Authors: William Poundstone
Tags: #Business & Economics, #Investments & Securities, #General, #Stocks, #Games, #Gambling, #History, #United States, #20th Century
E HAD A VERY INFORMAL HOUSE
Betty Shannon once explained. “If there was something that interested us, we did it.”
The Shannons’ home was a big three-story house in Winchester, Massachusetts. It sat on a large lot sloping down to the shore of one of the Mystic Lakes. The Shannons had three children, Robert, Andrew, and Margarita. Their amusement was the pretext for some of their father’s gadget-building. Shannon constructed a “ski lift” to help the family zip between house and lake. He rigged a tightrope a couple of feet above the ground; Shannon and the children used it for acrobatic feats. On placid summer days Shannon could occasionally be seen strolling across the green-black water of the lake. He achieved this by wearing outsized “shoes” made out of plastic foam.
The garage was a clutter of dusty unicycles and penny farthings. Inside, Shannon’s “Toy Room” was a curiosity cabinet of weird machines, globes, skeletons, musical instruments, juggling equipment, looms, chess sets, and memorabilia. The Shannons had five pianos and thirty-some instruments ranging from piccolos to sousaphones. There was a flamethrowing trumpet and a rocket-powered Frisbee.
Claude spent much time inventing new gismos in his basement workshop. “What it was was a collection of rooms,” Thorp recalled. “Some of the rooms had open shelving. We estimated he had about $100,000 worth of surplus equipment. At surplus rates, that’s a lot of stuff. There’d be whole sections of switches—toggles, mercury switches, and so on; capacitors, resistors, little motors. He liked both electrical and mechanical things. Something that was electromechanical was ideally suited for him.”
One of Betty’s first gifts to Shannon after their marriage was “the biggest Erector set you could buy in this country. It was fifty bucks and everyone thought I was insane!” Betty said. Claude insisted that the set was “extremely useful” for trying out scientific ideas. Today’s distinction between robotics and artificial intelligence was moot in the early 1960s. There were no inexpensive programmable computers and scarcely any video displays. The first experiments in AI were hard-wired machines that moved. Shannon was responsible for a number of them. One was “Theseus,” a robotic mouse capable of threading a maze. As it dated to the Stone Age of electronic miniaturization, Theseus was simply a metal toy on wheels guided magnetically by a special-purpose computer built into the base of the maze. When the mouse’s copper whiskers touched an aluminum wall of the maze, the mouse changed direction.
One of Shannon’s chess-playing machines was a three-fingered robot arm that moved pieces on a real board. The machine made sarcastic comments when it took a piece. Shannon built a computer that calculated not in his own scheme of binary, but in Roman numerals.
Shannon’s “Ultimate Machine” was the size and shape of a cigar box. On the front panel was a toggle switch. The unsuspecting visitor was invited to flip the switch on. When that happened, the top slowly opened. A robot hand emerged, reached down, and flipped the switch off. The hand retreated, and the lid snapped shut.
The Charles Addams-esque theme of disembodied limbs in boxes was a Shannon motif. In the kitchen was a mechanical finger. By pulling a cable in the basement, Claude could cause it to curl in summons to Betty.
Another device was a simple flexible metal arm that tossed a coin. It could be set to flip the coin through any desired number of rotations. This demonstrated a favorite theme of Shannon’s, the relativity of random. In American culture the coin toss is the paradigm of a random event. A coin toss decides who kicks off the Super Bowl. Looked at another way, a coin toss is not random at all. It is physics. An event is random only when no one cares to predict it—as Thorp and Shannon intended to demonstrate with their roulette machine.
HORP WORKED WITH
as time permitted from early 1960 to June 1961. Shannon’s free-spending ways came in handy. They needed a professional roulette wheel to study. Shannon ordered a reconditioned wheel from Reno. With a set of ivory balls, it cost $1,500.
They set the roulette wheel on a dusty old slate billiard table and filmed it using a strobe light. A special clock with a high-speed hand that made one revolution every second allowed them to time the motion more accurately than Thorp had.
A roulette wheel’s inner part (the rotor) rotates within a stationary outer part (the stator). The croupier spins the rotor in one direction and tosses the ball into the stator in the opposite direction. Initially the ball is moving so fast that centrifugal force presses it snug against the near-vertical rim of the stator. As momentum decreases, the ball drops onto the sloped part of the stator. Like a satellite in a decaying orbit, it falls inward in a spiral trajectory.
The stator contains “vanes” or “deflectors.” These are (typically) eight diamond-shaped metal pieces arranged in a neat pattern. A spiraling ball that hits a deflector will often carom off in a different direction. About half the time, though, the ball slips between the deflectors or skips over one without much changing its trajectory.
The ball then spirals down the inner part of the stator and skips over to the rotor. Since the rotor is spinning in a direction opposite to the movement of the ball, the friction increases. The ball slips farther inward, finally encountering the pockets.
There are thirty-eight numbered pockets in the American game. A divider called a “fret” separates each pocket from its neighbors. The ball usually hits a few frets before settling into a pocket. As in a head-on freeway collision, the relative speed between ball and frets is high. This part of the ball’s trajectory is hardest to predict.
They didn’t need an exact prediction. Narrowing down the ball’s destination to a
of the wheel would provide a whopping advantage.
During one of these sessions, Thorp discovered that he was able to guess approximately where the ball would land. It was like ESP. He and Shannon discovered the reason. The wheel was slightly tilted. This made the ball favor the downhill side of the wheel.
Picture a roulette wheel mounted vertically on the wall, like a clock. The ball would
to come to rest in the lowermost, six o’clock position. You would need to predict only which pocket of the rotor would end up in the six o’clock position. It is easier to predict one moving object than two, and the motion of the spinning rotor is much simpler than that of the skittering ball.
The effect was of course much subtler with a slightly tilted wheel. Shannon and Thorp put roulette chips under the wheel to experiment with different degrees of tilt. They concluded that a tilt amounting to half a chip’s thickness would give them a substantial advantage. They joked about slipping a chip under the wheel in the casinos. Shannon proposed slipping a sliver of ice under the casino’s wheel. It would destroy the evidence as it melted.
The device they built was the size of a cigarette pack. It contained twelve transistors and slipped into a pocket. The user needed to measure the initial position and velocity of the two moving objects, the ball and the rotor. To do that, the user mentally picked a reference point on the stator. When a point on the rotor passed this reference point, the user clicked a toe-operated switch concealed in his shoe. He clicked again when the rotor point passed the reference point again, having made a full revolution. A third click signaled when the ball passed the reference point, and a fourth when it had made a full revolution.
From this data the device predicted the segment of the wheel in which the ball was most likely to land. The device’s predictions were accurate only to within about ten pockets. There was not much point in informing the user of the exact “most likely number.” Imagine the roulette wheel as a pizza divided into eight equal pieces. Shannon called the pieces
. The device assigned a distinct musical tone to each octant and communicated its prediction via a concealed earphone. Thorp mentally ticked off the notes as
do re mi fa so la ti do
. The computer played notes while it was computing, then stopped. The last note told what octant to bet on.
Each octant consisted of five numbers that are close together on the rotor (some octants overlapped). One of the octants was 00, 1, 13, 36, 24. An octant’s numbers are not close on the betting table layout. The bettor would have to scramble to place bets on five assorted numbers. It was not crucial that he bet all the numbers as long as he only placed bets on the right numbers.
Shannon and Thorp 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.
HANNON HAD ANOTHER WORRY.
It is easy to lose money, even with a mathematical advantage.
Professional gamblers, who
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
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
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.”
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 Victorian name of “gambler’s ruin.” Gamblers have dozens of names for it, among them “having an accident” and “getting grounded.” Over the centuries, gamblers have devised all sorts of money management systems to minimize the chance of ruin.
The simplest and most foolproof system is to not gamble (with some or all of your money). If you’re going to Las Vegas with $1,000 and are determined to come back with at least $500, then put the $500 in the hotel safe and don’t gamble with it.
This is not the kind of advice that most gamblers want to hear. It does not fundamentally address the ruin problem at that. You still need a money management system for the amount you
gambling with. It is easy to lose all of that.
The best-known betting system is “martingale” or “doubling up.” This is the system where a bettor keeps doubling her bet until she wins.
You might begin by placing a dollar on an even-money bet like “red” in roulette. If you win, great. You’ve made a dollar profit. If you lose, you bet $2 on red the next time. Should you win
time, you get twice that back, or $4. Notice that $4 is a dollar more than the $2 plus $1 total that you have wagered.
Should you lose again, you place a new bet for $4. Win this time, and you get $8, for a $1 profit (you’ve then bet $7 total). Lose again, and you bet $8…then $16…$32…$64…An unlucky streak has to end sometime. When it does, you are guaranteed to be a dollar ahead. Repeat as desired.
The eighteenth-century journalist, gambler, and scoundrel Casanova used martingale in the Venetian casinos. He was playing a card game called Faro that offered even-money bets with little or no house advantage. Casanova was mostly betting the money of his mistress, the wealthy young nun he calls M—M—. “I still played on the martingale,” Casanova wrote, “but with such bad luck that I was soon left without a sequin. As I shared my property with M—M—I was obliged to tell her of my losses, and it was at her request that I sold all her diamonds, losing what I got for them; she had now only five hundred sequins by her.” This dashed M—M—’s hope of escaping the convent to marry Casanova—a long shot in any case, as the rest of the memoir makes clear.
Far from preventing gambler’s ruin, martingale
it. The amount a losing player must bet is soon $128…$256…$512…Either the player runs out of money (or nerve), or the casino refuses the bet as too large. That leaves the martingale player with no way of recouping the string of losses.
In the days of the Wild West, faro dealers traveled from saloon to saloon setting up portable betting layouts. Most of those faro dealers were cheats, it appears. The game survived into the early days of legalized gambling in Nevada. Faro still lured players who thought themselves smart for playing a game with no house advantage. The movie producer Carl Laemmle once staked Nick the Greek to three months of playing faro in Reno. Nick lost everything. So did an anonymous California woman in a tale told by Reno casino proprietor Harold S. Smith, Sr. (whom we are about to meet). The California woman was so addicted to faro that she was seen in Reno every weekend. It was a marvel how she could play for twelve hours straight.
The woman began dispensing with her trips home to California. Her real life was at the faro tables. After her husband divorced her, the woman moved to Reno full-time. She burned her way through a $50,000 divorce settlement. Then she turned prostitute on Douglas Alley to feed her gambling habit. As Smith told it,
she wasn’t any bargain beauty and the Line was open in Reno then with attractive young women selling for $3. Our woman had to offer cut rates and take what she could get. She sold herself for 50 cents an act. Fifty cents—the minimum bet on the Faro table, which—if it won—would pay exactly fifty cents.