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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.
Fractional odds are written a − b (a/b or a to b), meaning a winning bettor will receive their money back plus a units for every b units they bet. Decimal odds are a single value, greater than 1, representing the amount to be paid out for each unit bet. For example, a bet of £40 at 6 − 4 (fractional odds) will pay out £40 + £60 = £100.
The expected amount won is (1 × 0.978744) = 0.978744. The expected amount lost is (63 × 0.021256)= 1.339118. Thus, the total expected value for each application of the betting system is (0.978744 − 1.339118) = −0.360374 . In a unique circumstance, this strategy can make sense.
Super Bowl Squares are the second most popular office sports betting tradition in the United States (No. 1: March Madness brackets), maybe because the outcome is based entirely on luck. Here's how ...
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 ...
Any definition of expected value may be extended to define an expected value of a multidimensional random variable, i.e. a random vector X. It is defined component by component, as E[X] i = E[X i]. Similarly, one may define the expected value of a random matrix X with components X ij by E[X] ij = E[X ij].
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