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This work addresses such topics eloquently and with a remarkably satisfying level of detail. It is in essence a synthesis of mathematical rigour and pragmatic realism, striking an excellent balance between the two. Providing diagrams of gambling tables alongside mathematical equations and graphs alone makes this an unique contribution to the field. Beyond this, the prose is exceedingly perinent and well-written, leading even the uninitiated toward maturity and understanding of each topic under discussion.
Subject matter begins with one of the most basic probability topics, coin-tossing, and then progresses rapidly into realms of incredible richness and complexity. Card games, stock market speculation, games requiring pure skill including board games, and then other various ones such as horse-racing, discussion of fallacies, and military strategy, are dealt with in a mature, skillful, rigorous fashion. Upon completion of each chapter one can expect to have a fundamental mathematical framework on subjects which previously may have seemed utterly random and chaotic. Terms such as chance, luck, and fortune will be inevitably refined and redefined.
Mathematical maturity is requisite to gaining a full understanding of the contents of this book. If lacking in this arena, one recommendation is to begin by reading merely the prose, then when personal interest and motivation are sufficiently great, consult introductory works on the various math disciplines. Schaum's workbooks are ideal for this, as they provide both an introductory flavor and hundreds of fully solved problems. Dover publications on mathematics, logic and science are extremely affordable, and provide a tremendous range of subject matter. The latter have the decided disadvantages of often beginning with a higher initial level of sophistication, and typically leaving exercises unsolved.
Related scientific topics of interest to this work include discrete mathematics, including combinatorics, matrices, probability, statistics. Certainly the calculus and graph theory should be included in this list as being fundamental. Further reaching topics include game theory, information theory, mathematical programming, and then chaos theory, fractal geometry, and computability and complexity theory. Pertinence to the natural sciences and philosophy should be obvious as well. Enjoy the pursuit.
Here's an example: how many times do you need to shuffle a deck before it's essentially random? Very natural question, of big interest in gambling. Epstein gives a very slick argument, one of the gems of the book (measure entropy of a shuffle) that you need at least 5 shuffles -- but beyond that just writes some equations for 2 shuffles of a 4-card deck and says that a computer would help, and instead tabulates that 18 perfect shuffles of a 58-card deck return it to the original state.
The rest of the book is like this: some question begging for study, perhaps an insight, and then irrelevant and pedantic computations and tables.
There are gems in here (it's a grab-bag), and the writing is often amusing, but it's a frustrating read: it could be so much better.
This book covers the mathematics behind gambling, in an extraordinarily well-written yet technical manner. The author covers all sorts of games such as blackjack and bridge, and provides mathematical derivations of all sorts of probabilities. There is also a most interesting discussion of the pari-mutuel system used in wagering on horses. A good assortment of challenging problems for the reader are also presented.
The only warning I would give is that the book is probably not suitable for someone who has at least taken 1 university course in calculus and algebra. While Epstein doesn't use any advanced math, there are certainly a lot of formulas and a certain familiarity with math is essential.
This being said, the book is a classic in its field. If you're interested in the mathematical study of gambling you will not be disappointed. This is one book that you can read many times and always find something new and interesting to try.
I am writing this review mostly to deal with the criticism that this book has received from some of the other reviewers. I would agree with those critics that this book is not for the faint of heart. This book does require a certain comfort level with mathematics.
However, I don't think it's all that fair to bash this book for those alleged faults. Mr. Epstein's book does not pretend to be anything other than a serious treatment (and a serious treatment would require a great deal of mathematical analysis) of gambling. In fact, the serious analysis of gambling is what gave rise to the mathematical disciplines of probability and statistics. Mr. Epstein is (was) an engineer and the book makes that very clear. FAIR criticism would be based on citing problems with the book based on what the book was INTENDED to be. UNfair criticism of this book is based on what the mathematically challenged reader HOPED it would be.
BTW, I do agree with the math-challenged critics that there are some good books out there dealing with a more math-oriented approach to gambling that were written with the intention of appealing to people who wanted to make use of such information and wanted a lighter touch on the math. Among them are the *Theory of Poker* by Skalansky and the other books mentioned on this page.
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