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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.
Benter then met with Alan Woods, a like-minded gambler whose expertise in horse racing complemented his own in computers. The two became racing partners and in 1984, moved to Hong Kong. [3] Starting with US$150,000 (equivalent to US$439,910 in 2023), the pair relied on their mathematical skill to create a formula for choosing race winners. [2]
Some horse racing betting systems can be based on pure statistical analysis of the odds, while others also analyze physical factors (e.g. the horses' form, jockey form and lane draw). Common forms of betting systems for horse racing are: hedging - betting on multiple outcomes in a race; arbitrage - lay the horse a low price and back it at a ...
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 ...
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]
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.