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.