Fortune's Formula (14 page)

“H
OW THE HECK
do I know how he does it? I guess he’s got one of them mathematical minds or photographic memories, or something.”

The topic was Ed Thorp. The speaker was Cecil Simmons, casino boss at the Desert Inn. Simmons was speaking by phone to one of his competitors, Carl Cohen of the Sands.

“All I know,” Simmons went on, “is he wrote a book that teaches everyone how to win every time they play blackjack. I’m just telling you, this book-learning SOB has ruined us.” Simmons said they were “out of the blackjack business.” Another Las Vegas veteran said
Beat the Dealer
was the worst thing to hit the gambling business since the Kefauver hearings.

Simmons organized a conclave of casino bosses and representatives of Eastern crime families. It was held in a private room at the rear of the Desert Inn. As casino manager Vic Vickrey remembered it, one hard-boiled type had no doubt about the solution to their mutual problem: “Break a few legs, and I’ll betcha the word will get out real quick that it just ain’t healthy to try to play that count thing in our joints…that is, unless they like hospital food.”

The meeting’s chairman objected that they didn’t do things that way anymore. They were legitimate businessmen and needed to think like legitimate businessmen.

Another suggestion was to call in “Deuce-Dealing Dottie.” She was the best second-dealer in the business.

The calmer minds present appreciated that it was no longer practical for casinos to identify every counter. There were too many. Instead the group resolved to change the rules of blackjack.

The change applied to “doubling down,” an often favorable option many casual tourists don’t understand well enough to use. Under the revised rules, the player could double down only on “hard” totals of 10 or 11 (“hard” meaning no aces). Doubling down after splitting a pair would be forbidden. These changes would give the house an edge over the basic strategy player and make it more difficult for card-counters to achieve an advantage.

In April 1964, the Las Vegas Resort Hotel Association announced the new official rules of blackjack.

The new rules were like breaking everyone’s legs. People who had no intention of counting cards understood that the game was less advantageous than it had been. Blackjack play was down, tips to dealers were way down. Dealers grumbled to management. Within weeks casinos reverted to the old rules.

The casinos continued to experiment. Most settled on a solution originally known as the “professor stopper.” That term was in honor, more or less, of Thorp. The professor stopper, or “shoe,” is a holder that allows dealers to shuffle multiple decks together. Anywhere from two to eight decks are shuffled together. Cards are dealt from the combined deck. The dealer reshuffles when she comes to a faceup card that has been placed, typically, about fifty cards from the bottom.

Use of multiple decks makes counting more difficult and less profitable. Because the end cards are never dealt, the concentrations of good cards that occasionally occur at the end of the deck never come into play.

Thorp once computed that he could make $300,000 a year playing blackjack under ideal conditions. That’s assuming he could play forty hours a week, raising and lowering his bets between the table limits with no interference from the casinos.

No interference was becoming an unrealistic assumption. While playing at one Las Vegas strip casino, Thorp was offered a drink. He asked for coffee with cream and sugar. After drinking it, he noticed he was having problems concentrating. Thorp staggered up from the table and got to his room. His eyes were dilated. It took about eight hours for the effect to wear off.

The next day Thorp returned to the same casino. He was offered another drink. He asked for water this time. He sipped it carefully. “It tasted like they’d dumped a box of baking soda in it. Had I drunk more I would have been finished because just the few drops on my tongue were enough to wipe me out for the night.”

“I know of three beatings,” Thorp said. “One well-known blackjack card-counter had a lot of his face caved in. A guy I know had his arms held, and every time he tried to catch his breath they’d punch him in the solar plexus again.”

The latter player had been told to leave. He ignored the warning and continued playing. Thorp made it a policy to leave when asked on the hopeful theory that the thugs would always give one “fair” warning before getting violent.

Ed Reid and Ovid Demaris’s
The Green Felt Jungle
, an exposé of casino corruption published the year after
Beat the Dealer
, confirms that the casinos settled disputes with gangland violence well into the 1960s. Beatings often took place in the counting room, a soundproof room “ideal for such torture.” Reid and Demaris tell of a cheating dealer at the Riviera. Two casino enforcers forced him to place his closed fists on a table. Another used a lead-encased baseball bat to smash the man’s fists. He was dragged past the tourists in the casino. A mob doctor bandaged but did not set the hands. The man was driven to the edge of town. The thugs took his shoes off and pushed him out of the car. “Now you son of a bitch,” one thug said, “walk to Barstow. No goddamn hitchhiking, either. We’re gonna check on you all the way.”

J
OHN
K
ELLY
, J
R.,
published nothing more about gambling. As far as anyone knows, he never tried to use
G
_max
=
R
to make money. His close friend Ben Logan is not even certain that Kelly ever used his football circuits to place bets.

Kelly had become an important man at Bell Labs. He was promoted to head of the information coding and programming department. He applied Shannon’s theory to the problem of correcting for echo effects in satellite transmissions. Kelly devised a block diagram compiler that took a simple logic diagram and produced working code.

And he taught a computer to sing. This was an IBM 704, the model Thorp had used for his first blackjack studies. In 1961 Kelly and Carol Lochbaum demonstrated their new voice synthesis system by making a recording of the machine reciting a passage from
Hamlet
and singing the song “Daisy Bell,” better known as “Bicycle Built for Two.”

An occupational hazard of voice synthesis research is the “parrot effect.” Through long exposure, the researcher is better able to understand his pet creation’s words than anyone else is. Manfred Schroeder recalled proudly demonstrating a voice synthesis system to two Bell Labs executives in the mid-1950s. “They were very polite, but I’m pretty sure that what my machine was saying was unintelligible to them.”

Having a computer “sing” a popular song is cheating slightly—the familiar tune cues listeners to the words. It is thus easier to synthesize an acceptable singing voice. This fact was lost on journalists, who judged the singing computer more newsworthy.

John Pierce knew the British science fiction writer Arthur C. Clarke. Clarke visited Bell Labs in the mid-1960s, trying to get AT&T’s cooperation for the film that would become Stanley Kubrick’s
2001: A Space Odyssey
. It was Clarke and Kubrick’s idea that the film would show futuristic technology branded with logos of contemporary companies, such as an AT&T videophone. Pierce amused Clarke by playing Kelly’s recording of “Bicycle Built for Two.”

AT&T’s ever-cautious executives decided they didn’t want to have anything to do with the film. Their concern was that the technology shown might be wrong or never come to pass, and that could embarrass AT&T. Clarke remembered the Kelly recording when he was writing the screenplay for
2001
. In the movie, the homicidal computer HAL is unplugged and reverts to a childish state, singing the same song Kelly’s computer did.

Clarke and Kubrick assumed that by the year 2001, people like Kelly would have achieved their goal of synthesized voice indistinguishable from a human’s. They reasoned that HAL should
not
sound like a movie robot. Actor Douglas Rain was cast to voice HAL’s lines, including the rendition of “Bicycle Built for Two.”

By the year 2001, digital speech was ubiquitous on computers, telephones, and the Internet. It provided a voice for one of the world’s most distinguished physicists. In a way, the AT&T executives were right, though. The quality of those voices had advanced slowly. It still couldn’t be mistaken for a human speaker.

A legend has arisen that Clarke created the name “HAL” by rolling each letter’s place in the alphabet one position back from “IBM.” It was to IBM that John Kelly was going. On March 18, 1965, he and several colleagues took the Bell Labs limo into Manhattan for a meeting at the computer company’s offices. Walking along the street, Kelly held his hand to his head. “Wait a minute!” he cried out. Moments later, he slumped to the sidewalk. He was dead of a brain hemorrhage at the age of forty-one.

Kelly would thereafter be known for an incidental connection to a movie he never saw—and for the gambling formula that would carry his name on to posterity.

P
AUL
S
AMUELSON LOVED
H
ARVARD.
The love was not entirely requited. By the age of twenty-five, Samuelson had published more journal articles than his age. This distinction seemed to count little at Harvard, where Samuelson was boxed into a low-paying post as an economics instructor. Tenure was a remote prospect. One of Samuelson’s colleagues had been passed over for tenure because he had a disability. The disability was that he came from Kansas. Samuelson came from Gary, Indiana. The Kansas guy was not Jewish. Samuelson was.

In 1940 Samuelson accepted an offer to move three miles to the other end of Cambridge. As some saw it, MIT was a step down from Harvard. MIT was a science and engineering school, hardly known for its economics department, nor for training America’s economic and political leaders. In an era when Ivy League schools were often quietly anti-Semitic, it was an index of MIT’s outsider status that they were willing to hire a Jew just because he was smart.

MIT’s technical focus was a good match for Samuelson’s gifts. Samuelson chose to view economics as a mathematical science. That was an unconventional approach at the time. From Adam Smith through John Maynard Keynes, economics had been mostly talk. At Harvard, economics was talk. At MIT, Samuelson made it math.

Samuelson was as comfortable with differential equations as a physicist. His papers are full of “theorems,” as he called his results. To this Samuelson wedded an incisive wit that set his lectures and publications apart from the great, gray mass of economist-speak. Samuelson was a superb teacher. Probably no other economist of the day produced such a succession of brilliant followers as Samuelson did at MIT. His influence went far beyond Cambridge. In 1948 Samuelson channeled his encyclopedic knowledge and verbal flair into an “Economics 101” textbook. Titled simply
Economics
, it has been a perennial bestseller. “Let those who will, write the nation’s laws,” Samuelson once said, “if I can write its textbooks.”

Samuelson was a Democrat. He gave economic tutorials to presidential candidate Adlai Stevenson and President John Fitzgerald Kennedy. He remained a trusted adviser throughout the Camelot era. By the mid 1960s, Samuelson’s influence on the economic profession was unrivaled, and he had almost single-handedly raised the prestige of MIT’s economics department up to his own lofty level.

About 1950, Samuelson became interested in warrants. A warrant is a stock option issued by a company to allow purchase of its own shares. Some believed it was easier to make money in warrants than stocks. Samuelson shelled out $125 for a yearly subscription to
The RHM Warrant and Low-Price Stock Survey
. This purported to give profitable market tips. Samuelson figured that if he could make just one decent killing a year, he’d be in fine shape.

The service did not prove to be the lazy man’s road to riches. Samuelson learned much from his failure to strike it rich. If the warrant tips were any good, he reasoned, the service would sell for a lot more than $125. And why
should
the tips be any good? Why would the owner of a warrant sell it to you for anything less than its true value?

In 1953 a British statistician named Maurice Kendall gave a talk to the Royal Statistical Society in London. The subject was a dry one even for a statistical society: the weekly wheat prices in the Chicago commodity markets (from 1883 through 1934, excluding 1915 to 1920). Kendall wanted to see how well one could predict future wheat prices from past history.

Kendall’s unexpected conclusion was that you couldn’t predict wheat prices at all. He said that wheat prices wandered aimlessly, “almost as if once a week the Demon of Chance drew a random number…and added it to the current price to determine next week’s price.”

Kendall suggested that the same principle might apply to stock prices. The people who
thought
they could predict the stock market (that would be just about any broker, adviser, or money manager) were deluding themselves.

Kendall’s words were branded “nihilism.” They were said to “strike at the very heart of economic science.” Deconstruction: Economic science is about showing how things are predictable. Things
have
to be predictable.

Samuelson heard of Kendall’s ideas through a friend who attended the lecture. As a natural contrarian, Samuelson delighted in Kendall’s nihilism. He decided to see how far he could go with the hypothesis that stock and commodity prices aren’t predictable. He was reinforced in this project by a postcard he received from Leonard (“Jimmie”) Savage.

Savage was another statistician, an American one, with Coke-bottle-thick glasses and a taste for bow ties. He was then working at the University of Chicago. Savage used “Leonard” in his publications. Everyone knew him as “Jimmie.” He was also known for living up to his last name. Anyone who substantially disagreed with Savage was, in his freely offered opinion, stupid. It was rumored that Savage’s peripatetic career had something to do with his habit of informing associates of their stupidity.

In 1954 Savage was looking for a book on a library shelf. He came across a slim volume by Louis Bachelier. The thesis of Bachelier’s book was that the changes in stock prices are completely random. Savage sent postcards to a number of people he thought might be interested, including Samuelson. On the cards Savage wrote, “Ever hear of this guy?”

The answer was no. The world had forgotten Louis Bachelier. His 1900 thesis, “A Theory of Speculation,” argued that the day-to-day changes in stock prices are fundamentally unpredictable. When a stock’s price reflects everything known about a company and all reasonable projections, then future changes in price should be, by definition, unpredictable. A stock does not go up just because it lives up to everyone’s expectations. It goes up when it does better than people anticipated. It goes down when it does worse than predicted. A stock’s price should therefore vary randomly, subject to the buffeting of a constant stream of unpredictable news events, good and bad.

This implies that someone who buys a stock and sells it almost immediately is as likely to have a loss as a gain. Bachelier wrote that “the mathematical expectation of the speculator is zero.”

The thesis got a middling grade. Bachelier spent the rest of his career in such obscurity that virtually nothing is known of his life, save that he was born in 1870 and died in 1946. Bachelier died a decade before his rediscovery by Savage and (especially) Samuelson would make him one of the most influential figures in twentieth-century economic thought.

Ironically, the unpredictability of stock prices makes them somewhat predictable—in a statistical sense. Bachelier believed that stock prices follow a random walk. This term refers to a classic exercise in statistics classes. A drunk has fallen asleep at a lamppost. Every now and then he rouses himself, staggers a few steps in a random direction, and collapses for a nap. The process repeats indefinitely. After many stages of this aimless journey, how far is the drunk from the lamppost?

You might think there’s no possible way of telling. And of course, there’s no way of telling exactly. You can however calculate how far the drunk gets from the lamppost, on the average.

Imagine a crowd of drunks, all starting at the same lamppost and all moving randomly as described (ignoring collisions). The overall distribution of the crowd will remain centered on the lamppost. That’s because nothing is “pushing” the wandering drunks in any particular direction. All directions are the same to them. Over time, the crowd diffuses outward in all directions. This is nothing more than the familiar observation that when you’re lost and wandering aimlessly, you tend to get farther and farther from where you started.

Should you follow the paths of particular drunks, you find that they do a lot of backtracking and moving in “circles.” The few drunks who end up far from the lamppost do so because they happen to move in about the same direction for many legs of their journey, approximating a straight-line journey. Since each leg’s direction is chosen at random, this is unlikely, like a run of the same number in roulette.

The crowd’s
average
distance from the lamppost increases with time. More exactly, this average distance increases with the square root of time. If it takes an hour, on average, for a drunk to wander a block away from the lamppost, it will take four hours on average to wander two blocks from the lamppost, and about nine hours to wander three blocks.

Random walks happen in many contexts. As we’ve already seen, the fluctuations of a bettor’s bankroll in a game of chance constitute a random walk (a one-dimensional random walk, since wealth can only move up or down). With time, the gambler’s wealth strays further and further from its original value, and this eventually leads to ruin.

At about the time Bachelier was writing, Albert Einstein was puzzling over Brownian motion, the random jitter of microscopic particles suspended in a fluid. The explanation, Einstein surmised, was that the particles were being hit on all sides by invisible molecules. These random collisions cause the visible motion. The mathematical treatment of Brownian motion that Einstein published in 1905 was similar to, but less advanced than, the one that Bachelier had already derived for stock prices. Einstein, like practically everyone else, had never heard of Bachelier.