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Bernoulli's Book of Probability

Having myself attended functions where adjacent citizens were participating in games of chance, I cannot comfortably take a moral position on Bill Bennett’s affection for one-armed bandits. Like all addictions, gambling creates its own fevered logic which can overpower good mental hygiene and create disasters for individuals and families . It resists that easy rightwing mantra—espoused most enthusiastically and sanctimoniously by the same Bill Bennett--that “virtue” is something that can be willed through sheer force of character. I’m sure if you talked to Bennett today, he would assure you that he doesn’t have a problem, that he can afford it, that it’s legal and he could walk away from gambling anytime he wanted to.

But, of course he does have a problem. He is either addicted to a game he has no chance of winning or he honestly thinks he can beat the odds, which means he is stupid. Every rational person knows that the odds are always stacked in favor of the house—that’s how they make money. And every real gambler knows that slot machines offer the worst odds of all the casino games. If you play blackjack, you have some limited chance of bettering the odds by—for example—not taking a hit when you have 18 already. You have zero chance of influencing the outcome with slot machines. Stick your money in, pull the lever, and the machine does its random thing.

Bennett is a well-read man so I’m sure he knows that slot machine payouts are governed by a principle known as the Law of Large Numbers, discovered by Swiss mathematician Jacob Bernoulli in 1689. Bernoulli’s law has two parts:

First, it says, random outcomes such as a coin toss or pull on a slot machine lever are unaffected by previous tosses and pulls. Each has the same odds as the one before it and the one after. If you watch someone drop 100 quarters into a slot machine without a payout and then walk away in disgust, the next quarter or 100 quarters you drop in are no more or less likely to produce a win.

However, the overall result of random outcomes generally becomes more predictable as the number of outcomes increase. This is known as the Law of Averages. It means that flipping a coin 20 times may yield nineteen heads and a tail, but flipping it a million times will yield close to 500,000 of each.

That means that if a degenerate gambler—Bill Bennett, say—were to play thousands of times over many years he should break even, right? Wrong. Casino games are all rigged to give the house an advantage. Nevada law allows casinos to hold up to 25 percent of the amount gambled (New Jersey allows 17 percent) but to be competitive most Las Vegas slots pay out about $85 of every $100 bet. A handful of “loose” slots are usually programmed to pay out more often to create “buzz.”

Put it another way, slot machines are programmed to give the house a 4 or 5 percent edge on Bernoulli. Instead of the odds being 50-50, they are more like 55 percent to the house, 45 percent to the player. That’s enough to make casinos very rich and people like Bill Bennett less virtuous than they could be.

posted by Jerry Bowles 11:45 AM