Customer Reviews

Lady Luck: The Theory of Probability (Science Study Series)

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I could not put this book down. The author, Warren Weaver, writes in a very unpretentious, personal voice. He unravels the complex subject of probability in a manner that is both encouraging and challenging. The reader develops a personal intuition for applying basic probability formulae (with careful consideration of relevant factors and an increased sense of self-confidence). I believe this book could be understood by any person familiar with basic algebra. On the other hand, the average physics PhD would likely find it equally interesting, because its intuitive approach is so refreshing.

Some years ago I got the idea that I could, by studying probability and statistics, work out a way to beat the Las Vegas bookies by betting on baseball games.

Hmm..., one might say. Well, I was young and while not exactly foolish, I was adventurous and liked challenges.

Anyway, I knew a little mathematics and a little probability, but it was only when I picked up this absolutely charming book and began to read it that I realized with a kind of glee and something akin to a thrill that I was about to learn something of great value.

Warren Weaver, a good friend, by the way, of Claude Shannon, the great information theory pioneer, has a wonderful gift for expression and an equally wonderful gift for explaining things clearly and making his subject matter exciting. And the engaging illustrations by Peg Hosford do nothing but add to the excitement.

From the very first words in the book, "This book is, in one sense, about thinking. About a certain way of thinking, that is...," I knew immediately what he meant and that I had stumbled upon exactly the sort of book I was looking for.

Weaver begins literally with "Thoughts about Thinking" and illustrates how probabilistic reasoning, as he calls it, is the only kind of reasoning that can help us answer certain kinds of questions, questions such as will it rain today? or is Alex Rodriguez, who hasn't had a hit in five at bats, due for a hit this time up? or "if I have my left lung removed, what is the chance that the cancer will really be cured?" (p. 28) He follows this with a most interesting short chapter on the history of probability, "The Birth of Lady Luck." And then he explains "The Concept of Mathematic Probability." His exposition was so clear and such a pleasure to read that I can still recall the delight I experienced in reading it for the first time.

In the chapter on "The Counting of Cases," Weaver gets down to the basics of compound events and the difference between combinations and permutations--knowledge that is necessary, for example, in order to analyze a game of chance, especially games involving dice or playing cards..

The next chapter covers independent events, and then there are some famous problems including the one involving dice throwing that the Chevalier de Mere presented to the celebrated French mathematician Blaise Pascal. Weaver had mentioned it earlier, noting that this historical problem from 1654 actually marked the above mentioned "birth of Lady Luck."

In other chapters Weaver introduces us to the law of large numbers and explains the "maturity of chances" fallacy and some other fallacies. He explains in a particularly clear and utterly convincing manner why the so-called Martingale system and other "doubling up" systems yield no advantage to the bettor, and why, if any given independent event is disadvantageous for the bettor, no system of betting on such events will ever lead to an advantage for the gambler. In the case of doubling your bet after each loss, Weaver shows that every time you win, you will be one unit ahead no matter how many times you double up--except for one very deadly proviso: Sooner or later you will run into a streak of losses that will wipe you out--or, run you up against the betting limit of the casino or whomever you are betting against, and you will have to eat your losses. It is simply a matter of the observing the powers of two: 2,4,8,16,32,64,128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536.

In other words, if your betting unit is $100 and you decide to bet on National Football League games, betting $100 the first week, and if you lose doubling your bet to $200 the next week, and then to $400, the following week, etc., until you either win or the season ends, you will gain $100 for each time you win. Should you however run into a bad streak, say losing every week, you would lose $65,536 after the 16th game! (I have simplified this of course since, due to the bookie's vigorish, you actually have to wager $110 to win $100.)

If you double up on something like the throw of the dice at a casino where the odds of winning the bet are less than fifty-fifty, your chance of a ruinous streak is (markedly) increased.

A very interesting chapter is number XIII, "Rare Events, Coincidences, and Surprising Occurrences" where Weaver presents some of the coincidences he has experienced and collected over the years. He goes on to explain the nature of such rare events and gives a very interesting look at them from a mathematical point of view. One of the events is about a guy in Las Vegas who made an amazing 28 passes in a row at a dice table at the Desert Inn. He, cautious bettor that he was, made only about $750, while the side bettors made $150,000. Another event was thirteen spades having been dealt to a bridge player. Weaver discusses whether we should believe that this and some other very, very rare events could happen by chance.

Since reading this book, I have read a number of other popular books on probability, statistics and gambling, but I can say, as good as some of them were, none were nearly as exciting nor half as interesting as this book. As far as I am concerned Lady Luck is a classic of the genre, and more or less timeless.

As for the baseball betting...well, that's another story, but suffice it to say it ain't easy beating the spread.

The main strength of Mr. Weaver's "Lady Luck" lies in its sheer readability. Mr. Weaver is very careful about presenting his arguments so that they may have maximum intuitive appeal, while at the same time refusing to compromise the mathematical rigor that is necessary to construct any serious theory of rudimentary probability. What is most important about the work is that it provides the reader an extremely entertaining and well written framework for thinking about questions of probability. A concept such as "independent random variable" which a mediocre statistics textbook may quickly skip is a surprisingly philosophically complicated idea, and has troubled academicians, let alone lay people. Mr. Weaver's work, far from being in any sense "slow," deals with how we are to take into account this very basic ideas that form the starting point to this particular area of the mathematical sciences. Finally, Mr. Weaver's references to distinctively late 50s early 60s phenomenon provide an entertaining look at the thoughts of the time.

This is a great little book for self study and a springboard for further study. A lot of these Dover publications are a bit dated and sometimes not the most clearly written and this is no exception. (In their defense, though, they are often seminal works written by the actual practitioners in the field.) Still, though, the writer is fairly nontechnical and introduces the major concepts of probability in a thorough manner. He delves a bit into statistics and ends up with a chapter on gaming. Take the concepts of this book, throw in a little more stats and logic and you've got a good Spock in the making.

A classic. What it does, it does extremely well, though the tone of 1950s restrained earnestness may not resonate with the Jon Stewart generation. Has a leisurely, careful but not pedantic, verbal development of the basic mathematics of probability (expectation, binomial and Normal distributions, law of large numbers and central limit theorem, statistical sampling) plus the classic stories (birthday paradox, coincidence anecdotes, Poisson's "cavalry deaths by horse kicks" data). In other words it picks out the interesting parts of a freshman college course. Readers in the Jon Stewart generation might prefer Struck by Lightning: The Curious World of Probabilities.

A pleasant and insightful read. I finally understand Bayes theorem now in a practical sense. The idea of calling the chapter exercises 'puzzles' rather than 'problems' or 'exercises' is a good one - more math authors should adopt this convention I think.

Weaver's book (actually written in the early 1960's) is becoming somewhat dated. Since this was before calculators were readily available, the book's examples don't take advantage of the readers access to powerful number crunching such as factorials and exponentials. Having taken over 4 years of calculus in college, I don't consider myself mathematically challenged, but I often had a hard time following the author's reasoning and his sample problems. Those without a good mathematical background could easily get lost and discouraged in this book unless they just skimmed over the rough areas and picked up those subjects and anecdotes of possible interest to them. For a quick read of probability theory at a low price, this isn't too bad; but more modern books are available.

It's simple but not at all 'dumbed down'. It's clear. It's very readable. The math is not out of control so the material is very accessible for non-technical readers. You will get a good intuitive feel for probability; not many books privide that. What more could you want? If more mathematical rigor is required get Feller's book or take Weaver's advice on page 102-103.

The book arrived in timely fashion. It was of good quality.
Dr. R. I. Rothenberg; 6.26.09