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Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
Kelly betting or proportional betting is an application of information theory to investing and gambling. Its discoverer was John Larry Kelly, Jr. Part of Kelly's insight was to have the gambler maximize the expectation of the logarithm of his capital, rather than the expected profit from each bet. This is important, since in the latter case ...
John Larry Kelly Jr. (December 26, 1923 – March 18, 1965), was an American scientist who worked at Bell Labs. From a "system he'd developed to analyze information transmitted over networks," from Claude Shannon's earlier work on information theory , he is best known for his 1956 work in creating the Kelly criterion formula.
In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing. It was named and first discussed by Edward O. Thorp in 2008. [1]
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A betting strategy (also known as betting system) is a structured approach to gambling, in the attempt to produce a profit.To be successful, the system must change the house edge into a player advantage — which is impossible for pure games of probability with fixed odds, akin to a perpetual motion machine. [1]
In Kelly's paper the thing he refers to as a "criterion" is the idea that at every bet the gambler should maximise the expected value of the logarithm of their capital. I think this is probably what is meant by "Kelly criterion" -- which means that the Kelly criterion is not in fact a formula at all.
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