Calculate the optimal stake for a single bet given your win probability, the American odds, and your bankroll. Full Kelly maximizes long-run growth; fractional Kelly (1/4, 1/8) reduces variance.
Compute the mathematically optimal stake for a single bet given your win probability estimate, the offered odds, and your bankroll. Full Kelly maximizes long-run growth at the cost of variance. Fractional Kelly (1/2, 1/4, 1/8) reduces variance with modest growth loss.
Formula: f* = (prob × b - q) / b, where b = decimal odds - 1, q = 1 - prob. Sharp bettors use 1/4 Kelly; recreational bettors should use 1/8 Kelly or smaller.
The Kelly Criterion answers: "I have edge on this bet; how much of my bankroll should I stake to maximize long-run growth?" The answer balances two pressures, bet more to compound faster vs. bet less to survive variance. Kelly gives the optimal balance for known probability + odds.
f* = (p × b - q) / b
Convert American to decimal: positive odds → 1 + (odds/100); negative odds → 1 + (100/abs(odds)). Example: -110 → 1.909, +120 → 2.20.
Full Kelly maximizes growth ONLY if your probability estimate is exactly right. In real betting, estimates have error. Full Kelly with a slightly-overestimated probability leads to ruin. Fractional Kelly (1/4 or 1/8) reduces stake to the level where small probability errors do not compound to bankroll death. Sharp shops typically use 1/4 Kelly. Recreational bettors should use 1/8 Kelly.
p = 0.55, decimal = 1.909, b = 0.909, q = 0.45.
f* = (0.55 × 0.909 - 0.45) / 0.909 = 0.0500 / 0.909 = 5.5% (full Kelly)
1/4 Kelly = 1.4% of bankroll. On a $1,000 bankroll, stake $14 per pick at this confidence + price.