Roulette Beginner’s Luck: Alan Turing’s Casino Math

Perhaps the best roulette strategy is to rely on beginner's luck, chase the big wins and walk away as soon as you hit the jackpot

Pop Culture

Mathematician Alan Turing is best known for cracking the Nazi Enigma code that led to the end of the Second World War – yet the British math genius also applied his knowledge to many other conundrums.

One of these was calculating the chances of winning in the casino game roulette.

These days we can easily check the Return to Player and House Edge of classic roulette games before we place our chips in an online casino. But almost 90 years ago players either had to trust they were getting a good deal on the game or calculate the house edge themselves – something that only the biggest brains in the country were able to decipher.

In a letter recently unearthed, Turing wrote to family friend Alfred Beuttell about a strategy of how to break the bank in Monte Carlo casinos. Beuttell had boasted that he was effectively living off his winnings in the French Riviera and was enjoying life there as a result.

But could Beuttell’s success last for ever? In a seven-page letter sent by the then 21-year-old Turing, who was studying at Cambridge University in 1933, it appears as though beginner’s luck was the driving force behind Beuttell’s newfound income stream.

Turing’s conclusions

In the letter Turing explained how he calculated the probability of winning on roulette after 150, 1,520, 4,560 and 30,400 spins. We can assume Beuttell had been playing European roulette, which contains just one green pocket (0) compared to American roulette, which traditionally has both 0 and 00 on the wheel.

Turing discovered that there was some rationale behind Beuttell’s winnings. Effectively, if you play high-stakes roulette and strike lucky early on then you can swiftly build a sizeable pot of chips, which can then fund your lifestyle for weeks to come.

However, Turing also found that over a longer period of time any beginner’s luck that a player relies on eventually runs out, and you are going to lose more than you win.

In effect, the conclusion for Beuttell was that he struck lucky early, rather than he had discovered a roulette tactic that guaranteed wins.

“From the letter you really get the sense that Turing was enjoying himself doing all these calculations,” said Matthew Haley, head of books and manuscripts at Bonhams, where the letter is up for auction.

“In a polite way it appears his conclusion was Beuttell’s success was beginner’s luck. It does underline Turing’s fascination with probability… although I don’t imagine Turing would have been at a roulette wheel in Monte Carlo.”

Alan Turing roulette

Turing’s letter proved that beginner’s luck is what drives mega wins in roulette

What We Can Learn From Turing

While Turing most likely dampened Beuttell’s spirits following his letter, there are certainly some valuable points that online gambling fanatics can take from his calculations.

It turns out that no matter how many spins you play, there is always a house edge. This we know but is still something many gamblers forget when they actually hit the roulette table.

Tactically, there is a way of applying Turing’s findings to a game. As he explains, Beuttell struck lucky early in his casino play. The main roulette tactic, therefore, is to chase the big win at the start of your game, rather than gunning for a systematic gradual build-up of chips.

Over the long-run the house should always win at roulette, which means Beuttell’s best hope of winning was to strike lucky when he had most chips to bet with. And, once a player does hit the jackpot, then this is the time to walk away.

Joseph Ellison

Joseph is a dedicated journalist and horse racing fanatic who has been writing about sports and casinos for over a decade. He has worked with some of the UK's top bookmakers and provides Premier League soccer tips on a regular basis. You'll likely find him watching horse racing or rugby when he isn't writing about sport.

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