# Lost Letter Reveals Mathematician Alan Turing Roulette System Analysis

Posted on: September 6, 2021, 03:22h.

Last updated on: September 6, 2021, 11:24h.

British mathematician and codebreaker Alan Turing is sometimes credited with building the world’s first computer. But three years before he developed his Turing Machine, he turned his formidable intellect to gambling. And a decade before he famously helped crack the Nazi’s Enigma code during World War II, he was trying to crack roulette.

In a previously unknown letter written by Turing in 1933 to Alfred Beuttell, the inventor of strip lighting, Turing lays out detailed mathematical analysis of Beutnell’s personal roulette system.

The seven-page handwritten letter is now up for auction at Bonhams in London where it’s expected to fetch around £50,000 (\$70,000).

Turing was a 21-year-old undergraduate at Cambridge University when he responded to Beutnell’s request for his opinion on the gambling system.

Beutnell, then 88, claimed he played the system as a young man at the Grand Casino Monte Carlo and was able to live off his winnings for a month on the French Riviera.

## Flaws in the System

Although Beutnell’s original letter detailing his system is lost, from the response it appears to be a variation on the Martingale betting system — or at least the expected outcome is similar — and Turing isn’t sold on it.

“For short runs one most probably wins or else one loses an unexpectedly large sum. As the length of run is increased, the chances of winning becomes more remote,” Turing wrote in his analysis.

Turing describes how he used equations to figure out the diminishing probability of winning after 150, 1,520, 4,560 and 30,400 spins.

“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,” said Matthew Haley, head of books and manuscripts at Bonhams.

Turing letters with math content are pretty rare, and what makes this one so extraordinary and attractive is the gambling aspect, although I don’t imagine Turing would have been at a roulette wheel in Monte Carlo,” Haley continued.

“Although his analysis of Beuttell’s gambling system was conducted in a spirit of fun, it does underline Turing’s fascination with probability, and its application to cryptology. This was key to the decryption work at Bletchley Park for which he is, of course, best known.”

## Enigma and Downfall

Bletchley Park was an English country house that became the center of the British ‘Ultra’ Intelligence code-breaking effort during World War II. Turing led the team of cryptanalysts that cracked the German “Enigma” cipher.

This allowed the British to intercept German coded messages, which historians agree shortened the war in Europe, possibly saving hundreds of thousands of lives.

In 1951, Turing was prosecuted for “gross indecency” after admitting to his homosexuality, a crime at the time in the UK. Given the choice of prison or chemical castration, he chose the latter. Two years later, he committed suicide.

In 2009, the British government publicly apologized for its treatment of the man who is now revered as the father of modern computer science. The Queen granted him a posthumous pardon in 2013.