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The theory of gambling and statistical logic Hardcover – 1967
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Man invented a concept that has since been variously viewed as a vice, a crime, a business, a pleasure, a type of magic, a disease, a folly, a weakness, a form of sexual substitution, an expression of the human instinct. He invented gambling. Richard Epstein's classic book on gambling and its mathematical analysis covers the full range of games from penny matching, to blackjack and other casino games, to the stock market (including Black-Scholes analysis). He even considers what light statistical inference can shed on the study of paranormal phenomena. Epstein is witty and insightful, a pleasure to dip into and read and rewarding to study.
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Top Customer Reviews
Review of "The Theory of Gambling and Statistical Logic" follows:
Some parts are interesting, and the writing can be entertaining, but the book is short on insight and clarity and long on tedious tables and uninterpreted computations.
Buy this if you already know probability and would like to see -some- applications and cute games.
Don't buy it if you want insight into particular games; especially, the blackjack and bridge sections (and meager poker section) have virtually no value.
I am a graduate student in mathematics, and enjoy probability theory and games: I should be the ideal audience. The math is no problem for me, but much is boring, and much time is spent writing huge tables without giving much insight.
Research articles in statistics are easier to read, and far more informative.
The math background is awful: if you don't already know it, don't learn it here. (Instead, see "The Cartoon Guide to Statistics", or Feller's "Intro to Probability".) The writing is willfully obscure and florid (though, admittedly, entertaining): gymkhana, panjandrum, kubiagenesis?
My main objection is the lack of insight: the author does (mostly) correct computations and statements but seldom shows much depth of understanding and rarely conveys any to the reader.
Rather than answering questions or giving examples that convey the meaning of the theory, how it lets you understand questions, Epstein does many unillustrative examples.
This book won't teach you to understand games and gambling, which it could do and should do.
At best, it provides a basis from which you can (after too much work) begin to understand games. This is not because the subject is that hard (at least not what Epstein covers) -- it's because the material is undigested and Epstein is a poor expositor.
If you want to get something out of this book, be prepared to do the work that Epstein hasn't, and to look at more modern and insightful references.
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. (See the Wikipedia article on "Shuffling" for a much better discussion, with links to references.)
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.
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.
presentation of gambling ideas and lore. However, there are some errors in the "Basic Theorems" beginning on page 51. In particular,
Theorem V on page 60 is not correct. The "maximum boldness" strategy is need not be optimal in a subfair game when there is a bound on the
size of bets. Likewise "minimum boldness", also known as "timid
play" need not be optimal when there is a house minimum. (For
counterexamples, see the article by Heath, Pruitt, and Sudderth
in The Proceedings of the American Math. Soc. vol 43, pp. 498-507,
April 1972 and the article by Ruth in the Journal of Applied Probability, vol 36, pp. 837-851, September 1999.
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.