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What’s luck got to do with it? The maths of gambling


No one can predict the future, but the powers of probability can help. Armed with this knowledge, a high-school mathematics education and £50, I headed off to find out how Thorp, and others like him, have used mathematics to beat the system. Just how much money could probability make me?

When Thorp stood at the roulette wheel in the summer of 1961 there was no need for nerves – he was armed with the first “wearable” computer, one that could predict the outcome of the spin. Once the ball was in play, Thorp fed the computer information about the speed and position of the ball and the wheel using a microswitch inside his shoe. “It would make a forecast about a probable result, and I’d bet on neighbouring numbers,” he says.

Thorp’s device would now be illegal in a casino, and in any case getting a computer to do the work wasn’t exactly what I had in mind. However, there is a simple and sure-fire way to win at the roulette table – as long as you have deep pockets and a faith in probability theory.

A spin of the roulette wheel is just like the toss of a coin. Each spin is independent, with a 50:50 chance of the ball landing on black or red. Contrary to intuition, a black number is just as likely to appear after a run of 20 consecutive black numbers as the seemingly more likely red.

This randomness means there is a way of using probability to ensure a profit: always bet on the same colour, and if you lose, double your bet on the next spin. Because your colour will come up eventually, this method will always produce a profit. The downside is that you’ll need a big pot of cash to stay in the game: a losing streak can escalate your bets very quickly. Seven unlucky spins on a £10 starting bet will have you parting with a hefty £1280 on the next. Unfortunately your winnings don’t escalate in the same way: when you do win, you’ll only make a profit equal to your original stake. So while the theory itself is sound, be careful. The roulette wheel is likely to keep on taking your money longer than you can remain solvent.

With that in mind, I turned my back on roulette and followed Thorp into the card game blackjack. In 1962 he published a book called Beat the Dealer, which proved what many had long suspected: by keeping track of the cards, you can tip the odds in your favour. He earned thousands of dollars putting his proof into practice.

The method is now known as card counting. So does it still work? Could I learn to do it? And is it legal?

“It’s certainly not illegal,” Thorp assures me. “The casino can’t see inside your head – yet.” What’s more, after a brief tutorial, it doesn’t sound too difficult. “If you went into any casino that had basic blackjack rules, learned the method of card counting that I’ve taught you, you’d have a modest advantage without much effort,” says Thorp.

Follow your curiosity and read the rest.