Read Online Fortune's Formula by William Poundstone - Free Book Online
Authors: William Poundstone
Tags: United States, General, History, 20th Century, Business & Economics, Investments & Securities, Stocks, Games, Gambling
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estimated that with the octant system and a modest degree of tilt, they could achieve a 44 percent edge on the house. Both men realized how fragile their scheme was. If ever the casinos got word of the operation, they could simply refuse to accept bets after the ball had been thrown.
The scheme thus depended on keeping it secret. Shannon told Thorp that an analysis had shown that any two people in the United States were likely to be connected by a chain of about three mutual friends. (He must have been referring to the 1950s work of MIT political scientist Ithiel de Sola Pool rather than the now-better-known 1967 study of Harvard psychologist Stanley Milgram that found “six degrees of separation.”) Shannon was concerned that word might have already gotten out, maybe from the original UCLA discussion. A few nodes in the social network could link an MIT scientist to a Las Vegas casino boss.
Gambler’s Ruin
S HANNON HAD ANOTHER WORRY. It is easy to lose money, even with a mathematical advantage.
Professional gamblers, who have to have an advantage, speak of “money management.” This refers to the tricky and all-important issue of how to achieve the greatest profit from a favorable betting opportunity. You can be the world’s greatest poker player, backgammon player, or handicapper, but if you can’t manage your money, you’ll end up broke. The sad fact is, almost everyone who gambles goes broke in the long run.
Make a chart of a gambler’s wealth. The gambler starts with X dollars. Each time the gambler wins or loses a bet, the wealth changes.
If the wagers are “fair”—that is, if the gambler has no advantage and no one is skimming a profit off the bets—then the long-term trend of wealth will be a horizontal line. In mathematical terms, the “expectation” is zero. That means that in the long run, a gambler is just as likely to gain as to lose.
Expectation is a statistical fiction, like having 2.5 children. A gambler’s actual wealth varies wildly. The diagram’s jagged line shows the fate of a typical gambler’s bankroll. It is based on a simple simulation where the gambler bets the same dollar amount each time. The jagged line wavers without rhyme or reason. Mathematicians call this a “random walk.”
Gambler’s Ruin
The only trend you might notice is that the swings, both up and down, tend to get wider as time goes on. This is a mathematically demonstrable fact and would be more apparent were the chart continued indefinitely to the right. The gambler’s wealth tends to stray ever farther from the original stake. There are long runs of good luck in which the gambler is ahead, and long runs of bad luck in which he is behind. If someone could gamble forever, the line representing wealth would wander across the “original stake” line an infinite number of times.
But look: Relatively early in this chart, the wealth hits zero (the line marked “Bankrupt”). Had this happened in a casino, the gambler would be tapped out. He’d have to quit and go home a loser.
That means that the right part of the chart is irrelevant. Assuming the original stake is everything the gambler has or can get to gamble with, he’s out of the game permanently.
In casino games, the house normally has an edge. This means that the player tends to go broke faster. It is possible to go broke even in those unusual cases where the player has a small advantage.
When that happens, the gambler’s loss is someone else’s gain (a casino’s, a bookie’s, a pari-mutuel track’s). That “someone else” usually has more money. That means that the gambler is likely to go bust long before he has such a winning streak as to “break the bank.” The net effect of gambling is to extract the stake from the gambler’s pocket and give it to the house. How often have you heard of a friend who went to the casinos, won a nice little jackpot, and poured it all back?
Mathematicians give this phenomenon the faintly
The scheme thus depended on keeping it secret. Shannon told Thorp that an analysis had shown that any two people in the United States were likely to be connected by a chain of about three mutual friends. (He must have been referring to the 1950s work of MIT political scientist Ithiel de Sola Pool rather than the now-better-known 1967 study of Harvard psychologist Stanley Milgram that found “six degrees of separation.”) Shannon was concerned that word might have already gotten out, maybe from the original UCLA discussion. A few nodes in the social network could link an MIT scientist to a Las Vegas casino boss.
Gambler’s Ruin
S HANNON HAD ANOTHER WORRY. It is easy to lose money, even with a mathematical advantage.
Professional gamblers, who have to have an advantage, speak of “money management.” This refers to the tricky and all-important issue of how to achieve the greatest profit from a favorable betting opportunity. You can be the world’s greatest poker player, backgammon player, or handicapper, but if you can’t manage your money, you’ll end up broke. The sad fact is, almost everyone who gambles goes broke in the long run.
Make a chart of a gambler’s wealth. The gambler starts with X dollars. Each time the gambler wins or loses a bet, the wealth changes.
If the wagers are “fair”—that is, if the gambler has no advantage and no one is skimming a profit off the bets—then the long-term trend of wealth will be a horizontal line. In mathematical terms, the “expectation” is zero. That means that in the long run, a gambler is just as likely to gain as to lose.
Expectation is a statistical fiction, like having 2.5 children. A gambler’s actual wealth varies wildly. The diagram’s jagged line shows the fate of a typical gambler’s bankroll. It is based on a simple simulation where the gambler bets the same dollar amount each time. The jagged line wavers without rhyme or reason. Mathematicians call this a “random walk.”
Gambler’s Ruin
The only trend you might notice is that the swings, both up and down, tend to get wider as time goes on. This is a mathematically demonstrable fact and would be more apparent were the chart continued indefinitely to the right. The gambler’s wealth tends to stray ever farther from the original stake. There are long runs of good luck in which the gambler is ahead, and long runs of bad luck in which he is behind. If someone could gamble forever, the line representing wealth would wander across the “original stake” line an infinite number of times.
But look: Relatively early in this chart, the wealth hits zero (the line marked “Bankrupt”). Had this happened in a casino, the gambler would be tapped out. He’d have to quit and go home a loser.
That means that the right part of the chart is irrelevant. Assuming the original stake is everything the gambler has or can get to gamble with, he’s out of the game permanently.
In casino games, the house normally has an edge. This means that the player tends to go broke faster. It is possible to go broke even in those unusual cases where the player has a small advantage.
When that happens, the gambler’s loss is someone else’s gain (a casino’s, a bookie’s, a pari-mutuel track’s). That “someone else” usually has more money. That means that the gambler is likely to go bust long before he has such a winning streak as to “break the bank.” The net effect of gambling is to extract the stake from the gambler’s pocket and give it to the house. How often have you heard of a friend who went to the casinos, won a nice little jackpot, and poured it all back?
Mathematicians give this phenomenon the faintly
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