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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 decimal odds of a multiple bet is often calculated by multiplying the decimal odds of the individual bets, the idea being that if the events are independent then the implied probability should be the product of the implied probabilities of the individual bets. In the above case with fractional odds of 5 − 6, the decimal odds are 11 ⁄ 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.
Oscar's Grind divides the entire gambling event into sessions. A session is a sequence of consecutive wagers made until 1 unit of profit is won. [2] Each session begins by betting 1 unit, and ends by winning 1 unit of profit. If the gambler loses, the session continues and the bet is repeated.
Parimutuel betting differs from fixed-odds betting in that the final payout is not determined until the pool is closed – in fixed-odds betting, the payout is agreed at the time the bet is sold. Parimutuel gambling is frequently state-regulated, and offered in many places where gambling is otherwise illegal. Parimutuel gambling is often also ...
Even if the gambler can tolerate betting ~1,000 times their original bet, a streak of 10 losses in a row has an ~11% chance of occurring in a string of 200 plays. Such a loss streak would likely wipe out the bettor, as 10 consecutive losses using the martingale strategy means a loss of 1,023x the original bet.
In statistics, this is called odds against. For instance, with a royal flush, there are 4 ways to draw one, and 2,598,956 ways to draw something else, so the odds against drawing a royal flush are 2,598,956 : 4, or 649,739 : 1. The formula for establishing the odds can also be stated as (1/p) - 1 : 1, where p is the aforementioned probability.
With each bet, the player stakes an amount equal to the sum of the first and last numbers on the list. If only one number remains, that number is the amount of the stake. If the bet is successful, the two amounts are removed from the list. If the bet is unsuccessful, the amount lost is appended to the end of the list.
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