He used his math genius to crack the Nazis’ Enigma code, helping to hasten the Allied victory.

But before that, Alan Turing turned to a less vital but potentially more profitable task: going broke in Monte Carlo.

Almost a decade before his heroic efforts in World War II, he used equations to gauge the odds of winning at roulette.

Turing’s analysis was discovered in a letter written 88 years ago when he was a 21-year-old student at King’s College Cambridge.

It was inspired by the stories of the successful playing past of the inventor of strip lighting Alfred Beuttell, the father of a close school friend.

It was inspired by tales from the gaming past of the inventor of strip lighting Alfred Beuttell, who told Turing that he had devised a “Monte Carlo” method. Pictured: roulette table at the Monte Carlo casino

Beuttell told Turing that he designed his own “Monte Carlo” method and lived off his casino winnings for a month on the French Riviera.

Turing put Beuttell’s system to the test, calculating the odds of winning after 150, 1,520, 4,560, and 30,400 laps.

His calculations showed that it was possible to win “a surprisingly large sum” in the short term, but the longer the player plays, the lower “his chances.”

Turing signed: “Hi everyone and please don’t feel pressured into responding to my ravings.”

The seven-page handwritten letter, on King’s College letterhead, was sent in February 1933 and has remained in the family to this day.

It was sold by London auctioneer Bonhams on September 15 with an estimate of £ 50,000.

Turing’s analysis was discovered in a letter (pictured) written 88 years ago, which is now sold by London auctioneers with an estimate of £ 50,000

A photograph of Turing and Beuttell’s son, Victor, with other boys and masters at Sherborne in 1930, is also auctioned. It is valued at £ 4,000.

Turing became a longtime friend with Beuttell’s son, Victor, while they were students at Sherborne School in Dorset in the late 1920s.

They spoke on the phone the day before Turing’s suicide in 1954 following his prosecution for homosexual acts, then illegal in Britain.

The Queen granted him a posthumous pardon in 2013. Turing was played by Benedict Cumberbatch in the 2014 film The Imitation Game about the Enigma Crack.

Matthew Haley, responsible for Bonham’s books and manuscripts, said: “From the letter, you really get the impression Turing was having fun doing all these calculations.

“In a polite way, it seems his conclusion was that Beuttell’s success was beginner’s luck. It underscores Turing’s fascination with odds … although I don’t imagine Turing would have played roulette in Monte Carlo. ‘

A photograph of Turing and Victor with other boys and masters at Sherborne in 1930 is also sold. It is valued at £ 4,000.