Kelly Criterion

The Kelly Criterion is a staking formula that prescribes the fraction of your bankroll to wager on a bet, sized in proportion to your perceived edge. The formula is Kelly fraction = (b x p - q) / b, where b is the decimal odds minus 1, p is your estimated probability of winning, and q is the probability of losing (1 - p). It is mathematically optimal for maximising the long-run growth rate of a bankroll. Worked example: you back a selection at decimal odds of 2.50, so b = 1.5. You judge its true chance to be 45%, so p = 0.45 and q = 0.55. Kelly fraction = (1.5 x 0.45 - 0.55) / 1.5 = (0.675 - 0.55) / 1.5 = 0.125 / 1.5 = 0.083, or 8.3% of the bankroll. Note that with a true probability of 45% against an implied 40% (1 / 2.50), the bet has genuine value, which is why Kelly recommends a positive stake at all. Why it matters: full Kelly grows a bankroll faster than any other system but is highly volatile, and crucially it assumes your probability estimate is accurate. Because most bettors overestimate their edge, practitioners use fractional Kelly — typically a half or a quarter of the figure — which sharply reduces drawdowns at a small cost to growth. The classic mistake is feeding in an inflated win probability, which causes Kelly to recommend dangerously large, bankroll-threatening stakes. If the formula ever returns a negative number, the bet has no edge and should not be placed. See also bankroll, value bet and expected value.