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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.
The strategy had the gambler double the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. Thus the strategy is an instantiation of the St. Petersburg paradox.
Oscar's Grind is a betting strategy used by gamblers on wagers where the outcome is evenly distributed between two results of equal value (like flipping a coin). It is an archetypal positive progression strategy. It is also called Hoyle's Press. In German and French, it is often referred to as the Pluscoup Progression.
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 ]
The sixth chapter of the book moves from probability theory to game theory, including material on tic-tac-toe, matrix representations of zero-sum games, nonzero-sum games such as the prisoner's dilemma, the concept of a Nash equilibrium, game trees, and the minimax method used by computers to play two-player strategy games.
In making a bet where the expected value is positive, one is said to be getting "the best of it". For example, if one were to bet $1 at 10 to 1 odds (one could win $10) on the outcome of a coin flip, one would be getting "the best of it" and should always make the bet (assuming a rational and risk-neutral attitude with linear utility curves and have no preferences implying loss aversion or the ...
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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 ...