Kelly Criterion Calculator
Compute the mathematically optimal bet size given your bankroll, the offered odds, and your estimated probability of winning. Includes fractional Kelly presets for risk-controlled bettors.
All math runs in your browser. Recommendations assume calibrated probability estimates.
The Kelly Formula
The Kelly criterion solves for the bet fraction that maximizes the long-run expected logarithmic growth rate of your bankroll:
Where b is the decimal odds minus 1 (the multiple you win on top of stake), p is your estimated probability of winning, and q = 1 - p (probability of losing). The result f* is the fraction of your bankroll to bet.
Example: bankroll $1,000, offered -110 (decimal 1.91, b = 0.91), your estimate 55% chance to win:
Full Kelly bet: $60.40
Half Kelly: $30.20
Why fractional Kelly? Full Kelly is theoretically optimal but assumes your probability estimate is exactly right. In practice you usually overestimate your edge slightly. Half Kelly cuts your variance by half while still capturing about 75% of full Kelly's expected growth, a much better risk-adjusted return for most bettors.
If your edge is zero or negative, Kelly returns 0 or a negative number: meaning the bet is not profitable in expectation and you should pass.
Frequently Asked
What is the Kelly criterion?
The Kelly criterion is a mathematical formula for optimal bet sizing given an edge. It tells you what fraction of your bankroll to risk on a bet, given the offered odds and your estimated probability of winning. Maximizes long-run growth rate while preventing ruin.
Should I use full Kelly?
Most professional bettors use fractional Kelly (half-Kelly is the most common) rather than full Kelly. Full Kelly maximizes long-run growth but assumes your edge estimate is exactly correct. Fractional Kelly trades a small amount of expected growth for substantial reduction in variance and protection against overestimating your edge.
What if I have no edge?
The Kelly formula returns 0% (or negative) if you have no edge or a negative edge: meaning you should not bet. The formula respects expected value: it never recommends betting when the math is against you.
How do I estimate my probability of winning?
This is the hard part. Approaches: (1) build your own predictive model using historical data; (2) compare the no-vig fair odds across multiple sharp books and use the consensus probability; (3) pure judgment based on context (rarely beats the market). Even small edges (1-3%) compound substantially over volume if your estimates are calibrated.
Why does Kelly grow less aggressive at high probabilities?
When the probability of winning is very high but the payout is small, the maximum rational bet size is smaller in dollars (though larger as a percentage of bankroll). Kelly handles this by scaling bet size to the ratio of edge to odds, not just edge alone.