Read Fortune's Formula Online

Authors: William Poundstone

Tags: #Business & Economics, #Investments & Securities, #General, #Stocks, #Games, #Gambling, #History, #United States, #20th Century

Fortune's Formula (6 page)

The jury deadlocked, and Zwillman was a free man. But in January 1959 an FBI bug revealed that Zwillman had bribed two of the jurors. Agents arrested the two henchmen directly responsible, and J. Edgar Hoover himself announced the news. It was plain that prosecutors would be revisiting the Zwillman tax case.

Sometime after 2 a.m. on the morning of February 26, 1959, Zwillman left his wife in bed and descended to the basement of his twenty-room home at 50 Beverly Road, West Orange, New Jersey. He hung himself with a plastic electrical cord. Police found twenty-one tablets of a tranquilizer in his dressing gown and a half-empty bottle of Kentucky bourbon on a nearby table.

Inevitably, it was theorized that someone else killed Zwillman and made it look like suicide. Arguing against this are friends’ statements that Zwillman had been depressed in the days leading up to his death. The peculiar accommodation that Zwillman had come to with American society was crumbling.

Zwillman’s death left Manny Kimmel holding a portfolio of businesses, some legitimate and some not, some owned by Kimmel and others apparently in partnership with Zwillman’s estate and/or still other murky entities. Kimmel had an idea for parlaying this wealth. It was going to be the biggest gamble of his life.

It involved the stock market.

Edward Thorp

Edward Oakley Thorp as “the most precise man I have ever met.” This zeal for measurement was evident from earliest youth. It has been claimed that mathematical talent is, ironically, linked with a child being slow to speak. Ed Thorp was born in Chicago on August 14, 1932, and did not utter his first words until he was nearly three. The Thorp family was at a Montgomery Ward department store when a group of people stepped out of an elevator. “Where’s the man gone?” someone asked.

“Oh, he’s gone to buy a shirt,” Ed said. From that moment, Ed conversed almost like an adult. Six months after that first sentence, Ed knew how to count to a million. He could read and had a near-photographic memory. At the age of five, Ed was challenged to name the kings and queens of England. “Egbert, 802 to 839,” he began. “Ethelwulf, 839 to 857; Ethelbald, 857 to 860…” He continued without interruption or error, up to “Queen Victoria, I know when her reign began but I don’t know when it ended.” The book from which Ed had learned this was Charles Dickens’s
A Child’s History of England
. Dickens had no way of knowing that Victoria would die in 1901.

Thorp’s father was an army officer who had returned to civilian life as the American economy collapsed into depression. He had to take a job as a bank guard. He plied his gifted son with math and reading primers, telling Ed (and himself) that education was the key to success in America.

Growing up in hard times, Ed turned his wits to making money. He bet a grocer he could total customers’ bills in his head faster than the grocer could using an adding machine. Ed won, earning ice cream cones for his performance. He would buy a pack of Kool-Aid for five cents and sell the mixed beverage to hot WPA workers for one cent a glass. Ed could get six glasses from a pack for a penny profit. An older cousin took Ed to a gas station where gangsters had placed illegal slot machines in the restrooms. Ed learned how to jiggle the handles so the machines would pay off when they weren’t supposed to.

Ed’s life changed when his family moved to Los Angeles to take jobs in wartime defense plants. With both parents working, Ed and his younger brother, James, were latchkey kids. Ed would go to the public library to self-administer IQ tests. He usually scored 170 to 200. The absence of parental supervision facilitated an interest in blowing things up. Ed whacked homemade nitrocellulose with a sledgehammer to blow holes in the sidewalk. He built pipe bombs to blow craters in the cliffs of Palos Verde and a gunpowder-propelled “rocket-car.” By mixing ammonia water with iodine crystals, he made an incredibly sensitive explosive called ammonium iodide. He painted this onto the bottom of a hemispherical metal bowl, then set the bowl on the ground. The explosive became active as it dried. The weight of a fly landing on the prepared bowl would trigger a small explosion.



In spring 1955 Thorp was a physics graduate student at UCLA. He made do on a budget of $100 a month. To subsist on that, he lived in the student-run cooperative in Robinson Hall. Known as the “Glass House,” Robinson Hall was designed by Richard Neutra in the 1930s. The rent was $50 a month plus four hours of work per week.

Since time was money, Thorp put in fifty to sixty hours a week of classes and study. He read books on psychology for tips on how to learn faster. The books recommended taking a break every now and then. Study an hour, then take a ten-minute break to eat or run errands. Following this advice one Sunday afternoon, Thorp attended a faculty tea.

As sunlight streamed in through Neutra’s plate glass, the conversation turned to ways to make easy money. Someone mentioned roulette. The group was unanimous in the conviction that gambling systems are worthless. The discussion had to do with physics. Are roulette wheels so perfect that predicting likely numbers is impossible?

The group was of two opinions. Some felt that nothing in the world is perfect, not even perfectly random. Therefore, every roulette wheel must have slight physical defects that cause it to favor some numbers. It might be possible to identify these favored numbers and bet on them.

The other group countered that roulette wheels are manufactured to exacting specifications for just this reason.

Thorp had the most original argument. He said you could make money
way. If the wheels are physically perfect, simple physics can predict where the ball is going to go. If the wheels have flaws, some of the numbers ought to be favored.

Thorp did some further investigation on his own. He learned that casinos accept bets for a couple of seconds after the croupier releases the white ball. The reason is that the ball takes a fairly long time to come to rest. Anytime the croupier is not accepting new bets, the casino is not making money.

Thorp fantasized about building a portable electronic device to predict the winning numbers. It would be fast enough to make a prediction in the couple of seconds in which wagers are permitted after the ball is cast. Thorp sketched out an orchestrated attack on Las Vegas. One member of his entourage would stand next to the wheel, operating the prediction device. The device would radio its predictions to another person at the same table. This person, seated where he did
have a good view of the wheel, would pay no attention to the wheel as he casually placed last-second wagers.

Every now and then one of these two people would get up and walk to another table—for there would be a whole army of confederates, half with the devices and half placing bets. They could come and go at random.

Thorp bought a cheap roulette wheel. He put a stopwatch next to it and filmed it in motion. After examining the film frame by frame, Thorp concluded that the toy wheel was too erratic to permit a prediction.



During Christmas break of 1958, Ed and his wife, Vivian, took a trip to Las Vegas. Vivian Sinetar was a slender English major. Her parents had questioned the earning potential of a physics Ph.D. who had shown more talent for thrift than for making money. Ed told Vivian that Las Vegas was a great place for a bargain-priced vacation.

He wanted to get a look at the casino roulette wheels in action. Just before this trip, a friend gave Thorp an article from the
Journal of the American Statistical Association
. It was an analysis of the game of blackjack.

Until the computer age, it was impractical to calculate the exact probabilities in blackjack and many other card games. There are an astronomical number of possible arrangements of a deck of fifty-two cards. Unlike in the case of roulette, the blackjack player has decisions to make. The odds in blackjack therefore depend on what strategy the player uses. In 1958 no one knew what strategy was best. Casinos simply knew from experience that they made an excellent profit.

The journal article was by mathematician Roger Baldwin and three associates at the U.S. Army’s Aberdeen Proving Ground. They had analyzed blackjack with army “computers,” a term that still meant adding machines or the people operating them. Baldwin’s team spent nearly three years pecking away at calculators in order to devise an optimum blackjack strategy. Their conclusion was that the house edge was just 0.62 percent when a player used their optimal strategy. Thorp computed that he could play all day, placing one thousand $1 bets, and it would “cost” him only $6, on the average.

Relatively speaking, a 0.62 house edge is
. The house advantage in American roulette is usually 5.26 percent. For slot machines, it runs 10 to 20 percent. Writers on blackjack had previously claimed a house advantage of 2 or 3 percent. No one had really understood the game. The Baldwin group’s strategy differed from the intuitive one that “good” blackjack players had been using.

Thorp, who had never played blackjack, wanted to try the Baldwin strategy. He copied the article’s strategy chart onto a small card. When he got to Las Vegas, he bought ten silver dollars and sat down at a blackjack table.

Las Vegas people then considered blackjack—also known as twenty-one—to be a woman’s game, offered to give wives something to do while their men played craps. The game moved quickly. Thorp had to look up every decision on his card. The dealer and players wanted to know what he was looking at in his palm and why he was taking so long. When he told them, they thought it was funny.

Thorp’s pile of silver dollars shrank, but the mockers were losing faster. At the end of half an hour, Thorp quit. He was down to $1.50.

This experience preyed on Thorp’s mind in the following months. He saw a way to improve the strategy. It rested on the fact that the chances of drawing particular cards are not completely independent from hand to hand.

You might for instance see three aces played in one deal. Aces are good for the player. The dealer discards the played cards and, assuming she’s got enough cards to go on without shuffling, deals the next hands from the remainder of the deck. Since you’ve already seen three aces played, you know that there can at most be one ace in the new hands. You could use that information to adjust your strategy and/or the size of your bet.

This had not been considered in the Baldwin group’s study. They had pretended that the chance of drawing any card is fixed at exactly 1 in 52, in every hand dealt.

Thorp grew so convinced that he could beat blackjack that his roulette idea went on the back burner. He wrote Baldwin to ask if he could see the group’s original computations. In spring 1959 Baldwin sent a cardboard box full of the group’s notebooks.

That year, Thorp began a job as a mathematics instructor at MIT. He went to Massachusetts, alone, in June, for a summer research project. Thorp spent the humid Boston nights in his new office, hammering on a desk calculator and slapping the omnipresent mosquitoes. He was working on the blackjack system. After a couple of weeks, he concluded that the problem was too big to solve by hand. Then he realized that he might be able to do the computations on MIT’s mainframe computer. It was an IBM 704, a real, programmable, electronic computer. It had some free time during the summer break.

Thorp taught himself FORTRAN, the venerable programming language, and programmed the computer himself. His computations told him that the five cards make a bigger difference to the house advantage than any other rank. The fives are bad for the player and good for the house. By simply keeping track of how many fives have been played, the player could judge whether the remainder of the deck was favorable or not.

Thorp decided to publish the system. He determined that the most prestigious journal that might take the article was
The Proceedings of the National Academy of Sciences
. But articles had to be submitted by a National Academy member.

There was only one academy member at MIT who was a mathematician. That was the famous Claude Shannon. Thorp called Shannon’s secretary and made an appointment to meet him.



It was a chilly afternoon in November 1960. Before Thorp went in, the secretary warned him that Dr. Shannon had only a few minutes to spare. He didn’t spend time on subjects that didn’t interest him.

Conscious that the meter was running, Thorp handed Shannon his paper and quickly ticked off its main points. Shannon asked astute questions and was satisfied with Thorp’s answers. Shannon told Thorp that he appeared to have made the big theoretical breakthrough on the subject. Shannon’s main objection was the title.

Thorp had titled the paper “A Winning Strategy for Blackjack.” Shannon thought that was too much of a hard sell for the National Academy. The title should be more sedate.

Like what?
Thorp asked.

Shannon thought a moment and said: “A Favorable Strategy for Twenty-one.”

Shannon proposed a few editorial cuts. He told Thorp to type up a revision and send it to him. He would forward it to the academy.

“Are you working on anything else in the gambling area?” Shannon asked.

Thorp hesitated, then told Shannon about the roulette idea. Shannon was riveted. He was possibly more interested in the roulette scheme than the blackjack system because there was a gadget to build. They spoke for several hours. By the time they adjourned, Thorp had inadvertently set one of the century’s great minds on yet another tangent. It was agreed that Shannon and Thorp would collaborate on building a roulette prediction machine. Shannon said that the best place to work would be his home.

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