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It is based on the formula k% = bp–q/b, with p and q equaling the probabilities of winning and losing, respectively.

One rule to keep in mind, regardless of what the Kelly percentage may tell you, is to commit no more than 20% to 25% of your capital to one equity. Allocating any more than this carries far more investment risk than most people should be taking.

Kelly Criterion Example in Sports Betting From a sports betting perspective, let's say a proposed wager has odds of 3.00. The probability of winning is 0.40 making the probability of losing 0.60. Based on the formula, you should stake 0.2 (i.e. 20%) of your bankroll on the proposed wager.

equals approximately (2πn)1/2e-nnn; that is, n factorial (a product of integers with values descending from n to 1) approximates the square root of 2πn, times the exponential of -n, times n to the nth power.

For example, consider you are betting on a coin to land on heads at 2.00. However, the coin is biased and has a 52% chance of ending up on heads. B = 2-1 = 1. Therefore the Kelly Criterion would recommend you bet 4%.

The linear approximation formula is based on the equation of the tangent line of a function at a fixed point. The linear approximation of a function f(x) at a fixed value x = a is given by L(x) = f(a) + f '(a) (x - a).