Fortune's Formula (10 page)

In the more realistic case where the inside tips are not always right, an equivocation term must be deducted, and the true information rate is less than 3 bits per race. With less-than-totally-reliable tips, the optimal gambler’s wealth grows more slowly.

E
=
mc
²
implies that the merest speck of matter contains enough energy to power a city, or incinerate it.
G
_max
=
R
claims that a few bits can generate a return beyond the dreams of any portfolio manager or loan shark. A single bit (per year, or per any time unit you choose)—such as one giving certain word of the outcome of a fixed prizefight at even odds—would allow a bettor to double his money. That is a 100 percent return for 1 bit.

To translate
G
_max
=
R
into the language of Wall Street: A bit is worth 10,000 basis points.

I
N ITS BROADEST MATHEMATICAL FORM,
Kelly’s betting system is called the “Kelly criterion.” It may be used to achieve the maximum return from any type of favorable wager. In practice, the biggest problem is finding those rare situations in which the gambler has an advantage. Kelly was aware that there is one type of favorable bet available to everyone: the stock market. People who are willing to “gamble” on stocks make a higher return, on the average, than people choosing safer investments like bonds and savings accounts. Elwyn Berlekamp, who worked for Kelly at Bell Labs, remembers Kelly saying that gambling and investment differ only by a minus sign. Favorable bets are called “investments.” Unfavorable bets constitute “gambling.”

Kelly hints at an application to investing in his 1956 paper.

“Totality of inside information available to the investor” may suggest insider trading. Shannon was once asked what kind of “information” applied to the stock market. His slightly alarming answer was “inside information.”

The informational advantage need not be an illegal one. An investor who uses research or computer models to estimate the values of securities more accurately than the rest of the market may use the Kelly system. Yet it may be worth acknowledging that a certain ethical ambiguity has always been attached to Kelly’s system. In describing his system, Kelly resorted to louche examples (rigged horse races, a con game involving quiz shows…). The subtext is that people do not
knowingly
offer the favorable opportunities that the Kelly system exploits. The system’s user must keep quiet about what he or she is doing. Just as a steam engine cannot move when all temperature differences are eliminated, the Kelly gambler must stop when his private information becomes public knowledge.

The story of the Kelly system is a story of secrets—or if you prefer, a story of entropy.

Some AT&T executives detected an unwholesome moral tone in Kelly’s article. He had submitted it to the
Bell System Technical Journal
. The executives worried about the title, “Information Theory and Gambling.” They feared the press might get hold of the article and conclude that Bell Labs was doing work to benefit illegal bookies. That was still a touchy subject with AT&T. Bookies were still big customers.

Kelly played good employee. He changed the title of his paper to the understated “A New Interpretation of Information Rate.” Shannon refereed the paper, and it appeared under that title in the July 1956 issue.

Kelly didn’t mention TV quiz shows in his article. He had no way of knowing that many of the contestants were being fed advance knowledge of questions or answers. (The quiz show scandal broke in 1958.) Kelly’s chosen metaphor, of a racetrack wire service, was topical enough in the post-Kefauver era. It too had a significance Kelly probably didn’t appreciate.

J. Edgar Hoover had long denied the existence of a nationwide organized crime syndicate. This stance changed only modestly with the Kefauver hearings. Hoover biographers have theorized that the FBI head felt the Combination was too well connected to eliminate and he preferred not to pick a fight he couldn’t win; that the virulently anti-Communist Hoover harbored sympathy for self-made mob figures, whom he saw as examples of the American capitalist system; that Meyer Lansky or Frank Costello had a photograph of Hoover in a sexual situation with a male friend and were blackmailing him.

The best-supported explanation (it need not exclude the other theories) is this: Hoover and his partner Clyde Tolson would regularly leave the office when the horses were running. They would take a bulletproof car to Pimlico, Bowie, Charleston, or other area racetracks. News photographers snapped Hoover at the $2 betting windows, and Hoover had a form letter he sent irate citizens who complained about his wagering. The letter said he had made a few minimal bets in order not to offend business associates.

In a 1979 book,
The Bureau: My Thirty Years in Hoover’s FBI
, the agency’s William C. Sullivan reported that Hoover “had agents…place his real bets at the hundred-dollar window, and when he won Hoover was a pleasure to work with for days.”

According to FBI sources and staffers of gossip columnist Walter Winchell, Hoover was getting inside tips from Frank Costello. When the mob fixed a race—and this apparently meant with close to 100 percent certainty—Costello passed the name of the winning horse to Hoover by way of Winchell, a mutual friend. These tips let Hoover make a small fortune—and presumably left him disinclined to pursue Costello and his business partners.

After Hoover’s 1972 death, Costello told a Justice Department chief: “You’ll never know how many races I had to fix for those lousy bets of his.”

I
N
J
ANUARY
1961
the American Mathematical Society held its winter meeting in Washington. Ed Thorp was there to present a version of the paper Shannon submitted to the National Academy. Since this paper was not for the National Academy, Thorp titled it “Fortune’s Formula: A Winning Strategy for Blackjack.”

That title caught the eye of an AP reporter in Washington. Thorp did an impromptu interview and photo session. The morning of January 21, a feature appeared on the front page of
The Boston Globe
and in papers nationwide.

Gamblers from all over the country began calling Thorp’s hotel to ask for copies of his paper. Some of the callers wanted to buy Thorp’s blackjack system or take private lessons. Others wanted to finance Thorp in the casinos for a share of the profit.

The messages continued after he returned home. Vivian filled every page of a legal pad with messages. Then she said enough and refused to take any more. The Pavlovian connection between the telephone ringing and family discord affected the Thorps’ baby daughter. She burst into tears whenever the phone rang.

At MIT Thorp shared a group of six secretaries with his department. Thorp got more mail from the blackjack paper than all the other mathematics instructors had gotten for every paper they ever published put together. The university told Thorp they could not permit the secretaries to deal with any more gambling correspondence. In all, Thorp received thousands of letters.

Thorp discussed the situation with Shannon. Thorp wanted to accept one of the offers. It would be fun to try the blackjack system out in a real casino. Shannon suggested that Thorp use Kelly’s formula to decide how much to bet. Thorp read Kelly’s 1956 article and instantly appreciated its relevance. It told exactly how much to bet, depending on how favorable the deck was. Despite the Kelly formula’s theoretical protection against ruin, both Shannon and Thorp realized that there are many variables in casino play. They agreed that Thorp needed to make sure his financial backer could afford to lose the money he put up. Some of the offers had the reek of desperation.

Thorp decided that the best offer was the biggest one. A syndicate of two wealthy New Yorkers was offering $100,000 to take on the Nevada casinos. Thorp dialed the number on the letter and asked to speak to Emmanuel Kimmel.

One Sunday in February 1961, a midnight blue Cadillac pulled up to the Thorps’ Cambridge apartment. Driving the car was a dazzling young blonde woman in a mink coat. Next to her was another blonde, also in a mink coat. Not until the women got out of the car was it evident that there had been someone sitting between them. The someone was “Manny” Kimmel.

Kimmel was an elderly, gnomelike man standing about five feet five. He wore a long cashmere coat and had a ruddy face topped with a shock of white hair. He introduced the two blondes as his nieces. He did not seem to be joking.

The minks and cashmere were justified by the bitter weather. Kimmel complained that the snow in New York had just cost him $1.5 million. Asked how, he explained that he owned sixty-four parking lots. They had been snowed out for two days.

I hope you’ve been practicing, Kimmel said. Thorp said he had. Kimmel pulled out a deck and began dealing hands to Thorp.

The goal in blackjack is to get a hand whose cards total more than the dealer’s hand without exceeding 21. A player who exceeds 21 loses.

In a casino, there can be one to six players. Each places a bet and is dealt two cards facedown. The dealer also deals himself a hand, one card faceup. Numbered cards count as their face value. Tens and all the face cards count as 10. Aces can count as 1 or 11, whichever is better. Should you get a 10-value card and an ace on the initial deal, that is “blackjack.” A player getting blackjack wins—unless the dealer also has blackjack for a tie. A winning blackjack pays off 3 to 2.

Otherwise, players have the option of asking for more cards, one at a time. These additional cards are dealt faceup. A player may keep “hitting” as long as her hand is less than 21. Once her hand totals over 21, she loses. The trick is to know when to stop. The decision should take account of the dealer’s faceup card. Unlike the players, the dealer is required to follow a fixed strategy. He must draw cards until his hand totals 17 or more.

Say you’ve got a queen and a six for a total of 16. That’s not a very good total. By drawing another card, you risk going bust (there are all those tens, and a ten would take your total to 26). Computer studies have shown what to do for every possible point total and faceup dealer card. When the dealer has a seven showing, you’re better off hitting your 16 hand. A normal winning hand pays even money.

Kimmel appeared to be interested only in finding out whether Thorp’s system worked. He showed no interest in Thorp’s paper, and as far as Thorp could tell, the math was “Greek” to Kimmel. Kimmel demanded that they play each other.

Thorp used a “ten-count” system, different from the five-count detailed in the article. Though each five affects the odds more than each ten, there are 16 “tens” (including the face cards) in the deck, making it easier to identify favorable or unfavorable conditions. They played the rest of the day and had a rematch the following day.

Kimmel said he could back Thorp only on the condition that he and his partner get a cut of the profits. Kimmel said their cut would be 90 percent.

Thorp agreed to that. He was more interested in proving the concept than in making a lot of money. Thorp was also worried about cheating. He had concluded that a cheating dealer was the only thing that might upset the system. Kimmel, an experienced gambler, assured Thorp that he was an expert at spotting cheaters.

To seal the deal, Kimmel dipped into a deep cashmere pocket and pulled out a handful of jewels. From this he extracted a pearl necklace and presented it to Vivian.

Thorp flew to New York each Wednesday to play cards against Kimmel. He won regularly, convincing Kimmel of his playing skills and the merit of the counting system. Kimmel occasionally presented Thorp with the gift of a salami.

During one of these meetings, Thorp met his other backer, Eddie Hand. Hand was a dark-haired heavyset man in his late forties, maybe five feet nine, with a taste for flashy, bright-colored leisure wear. He owned a trucking business that shipped cars and trucks for Chrysler. He did a lot of negotiating with Teamsters. Hand had a perpetually irritated, cranky tone to his voice. He was irresistible to women.

Hand had been married to “Gorgeous Gussie” Moran, a 1940s tennis star who shocked Wimbledon by wearing outfits that exposed the fringe of her lace panties. Hand was a decent tennis player himself. Moran had said she was astounded that Hand could play tennis all day and then have sex all night.

Thorp was present once when Hand was leafing through
Time
magazine on a plane and suddenly grew choked up over an item about a Chilean copper heiress remarrying. Hand had dated her.

There was a lot that Thorp didn’t know about Manny Kimmel.

Kimmel was then one of the biggest bookies in New York City. “What was he a bookie for? For everything!” claimed Eddie Hand in an interview. “Vegas, football, baseball, the horses. Manny was great at talking people into betting. He could always find a sucker.”

Kimmel’s territory covered the East Coast horse tracks and the sports book operations at the El Rancho Hotel in Las Vegas. “At Saratoga in the old days he used to straighten out the jockeys,” explained Hand.
Straighten out the jockeys
means to fix the race. Kimmel was the living embodiment of John Kelly’s new interpretation of the information rate.

In the 1960s, Kimmel took bets from one of the highest rollers of all, Texas oil tycoon H. L. Hunt. Hunt had won an oil field in a poker game. As a billionaire he still had a taste for risk, reportedly betting as much as a million dollars on a football game.

The FBI had been following Kimmel’s career for years. “Kimmel is known to be a lifetime associate of several internationally known hoodlums,” read one 1965 FBI memo. “He is an admitted gambler and consorts with many well known gamblers throughout the United States.”

Kimmel also knew more about card-counting than he let on. Kimmel had a gambling buddy named Joe Bernstein. In 1960 Bernstein found himself in a mob-run club in San Francisco. Bernstein owed his bookie $3,000. He had $1,500 in his pocket. While deciding what to do, Bernstein watched a game of blackjack. He noticed that three-quarters of the deck had been dealt and not one ace had turned up. Bernstein bet two hands of $500 each. He won both (one was blackjack), and had enough to pay off the bookie.

As a born gambler, Bernstein felt he had discovered the secret of life itself. He soon determined that the situation he had happened onto—having all the aces in the last quarter of the deck—was extremely rare. After a couple of days of mixed luck trying to exploit the idea, Bernstein called Kimmel in New York to tell him of his momentous discovery. Bernstein and Kimmel went to Las Vegas and experimented with various counting systems. Then Kimmel heard about Thorp’s paper. A mathematician was just what they needed to devise a practical strategy.

Kimmel divulged nothing of this to Thorp. He also had his people run a background check on Edward and Vivian Thorp to make sure they weren’t grifters.