How Alan Turing cracked the casinos before Nazi code: Maths genius used equations to assess the chances of winning at roulette before he was tasked with Enigma

He used his genius at maths to crack the Nazis' Enigma code, helping speed up the Allies' victory.

But before that, Alan Turing turned his mind to a less vital but potentially more profitable task – breaking the bank at Monte Carlo.

Almost a decade before his heroic efforts in the Second World War, he used equations to assess the chances of winning at roulette.

Turing's analysis has been unearthed in a letter written 88 years ago while he was a 21-year-old undergraduate at King's College, Cambridge.

He was prompted by tales of the successful gambling past of strip lighting inventor Alfred Beuttell, the father of a close school friend.

Almost a decade before his heroic efforts in the Second World War, Alan Turing used equations to assess the chances of winning at roulette at The Monte Carlo Casino  

He was prompted by tales of the gambling past of strip lighting inventor Alfred Beuttell, who told Turing he devised a 'Monte Carlo' method. Pictured: Roulette table at Monte Carlo casino

Beuttell told Turing he had devised 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, working out the probabilities of winning after 150, 1,520, 4,560 and 30,400 spins. 

His calculations showed it was possible to win 'an unexpectedly large sum' in the short term but the longer the gambler plays, the 'more remote his chances'.

Turing signed off: 'Regards to everyone and please don't feel there's any need to answer these ravings of mine.'

The seven-page handwritten letter, on King's College headed paper, was sent in February 1933 and has remained in the family until now.

It is being sold through London auctioneers Bonhams on September 15 with an estimate of £50,000.

Turing's analysis has been unearthed in a letter written 88 years ago, which is now being sold through London auctioneers with an estimate of £50,000

Also being sold at auction is a photograph of Turing and Beuttell's son Victor with other boys and masters at Sherborne in 1930. It is valued at £4,000

Turing became lifelong friends with Beuttell's son Victor when they were pupils at Sherborne School in Dorset in the late 1920s. 

They spoke on the phone the evening 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 cracking of Enigma.

Matthew Haley, Bonhams head of books and manuscripts, said: 'From the letter you really get the sense that Turing was enjoying himself doing all these calculations.

'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.'

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