaotic behaviour. Including examples of atmospheric turbulence, where the chaos arises intrinsically from the equations of classical dynamics. Hence the saying about a butterfly flapping its wings triggering changes a world away.

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With its many easy-to-follow mathematical examples, this book takes the reader on an almost chronological trip through the fascinating and amazing laws of chance, omnipresent in the natural world and in our daily lives. Along the route many fascinating topics are discussed, such as: challenging probability paradoxes; "paranormal" coincidences; game odds; causes and effects; interpretation of opinion polls; winning chances as a game proceeds; the nature of randomness; entropy and randomness; randomness in life; algorithmic complexity and the undecidability of randomness; possibilities and limitations of learning the laws of a Universe immersed in chance events. This charming book will inform and entertain the scientist and non-scientist alike.

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