Drunkard's Walk - Leonard Mlodinow [45]
When the casino shut that night, Jagger was up $70,000. His winnings did not go without notice. Other patrons swarmed his table, tossing down their own cash to get in on a good thing. And casino inspectors were all over him, trying to decipher his system or, better, catch him cheating. By the fourth day of betting, Jagger had amassed $300,000, and the casino’s managers were desperate to get rid of the mystery guy, or at least thwart his scheme. One imagines this being accomplished by a burly fellow from Brooklyn. Actually the casino employees did something far more clever.
On the fifth day, Jagger began to lose. His losing, like his winning, was not something you could spot immediately. Both before and after the casino’s trick, he would win some and lose some, only now he lost more often than he won instead of the other way around. With the casino’s small margin, it would take some pretty diligent betting to drain Jagger’s funds, but after four days of sucking in casino money, he wasn’t about to let up on the straw. By the time his change of luck deterred him, Jagger had lost half his fortune. One may imagine that by then his mood—not to mention the mood of his hangers-on—was sour. How could his scheme have suddenly failed?
Jagger at last made an astute observation. In the dozens of hours he had spent winning, he had come to notice a tiny scratch on the roulette wheel. This scratch was now absent. Had the casino kindly touched it up so that he could drive them to bankruptcy in style? Jagger guessed not and checked the other roulette wheels. One of them had a scratch. The casino managers had correctly guessed that Jagger’s days of success were somehow related to the wheel he was playing, and so overnight they had switched wheels. Jagger relocated and again began to win. Soon he had pumped his winnings past where they had been, to almost half a million.
Unfortunately for Jagger, the casino’s managers, finally zeroing in on his scheme, found a new way to thwart him. They decided to move the frets each night after closing, turning them along the wheel so that each day the wheel’s imbalance would favor different numbers, numbers unknown to Jagger. Jagger started losing again and finally quit. His gambling career over, he left Monte Carlo with $325,000 in hand, about $5 million in today’s dollars. Back home, he left his job at the mill and invested his money in real estate.
It may appear that Jagger’s scheme had been a sure thing, but it wasn’t. For even a perfectly balanced wheel will not come up on 0, 1, 2, 3, and so on, with exactly equal frequencies, as if the numbers in the lead would politely wait for the laggards to catch up. Instead, some numbers are bound to come up more often than average and others less often. And so even after six days of observations, there remained a chance that Jagger was wrong. The higher frequencies he observed for certain numbers may have arisen by chance and may not have reflected higher probabilities. That means that Jagger, too, had to face the question we raised at the start of this chapter: given a set of underlying probabilities, how closely can you expect your observations of a system to conform to those probabilities? Just as Pascal’s work was done in the new climate of (the scientific) revolution, so this question would be answered in the midst of a revolution, this one in mathematics—the invention of calculus.
IN 1680 a great comet sailed through our neighborhood of the solar system, close enough that the tiny fraction of sunlight it reflected was sufficient to make it prominent in the night sky of our own planet. It was in that part of earth