Excerpted from The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It by Scott Patterson. Copyright 2010 by Crown Business. Reprinted by Permission of Crown Business, an imprint of the Crown Publishing Group, a division of Random House, Inc.
Chapter 2: The Godfather: Ed Thorp
Just past 5 a.m. on a spring Saturday in 1961, the sun was about to dawn on a small, ratty casino in Reno, Nevada. But inside there was perpetual darkness punctuated by the glow of neon lights. A blackjack player sat at an otherwise empty table, down $100 and exhausted. Ed Thorp was running on fumes, but unwilling to quit.
"Can you deal me two hands at once?" he asked, wanting to speed up play.
"No can do," she said. "House policy."
Thorp stiffened. "I've been playing two hands all night with other dealers," he shot back.
"Two hands would crowd out other players," she snapped, shuffling the deck.
Thorp looked around at the empty casino. She'll do whatever it takes to keep me from winning. The dealer started rapidly shooting out cards, trying to rattle him. At last, Thorp spied the edge he'd been waiting for. Finally — maybe — he'd have a chance to prove the merits of his blackjack system in the real-world crucible of a casino. Twenty-eight, with dark hair and a tendency to talk out of the corner of his mouth, Thorp resembled hordes of young men who passed through Nevada's casinos hoping to line their pockets with stacks of chips. But Thorp was different. He was a full-blown genius, holder of a Ph.D. in physics from UCLA, a professor at the Massachusetts Institute of Technology, and an expert in devising ingenious strategies to beat all kinds of games, from baccarat to blackjack.
As night stretched into morning, Thorp had kept his bets small, wagering $1 or $2 chips at a time, as he fished for flaws in his system. None were apparent, yet his pile of chips kept shrinking. Lady Luck was running against him. But that was about to change. It had nothing to do with luck and everything to do with math.
Thorp's system, based on complex mathematics and hundreds of hours of computer time, relied primarily on counting the number of Ten cards that had been dealt. In blackjack, all face cards — kings, queens, and jacks — count as Tens along with the four natural Tens in every deck of fifty-two cards. Thorp had calculated that when the ratio of Tens left in the deck relative to other cards increased, the odds turned in his favor. For one thing, it increased the odds that the dealer would bust, since dealers always had to "hit," or take another card, when their hand totaled 16 or less. In other words, the more heavily a deck was stacked with Ten cards, the better Thorp's chances of beating the dealer's hand and winning his bet. Thorp's Tens strategy, otherwise known as the Hi-Lo strategy, was a revolutionary breakthrough in card counting.
While he could never be certain about what card would come next, he did know that statistically he had an edge according to one of the most fundamental rules in probability theory: the Law of Large Numbers. The rule states that as a sample of random events, such as coin flips — or the hands in a game of blackjack — increases, the expected average also increases. Ten flips of a coin could produce seven heads and three tails, 70 percent heads, 30 percent tails. But 10,000 flips of a coin will always produce a ratio much closer to 50-50. For Thorp's strategy, it meant that because he had a statistical edge in blackjack, he might lose some hands, but if he played enough hands he would always come out on top — as long as he didn't lose all of his chips.
As the cards shot from the dealer's hands, Thorp saw through his exhaustion that the game was tipping his way. The deck was packed full of face cards. Time to roll. He upped his bet to $4 and won. He let the winnings ride and won again. His odds, he could tell, were improving. Go for it. He won again and had $16, which turned into $32 with the next hand. Thorp backed off, taking a $12 profit. He bet $20—and won. He kept betting $20, and kept winning. He quickly recovered his $100 in losses and then some. Time to call it a night.
Thorp snatched up his winning and turned to go. As he glanced back at the dealer, he noticed an odd mixture of anger and awe on her face, as if she'd caught a glimpse of something strange and impossible that she could never explain.
Thorp, of course, was proving it wasn't impossible. It was all too real. The system worked. He grinned as he stepped out of the casino into a warm Nevada sunrise. He'd just beaten the dealer.
Thorp's victory that morning was just the beginning. Soon, he would move on to much bigger game, taking on the fat cats on Wall Street, where he would deploy his formidable mathematical skills to earn hundreds of millions of dollars. Thorp was the original quant, the trailblazer who would pave the way for a new breed of mathematical traders who decades later would come to dominate Wall Street — and nearly destroy it.
Indeed, many of the most important breakthroughs in quant history derived from this obscure, puckish mathematician, one of the first to learn how to use pure math to make money — first at the blackjack tables of Las Vegas, and then the global casino known as Wall Street. Without Thorp's example, future financial titans such as Griffin, Muller, Asness, and Weinstein may never have converged on the St. Regis Hotel that night in March 2006.
Edward Oakley Thorp was always a bit of a troublemaker. The son of an Army officer who'd fought on the Western Front in World War I, he was born in Chicago on August 14, 1932. He showed early signs of math prowess, like mentally calculating the number of seconds in a year by the time he was seven. His family eventually moved to Lomita, California, near Los Angeles, and Thorp turned to classic whiz-kid mischief. Left alone much of the time — during World War II, his mother worked the swing shift at Douglas Aircraft and his father worked the graveyard shift at the San Pedro shipyard — he had the freedom to let his imagination roam wild. Blowing things up was one diversion. He tinkered with small homemade explosive devices in a laboratory in his garage. With nitroglycerine obtained from a friend's sister who worked at a chemical factory, he made pipe bombs to blow holes in the Palos Verdes wilderness. In his more sedate moments, he operated a Ham radio and played chess with distant opponents over the airwaves.
He and a friend once dropped red dye into the Plunge at Long Beach, then California's largest indoor pool. Screaming swimmers fled the red blob, and the incident made the local paper. Another time, he attached an automobile headlight to a telescope and plugged it into a car battery. He hauled the contraption to a lover's lane about a half mile from his home and waited for cars to line up. As car windows began to fog, he hit a button and lit up the parked assemblage like a cop's spotlight, laughing as frantic teens panicked and pulled themselves together.
During high school, Thorp started thinking about gambling. One of his favorite teachers returned from a trip to Las Vegas full of cautionary tales about how one player after another got taken to the cleaners at the roulette table. "You just can't beat these guys," the teacher said. Thorp wasn't so sure. Around town, there were a number of illegal slot machines that would spit out a stream of coins if the handle was jiggled in just the right way. Roulette might have a similar hidden weakness, he thought, a statistical weakness.
Thorp was still thinking about roulette in his second year of graduate school physics at UCLA, in the spring of 1955. He wondered if he could discover a mathematical system to consistently win at roulette. Already, he was thinking about how to use mathematics to describe the hidden architecture of seemingly random systems — an approach he would one day wield on the stock market and develop into a theory that lies at the heart of quant investing.
One possibility was to find a roulette wheel with some kind of defect. In 1949, two roommates at the University of Chicago, Albert Hibbs and Roy Walford, found defects in a number of roulette wheels in Las Vegas and Reno and made several thousand dollars. Their exploits had been written up in Life magazine. Hibbs and Walford had been undergraduate students at the California Institute of Technology in Pasadena, and their accomplishments were well known to astute denizens of CIT's neighbor, UCLA.
Thorp believed it was possible to beat roulette even without help from flaws in the wheel. Indeed, the absence of defects made it easier, since the ball would be traveling along a predictable path, like a planet in orbit. The key: Because croupiers take bets after the ball is set in motion, it is theoretically possible to determine the position and velocity of the ball and rotor, and to predict approximately which pocket the ball will fall into.
The human eye, of course, can't accomplish such a feat. Thorp dreamed of a wearable computer that could track the motion of ball and wheel and spit out a prediction of where it would land. He believed he could create a machine that would statistically forecast the seemingly random motion of a roulette wheel: An observer would don the computer and feed in information about the speed of the wheel; a bettor, some distance away, would receive information via a radio link.
Thorp purchased a cheap half-scale wheel and filmed it in action, timing the motion with a stopwatch that measured in splits of one-hundredths of a second. Thorp soon realized that his cheap wheel was too riddled with flaws to develop a predictive system. Disappointed, he tabled the idea as he worked to finish graduate school. But it gnawed at him, and he continued to fiddle with experiments.
One evening, his in-laws visited him and his wife Vivian for dinner. They were surprised when Thorp didn't greet them at the door and wondered what he was up to. They found him in the kitchen rolling marbles down a V-shaped trough and marking how far the marbles spun across the kitchen floor before stopping. Thorp explained that he was simulating the path of an orbiting roulette ball. Surprisingly, they didn't think their daughter had married a lunatic.
The Thorps made their first visit to Las Vegas in 1958, after Thorp had finished his degree and begun teaching. The frugal professor had heard that the rooms were cheap, and he was still toying with the idea of beating roulette with a wearable computer. The smoothness of the wheels in Las Vegas convinced Thorp that he could predict the outcome. Now, he just needed a solid, regulation-size wheel and suitable laboratory equipment.
In the meantime, during this trip Thorp decided to try out a blackjack strategy he'd recently come across. The strategy was from a ten-page article in the Journal of the American Statistical Association by U.S. Army mathematician Roger Baldwin and three of his colleagues — James McDermott, Herbert Maisel, and Wilbert Cantey — who'd been working at the Aberdeen Proving Ground. Among blackjack aficionados, Baldwin's group came to be known as the "Four Horsemen," although no one in the group actually tested the strategy in Las Vegas. Over the course of eighteen months, the Four Horsemen punched a massive amount of data into desktop calculators plotting the probabilities involved in thousands of different hands of blackjack.
Ever the scientist, Thorp decided to give Baldwin's strategy a whirl during a Christmas vacation to Las Vegas with his wife. While the test proved inconclusive (he lost a grand total of $8.50), he remained convinced the strategy could be improved. He contacted Baldwin and requested the data behind the strategy. It arrived in the spring of 1959, just before Thorp moved from UCLA to MIT.
At MIT, Thorp found a hotbed of intellectual creativity that was quietly revolutionizing modern society. The job he stepped into, the coveted position of C.L.E. Moore Instructor, had previously been held by John Nash, the math prodigy who'd won the Nobel Prize in economics in 1994 for his work on game theory, a mathematical approach to how people compete and cooperate. (He later became known as the subject of "A Beautiful Mind," the book and movie about the competing forces of his genius and mental illness.)
That first summer in Cambridge, Thorp crunched the numbers on blackjack, slowly evolving what would become an historic breakthrough in the game. Thorp fed reams of unwieldy data into a computer, seeking hidden patterns that he could exploit for a profit. By the fall, he'd discovered the rudimentary elements of a blackjack system that could beat the dealer.
Eager to publish his results, he decided on the prestigious industry journal, The Proceedings of the National Academy of Sciences. The trouble: The journal only accepted papers from members of the academy. So he sought out the only mathematics member of the academy at MIT, Dr. Claude Elwood Shannon, one of the most brilliant, and eccentric, minds on the planet.
Excerpted from The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It by Scott Patterson. Copyright 2010 by Crown Business. Reprinted by Permission of Crown Business, an imprint of the Crown Publishing Group, a division of Random House, Inc.
