Alex's Adventures in Numberland - Alex Bellos [143]
Ed Thorp is now 75 but I suspect he doesn’t look that different from how he looked half a century ago. Slim, with a long neck and concise features, he has a clean-cut college-boy haircut, unpretentious glasses, and a calm, upright posture. After returning from Vegas, Thorp reread the journal article. ‘I saw right away, within a couple of minutes, how you could almost certainly beat this game by keeping track of the cards that were played,’ he remembered. Blackjack is different from, say, roulette, since the odds change once a card has been dealt. The chance of getting a 7 in roulette is 1 in 38 every time you spin the wheel. In blackjack the probability>
first dealt card being an ace is 113. If the first dealt card is an ace, the probability of the second card being an ace, however, is not – it is , since the pack now has 51 cards and there are only 3 aces left in it. Thorp thought there must be a system that turned the odds in the favour of the player. It then became just a matter of finding it.
In a 52-card deck there are 52×51×50×49×…×3×2×1 ways of the cards being ordered. This number is about 8×1067, or 8 followed by 67 zeros. The number is so huge that it is very unlikely that any two randomly shuffled decks will ever have had the same order in the history of the world – even if the world’s population had started playing cards at the Big Bang. Thorp reasoned that there are too many possible permutations of cards for any system of memorizing permutations to be feasible for a human brain. Instead he decided to look at how the house advantage changes depending on which cards have already been dealt. Using a very early computer, he found that by keeping track of the number-five cards of each suit – the five of hearts, spades, diamonds and clubs – a player could judge whether the deck was favourable. Under Thorp’s system, blackjack morphed into a beatable game, with an expected return of up to 5 percent depending on the cards left in the pack. Thorp had invented ‘card-counting’.
He wrote up his theory and submitted it to the American Mathematical Society (AMS). ‘When the abstract came through everybody thought it was ridiculous,’ he remembered. ‘It was gospel in the scientific world that you couldn’t beat any of the major gambling games, and that had rather strong support from the research and analysis that had been done over a couple of centuries.’ Proofs that demonstrate that you can beat the odds at casino games are rather like proofs that you can square the circle – surefire evidence of a crackpot. Luckily, one of the members of the AMS’s submission committee was an old classmate of Thorp’s, and the abstract was accepted.
In January 1961 Thorp presented his paper at the American Mathematical Society’s winter meeting in Washington. It made national news, including the front page of his local paper, the Boston Globe. Thorp received hundreds of letters and calls, with many offers to finance gambling sprees for a share of the profit. A syndicate from New York was offering $100,000. He called the number on the New York letter and the following month a Cadillac pulled up outside his apartment. Out stepped a pint-sized senior citizen, accompanied by two spectacular blondes in mink coats.
The man was Manny Kimmel, a mathematically astute New York gangster and inveterate high-stakes gambler. Kimmel had taught himself enough about probability to know the birthday paradox – one of his favourite things to bet on was whether two people in a group shared the same birthday. Kimmel introduced himself as the owner of 64 parking lots in New York City, which was true. He introduced the girls as his nieces, which probably wasn’t. I asked Thorp if he suspected