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The optimal betting strategy according to this Bell Labs scientist

The optimal betting strategy according to this Bell Labs scientist


Say there is a bet which involves flipping a coin. Tails and you make a whopping 150%, that is a $10 bet becomes $25. You are allowed to repeat the bet as many times as you like for an hour.

The question is, how much money should you be betting each time? The more you bet the more you can potentially make, but you also stand to lose it all.

In one experiment that offered participants to bet money on a similar coin flip bet, 30% of the participants lost their entire stake. No more than 21% won the maximum allowable amount. The results were troubling considering that the participants were students in economics and financial analysts. They had not followed the optimal betting strategy.

Meet the Kelly Criterion

John Larry Kelly Jr was a scientist at Bell Labs, at the time one of the most prestigious scientific research centers. Prior to that he was a WWII air force pilot and survived a plane crash into the ocean. He was a chainsmoker and had a strong love for firearms. He was believed to be the smartest person at Bell Labs after Claude Shannon, a key contributor to the development of the computer and the father of information theory.

In 1955, A new show called The $64,000 Question was aired on American television. The show became hugely popular and inspired many copycat shows. Kelly read in the news about a scam. Some viewers of The $64,000 Question were betting on which participants would win the show. Because the show was produced in New York and aired live there it was delayed three hours in California. One Californian gambler would learn the winners by phone and place his bets before the California airing of the show.

Kelly realized a gambler with such inside information could use some of Shannon’s equations to achieve the highest possible return. Persuaded by Shannon, Kelly proceeded to publish his findings under the title “Information Theory and Gambling”. Bell Labs didn’t appreciate the title, and Kelly’s article was finally published in 1956 under the title “A New Interpretation of Information Rate” in the Bell System Technical Journal.

Kelly introduced his idea as a system for betting on fixed horse races. A gambler gets insider information of the races’ final result. Naturally, a gambler would put everything on the horse that is supposed to win. The problem is the gambler is certain to lose everything on the first case of wrong information.

Kelly suggested, a smart gambler would bet a small amount on each race. This strategy diminishes somewhat the advantage insider information gives, but offers important protection against big loses.

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