Drunkard's Walk - Leonard Mlodinow [44]
The difference between the two interpretations is more nuanced than it may seem. For example, in a perfect world a throw of a die would be random by the first definition but not by the second, since all faces would be equally probable but we could (in a perfect world) employ our exact knowledge of the physical conditions and the laws of physics to determine before each throw exactly how the die will land. In the imperfect real world, however, a throw of a die is random according to the second definition but not the first. That’s because, as Moshe pointed out, owing to its imperfections, a die will not land on each face with equal frequency; nevertheless, because of our limitations we have no prior knowledge about any face being favored over any other.
In order to decide whether their table was random, the Rand scientists subjected it to various tests. Upon closer inspection, their system was shown to have biases, just like Moshe’s archetypally imperfect dice.6 The Rand scientists made some refinements to their system but never managed to completely banish the regularities. As Moshe said, complete chaos is ironically a kind of perfection. Still, the Rand numbers proved random enough to be useful, and the company published them in 1955 under the catchy title A Million Random Digits.
In their research the Rand scientists ran into a roulette-wheel problem that had been discovered, in some abstract way, almost a century earlier by an Englishman named Joseph Jagger.7 Jagger was an engineer and a mechanic in a cotton factory in Yorkshire, and so he had an intuitive feel for the capabilities—and the shortcomings—of machinery and one day in 1873 turned his intuition and fertile mind from cotton to cash. How perfectly, he wondered, can the roulette wheels in Monte Carlo really work?
The roulette wheel—invented, at least according to legend, by Blaise Pascal as he was tinkering with an idea for a perpetual-motion machine—is basically a large bowl with partitions (called frets) that are shaped like thin slices of pie. When the wheel is spun, a marble first bounces along the rim of the bowl but eventually comes to rest in one of the compartments, which are numbered 1 through 36, plus 0 (and 00 on American roulette wheels). The bettor’s job is simple: to guess in which compartment the marble will land. The existence of roulette wheels is pretty good evidence that legitimate psychics don’t exist, for in Monte Carlo if you bet $1 on a compartment and the marble lands there, the house pays you $35 (plus your initial dollar). If psychics really existed, you’d see them in places like that, hooting and dancing and pushing wheelbarrows of cash down the street, and not on Web sites calling themselves Zelda Who Knows All and Sees All and offering twenty-four-hour free online love advice in competition with about 1.2 million other Web psychics (according to Google). For me both the future and, increasingly, the past unfortunately appear obscured by a thick fog. But I do know one thing: my chances of losing at European roulette are 36 out of 37; my chances of winning, 1 out of 37. That means that for every $1 I bet, the casino stands to win (36/37 × $1) – (1/37 × $35). That comes to 1/37 of a dollar, or about 2.7¢. Depending on my state of mind, it’s either the price I pay for the enjoyment of watching a little marble bounce around a big shiny wheel or else the price I pay for the opportunity of having lightning strike me (in a good way). At least that is how it is supposed to work.
But does it? Only if the roulette wheels are perfectly balanced, thought Jagger, and he had worked with enough machines to share Moshe’s point of view. He was willing to bet they weren’t. So he gathered his savings, traveled to Monte Carlo, and hired six assistants, one for each of the casino’s six roulette wheels. Every day his assistants observed the wheels,