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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.
David Harville first developed the model in a 1973 paper on horse racing; [2] in 1987, Mason Malmuth independently rediscovered it for poker. [3] In the ICM, all players have comparable skill, so that current stack sizes entirely determine the probability distribution for a player's final ranking.
In Betting Thoroughbreds, Steve Davidowitz claimed that (in 1974), "the top-figure horse wins 35 percent of the time, at a slight loss for every $2.00 wagered." This is an example of using the top figure as a "power rating," or singular measure of a horse's ability. In horse racing, power ratings are generally called class ratings.
In some situations, a negative breakage may occur — for example, in horse racing when an overwhelming favorite wins (or shows or places). [3] The parimutuel calculation results might call for a very small winning payout (say, $1.02 or $1.03 on a dollar bet), but legal regulations might require a larger payout (e.g., minimum $1.10 on a dollar ...
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
A study on soccer betting found that the probability for the home team to win was generally about 3.4% less than the value calculated from the odds (for example, 46.6% for even odds). It was about 3.7% less for wins by the visitors, and 5.7% less for draws. [14] To understand roulette probabilities and calculate them, you need to know the formula.
Trifecta. A trifecta is a parimutuel bet placed on a horse race in which the bettor must predict which horses will finish first, second, and third, in the exact order. [1] Known as a trifecta in the US and Australia, [2] this is known as a tricast in the UK, [3] a tierce in Hong Kong, [4] a triactor in Canada [5] and a tiercé in France. [6]
It was also determined at that time that few horses with no chef-de-race influences in the two most stamina-laden groups, Solid and Professional, had won major races at distances of 1 + 1 ⁄ 4 miles or longer even if the horse had a sufficient Classic presence in its pedigree to keep the Dosage Index from being over 4.00 (when Affirmed won the ...