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'The Physics of Wall Street': The Most Arrogant Book in the World? Part 3

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To see the world in a grain of sand, to see the financial system in a roulette wheel.

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Editor's note: The following column is the third part of an ongoing series of articles by Aaron Brown examining the claims made in The Physics of Wall Street: A Brief History of Predicting the Unpredictable, a new book by James Owen Weatherall. Click here to read Part 1. Click here to read part 2.

MINYANVILLE ORIGINAL Several weeks ago, I started an account of James Weatherall's new book, The Physics of Wall Street, which I claim is one of the most arrogant books in the world, and therefore an invaluable teaching aid. This week I want to talk about how Weatherall misunderstands the important research that began with a study of roulette wheels.

Weatherall appears to have skimmed mathematician Ed Thorp's classic work Beat the Dealer. He refers to Ed as a "dilettante" for working with Claude Shannon to beat roulette before moving on to finance. (However, when physicist Doyne Farmer did the same thing years later, beating roulette is referred to as a suitable topic for a physics dissertation; there are different rules for physicists and mortals.) In fact, the attack on roulette was a key moment in the development of financial theory.

The traditional way to beat roulette was to use a random walk model, the only kind of model Weatherall recognizes in finance. You assume each number comes up at random, and independently, but according to a non-uniform probability distribution. You watch a wheel for an extended period, recording the results, and look for numbers that come up often enough to overcome the house edge and be profitable bets. However, many people claimed that method was impossible in large casinos because the probability distribution of numbers was too close to uniform.

Ed's insight was that you could make money either way. If the wheels were sufficiently non-uniform, you could do it the traditional way. But if they were so precisely engineered that outcomes were uniform, they would be predictable if you had even a tiny amount of information about the spin. The effort to ensure uniform randomness creates predictability. This duality is at the heart of modern finance.

In the roulette case, it was possible to measure the speed of the ball and the speed of the wheel before you had to place your bets. The precision of the wheels meant that it was possible to compute with considerable accuracy the number that would be under the ball at the time it left the rim of the wheel. From that point on, the process is chaotic, so it's not practical to predict the final number exactly. But the distribution of final numbers, conditional on knowing the number under the ball when it starts its descent, is highly non-uniform and profitable betting strategies are possible.

We have to tease out a distinction between concepts that are often covered by the word "random": unpredictable and uniform. One person says the roulette wheel is random; because you know nothing about the next spin different from any other spin, the wheel is unpredictable. Another person says the wheel is random because each number comes up with exactly the same long-term frequency, the wheel is uniform.

It's easy to select numbers with uniform distribution -- just call them out in order, going back to the beginning when you reach the end. It's also pretty easy to select numbers at random; you don't need precise engineering, just a system chaotic enough to make computing the outcome impractical using the information available to players. But casinos have to make devices that are both uniform and random. That's not only tricky, but Ed and many followers proved it is beyond the ability of casinos, and no one has yet demonstrated convincingly that it's possible in practice at all.
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