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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.
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.
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 ...
The most popular, and mathematically superior, system is the Kelly criterion. It is a formula for maximizing profits and minimizing losses based on payout odds and win probability of the underlying asset. The Kelly criterion is often used to determine units in sports betting which some handicappers assign to weight each prediction.
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]
The Kelly criterion also describes such a utility function for a gambler seeking to maximize profit, which is used in gambling and information theory; Kelly's situation is identical to the foregoing, with the side information, or "private wire" taking the place of the experiment.
Portrait of Nicolas Bernoulli (1723) The St. Petersburg paradox or St. Petersburg lottery [1] is a paradox involving the game of flipping a coin where the expected payoff of the lottery game is infinite but nevertheless seems to be worth only a very small amount to the participants.
In statistics, gambler's ruin is the fact that a gambler playing a game with negative expected value will eventually go bankrupt, regardless of their betting system.. The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet ...