Kelly Criterion Calculator
Calculate optimal bet sizing using the Kelly Criterion. See full, half, and quarter Kelly recommendations with risk-of-ruin estimates to manage your bankroll effectively.
How the Kelly Criterion Works
The Kelly Criterion tells you exactly how much of your bankroll to bet to maximize long-term growth. It balances the desire for aggressive betting (to grow faster) with the need for capital preservation (to avoid going broke).
The Formula
Kelly fraction = (bp - q) / b, where b = decimal odds - 1 (your net profit per dollar), p = true probability of winning, q = 1 - p (probability of losing). If the result is negative, don't bet.
Example Calculation
With a 55% true probability at -110 odds (decimal 1.909): b = 0.909, p = 0.55, q = 0.45. Kelly = (0.909 × 0.55 - 0.45) / 0.909 = 5.5%. So bet 5.5% of your bankroll. At half Kelly, bet 2.75%.
Fractional Kelly
Because we can never know true probabilities precisely, most professionals use fractional Kelly (typically half). This provides a buffer against estimation errors and reduces the psychological stress of large drawdowns.
Frequently Asked Questions
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that determines the optimal percentage of your bankroll to wager on a bet with positive expected value. Developed by John L. Kelly Jr. at Bell Labs in 1956, it maximizes the long-term geometric growth rate of your bankroll. The formula is: f = (bp - q) / b, where f is the fraction to bet, b is the net odds (decimal - 1), p is win probability, and q is loss probability (1-p).
Why is half Kelly recommended over full Kelly?
Full Kelly is mathematically optimal for bankroll growth but produces extreme variance. Half Kelly achieves about 75% of the growth rate of full Kelly but with significantly less volatility and a much lower risk of large drawdowns. Most professional bettors use somewhere between quarter and half Kelly because true probabilities are estimated, not known exactly, and overestimating your edge can be devastating.
What is risk of ruin?
Risk of ruin is the probability that you will lose your entire bankroll before it grows significantly. At full Kelly, risk of ruin is theoretically zero if you can bet infinitely small fractions, but in practice it can be substantial. Fractional Kelly (half or quarter) dramatically reduces risk of ruin while still capturing most of the long-term growth.
When should I not use the Kelly Criterion?
Kelly assumes you know the true probability exactly, which is never the case in sports betting. If your probability estimates are even slightly wrong, full Kelly can lead to overbetting and ruin. Also avoid Kelly when: you cannot accurately estimate probabilities, you are betting correlated events, or the potential loss exceeds what you can emotionally handle. Always use fractional Kelly as a safety margin.