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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) cuts variance sharply but gives up growth: under the standard approximation, 1/2 Kelly keeps about 75% of full Kelly's growth rate, 1/4 about 44%, and 1/8 about 23%.
Formula: f* = (prob × b - q) / b, where b = decimal odds - 1, q = 1 - prob. Professional bettors commonly bet a fraction of full 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. Professional bettors commonly bet a fraction of full 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.
The Kelly Criterion is a formula for the mathematically optimal stake size given a known win probability and odds. Formula: f* = (p × b - q) / b, where p is win probability, q is 1-p, and b is decimal odds minus 1. Full Kelly maximizes long-run bankroll growth.
Fractional Kelly is full Kelly divided by 2, 4, or 8. It reduces stake to protect against errors in probability estimation. Full Kelly assumes perfect calibration; real estimates have noise. Professional bettors commonly bet a fraction of full Kelly; 1/8 Kelly is a safer choice for recreational bettors.
Negative American (favorites): decimal = 1 + (100 / abs(odds)). Example: -150 → 1.667. Positive American (underdogs): decimal = 1 + (odds / 100). Example: +135 → 2.35.
Negative Kelly means the bet has no edge or is -EV at the given probability and odds. Do not bet. If you keep getting negative Kelly across multiple picks, your probability estimates are below market, your edge is gone, or the price changed against you.
Every recommended MLB moneyline pick displays a 1/8-Kelly unit recommendation (1u = 1% of bankroll, capped at 5u) based on the model's calibrated win probability and the published price; the stake also trims the probability for model uncertainty. First-inning reads and NFL picks carry no stake. The displayed stake is bankroll-agnostic; apply it to your own bankroll. See the methodology page for full sizing detail.