Customer Reviews

Taking Chances: Winning with Probability

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There are many textbooks on college-level mathematical probability, but a smaller number of what I call "textbooks lite" aimed at a reader who is willing to work to learn some interesting parts of a subject. This wonderful book teaches the basic calculations in mathematical probability, but with a combination of breadth and concreteness unrivaled by any other book I know. The book consists of short sections, each giving verbal discussion of problems involving probability, games of chance and related material, and deriving solutions using only arithmetic and occasional elementary combinatorics and algebra. It covers an impressive breadth of topics: lotteries, dice and card games, casino games, TV show games, racetrack betting, some game theory (Prisoners Dilemma, Hawk-Dove games, Male-Female reproductive strategies), combined with the basic laws of probability and the familiar birthday and coupon collector's problems. Part of the content is distinctly British rather than American (cricket and snooker; premium bonds; the particular TV shows). In addition to familiar types of elementary probability calculations such as the craps example, there are more elaborate stories and calculations involving strategies as games progress. I particularly like the chapter giving a gentle yet entertaining introduction to two-person game theory.

While the book is mainly written on probability in games, which has already been covered in many books, the author coveres the basics of probability and coin tossing very nicely. He also covers the theory of dices thoroughly and approaches "Games with few choices" (Game Theory) with great enthusiasm. Finally the chapter "Probability for Lawyers" with it's terms such as the prosecutors fallacy and the defence attorne's fallacy are a must read for every person interested in the fascinating subject of probabiliy. PS: second edition covers now Bayes's theorem (previous readers criticised the author of missing this important theory in the first issue)

An excellent account of probability theory. Whilst definitely geared towards gambling it also sheds new light on some fundamental probability topics.

The text sometimes does get a little numerical - at the expense of the theoretical - but this is not necessarily a bad thing.

The only question I have about the book is why is there no mention of Bayes? Surely a fundamental contributor to probability theory.

This book has an extremely practical approach, since in each chapter it explains several games and their related probabilities. These related probabilities are of the sort of: when is it advisable to double the bet, when is it advisable to let your opponent "eat" one of your chips in backgammon, how long will it take you on average to get your chip back on the game board, which streets in Monopoly are more likely to be visited by other players and which have a better payback, how high is your chance to win at the lottery, at sports pools, at the races, how can you minimize your losses at casino games like roulette, how likely is it that you will be winning after "n" games or how likely is it that a tennis player will win the match if he has a probability of "p" to win one point.

This approach gives the book a special character and keeps your interest on the subject; on the other hand, there is little room for theoretical explanations of the probability basics, so you need to do the calculations done by the author over and over until you figure out the principles behind his math. In the appendices there are a few explanations, but definitely not enough, specially regarding the different probability distributions and when each is better suited. This is not a textbook... The fact that the theory is back in appendices and not in the main text makes the reading a bit more difficult, since you need to jump back and forth between the chapter and the appendix. I tried reading the appendices first but these are not stand alone theory chapters, but refer to specific problems in the main text, which by the way can come from different chapters (different games may require the same probability basics); so you cannot avoid the back and forth between one or more appendices and one or more chapters, add a pencil and a notebook to follow the calculations and you cannot read anymore in bed... Another problem was that some of the british games were unfamiliar to me (like cricket, bridge, etc.), I do not know the rules, what is required to win the game or how the points are assigned, so understanding the underlying probabilities was somewhat difficult. If you are a beginner in this topic, I strongly recommend reading The Drunkard's Walk: How Randomness Rules Our Lives (Vintage) first. This books does not require that you perform any calculations but explains the very basics in an easy to understand manner.

The chapter on game theory was really interesting; I had already read a bit about these games but had not seen the math that is applied to their solutions. The games explained in this chapter are very simple, so the calculations can be followed easily.

I bought this book mainly because Mr. Plous, author of The Psychology of Judgment and Decision Making (McGraw-Hill Series in Social Psychology) made it quite clear that most people (myself included) are poor at probability and statistical analysis and that people would make more "rational" decisions had they some basic knowledge in these topics. After emphasizing this fact, Mr. Plous did not consider it necessary to explain the math he used in his examples, so I decided to get myself some literature on probability. I am not sure I can take now more rational decisions, but I certainly know now a bit of probability, specially related to gaming, e.g. I had never bothered to calculate the preestablished margin for the casino at the roulette game, now I can calculate how to bet in order to loose my money more slowly and play longer or take my chances in one shot with a 47.5% chance of doubling my fortune.

This is a very practical book on probability using common games (cards, dice, coin-toss, etc.) as examples. Explanations are thorough without being too technical. The appendices go into more mathematical detail for those so inclined. The author is British so everything has that slant (money in pounds and pence, Grand National, and so on), but that's not a problem. There's a lot of information packed into the 330 pages of this paperback since the type is fairly small.