Sixteen Volts

Yesterday I read the excellent and thoroughly enjoyable book "Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street" by William Poundstone. In fact, this book was so good that I am going to issue a memo to myself: find and read everything else that Mr. Poundstone has ever written. In fact, now that I browsed the list of his books, I have already read "Labyrinths of Reason: Paradox, Puzzles, and the Frailty of Knowledge", which I remember also to have been great.

The book discusses how the mathematics of information theory and risk management were successfully applied to both investment and gambling (which, as the book notes, differ only by a preceding minus sign and are otherwise the same thing) during the twentieth century by such well-known figures as Ed Thorp, who is perhaps best known for his blackjack basic strategy, and Claude Shannon, the father of information theory.

The book is divided into seven parts, and the first two discuss the work of Ed Thorp and Claude Shannon. After pointing out how Shannon's famous theorem about maximum communication capacity over noisy channels actually directly applies to wagering with inside information that gives you an extra edge (the problems of communication over noisy line and wagering are actually the same, if I understood correctly), the book moves on to the question of how much of your bankroll should you wager on a bet whose expected value is positive but there is still a possibility of losing. If you greedily bet everything you have, you risk losing everything (which will eventually happen in repeated bets), but if you keep betting on a flat rate, you are not earning as much as you could. The answer is given by the Kelly criterion, a betting strategy that maximizes the long-term growth rate of such bets.

Part three, "Arbitrage", moves from betting to stock market, and examines the efficient market hypothesis in light of the mathematics established earlier, and agrees with it. And what is certainly true is that unlike in Lake Wobegon, not everybody can be above average, and a simple arithmetic proves that most people who think that they can beat the market do worse than the market, once the transaction costs are accounted in.

Part four, "St. Petersburg Wager", returns to the question of what kind of risk-taking is rational in the stock market. After a short jaunt to the utility theory, the book notes that we can't really get rid of the famous paradox that way, since the game could be modified so that instead of a geometric progression of money, it offers a geometric progression of utility units. Put that in your pipe and smoke it for a minute. Another intesting topic in this part was the discussion of Shannon's rebalancing portfolio strategy in which you, unlike the common sense might tell you, sell the stocks that rise and buy more of the stocks that fall. In an extremely volatile market this would be a good strategy, but under real-world conditions the little profit that it gives would be wiped out with commissions.

Part five moves to the computer era of the freewheeling eighties in which names such as Michael Milken and Ivan Boesky, men whose names are forever associated with insider trading in the public mind. Part six examines the collapse of Long-Term Capital Management fund and its 1998 collapse. To put it briefly, massive leverage can potentially lead to a quick ruin when enough things turn against you.

The book was personally enjoyable for me also for the reason that it reminded me of the five-credit information theory course that I took when I was still an undergrad, taught by a visiting professor who was an expert in that particular field. Even though I enjoyed the course quite a lot and did eventually get an A, I have by now blissfully forgotten most of the things taught there, but at least some of this stuff came back to me. However, I can remember the final exam, during which some other student got up and took his exam paper to the TA and said that one question just must be wrong, which led to a muted debate between the student and the hapless TA. The professor was away that day, so the problem could not be settled, but after I while I got up and simply said that there is nothing wrong with that question, sat down and continued working on my exam. I guess my voice and demeanor were convincing enough, since neither that student or the TA said anything but just returned to their seats, and the exam could continue without further interruption.

Coming back to the book for a minute, it had just the right amount of math, and the historical accounts of card counting in blackjack in the old times should be interesting to many people in this current boom of mob-related entertainment. The author points out that for all the headache that card counting caused to casinos, in the end it actually only benefited them since for every competent card counter, the publicity attracted a hundred new incompetents to the casino to lose all their money.

Hey, while I am at the topic of blackjack, as a comical contrast to this book I should mention another book that I also read, "Twenty-First Century Blackjack" by Walter Thomason. Well, I just skimmed most of it, since most of the book is just numerical tables and lists of results. This book promises to use "logic" and "real-world data" to prove that you don't need to count cards to have an edge against the house in blackjack, but using a simple money management system in which you increase your bet after each winning hand is by itself enough to give you a positive edge, especially if you utilize "quit points" so that if you lose enough hands in a row, you step away of that table. You don't need to go through all that work of card counting, but this undetectable system is enough! The author sure knows what he is talking about, since he first tried his system by simulating 5,000 hands and profited. Then he took his friends to a blackjack cruise ship sailing outside Florida, where they also won a few hundred dollars, plus a few folksy stories about stupid pit bosses for this book. We certainly can't argue with success!

The shilling reader reviews at Amazon are comical, but the most humorous chapter in this book is definitely the "The opposition opinion, and why it is wrong!" where the author "answers" his critics who say that this system can't possibly work. Jesus, I so wish that I could copy the whole chapter here for my readers to enjoy (and simultaneously learn how to use bullshit to confuse prenumerical people), but I guess that would be some kind of copyright violation. So maybe I'll just include his argument why we can't dismiss his system because of computer simulations and the general theory of probability:

So here's what I believe:

1. Most computer-generated simulation programs are incapable of judging the validity of progressive betting systems, due to faulty, incorrect or non-existent programming. The results of consecutive hands of play are totally ignored. The program recently developed by my associate, Mr. I.B. Winner, is the only one I know of that attempts to compare progressive, flat and card counting systems.

2. Bayes' Theorem, a theoretical concept, should not be used to pass judgment on empirical evidence.

His words, not mine, in a book published in 1999. The author then goes on to explain that his system works against the theory in practice because "studies of mathematics confirm" that winning and losing streaks occur, but in this system you bet little on the losing streaks, whereas you bet more on the winning streaks. This truly is so clear and logical to anybody who is not a card counter who "have never been able to accept the value of empirical observation" but who believe that only card counting can give you an edge, because of their silly adherence to Bayes' Theorem. (To my disappointment, the book doesn't say that Bayes' Theorem is "only a theory".) The author then goes on to lament the "card counters" whose criticism of progressive betting is unfair and one-sided. After all, the proponents of progressive betting don't question the theoretical basis of card counting systems, so why can't we all just get along?

The "table tactics" and "money management" chapters that follow this one are full of rare and useful blackjack wisdom of "don't bet what you can't afford to lose" and "play in a comfortable environment", but even here the author occasionally demonstrates his ability to combine his flights of fancy with cold logical reason. For example, consider the advice of never quitting while you are winning (which the author even cheerfully admits contradicts his previous advice of setting win goals and sticking to them), because as all experienced gamblers will tell you, winning streaks do occur! But where the author proves himself to be practically a zen master is the following piece of advice:

5. Don't fall in love with a table or a dealer. The cards don't know who's dealing them, and they don't know upon which table they are being dealt. I know this sounds silly, but you would be surprised at how many players stay at a losing table because they like the dealer or because they had been winning at that table. If you're capable of entering a casino, you most likely have some method of transporting yourself from one table to another. Do so when necessary!

Posted by Ilkka Kokkarinen on Tuesday, August 29, 2006 at 8:11 AM