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🎯 Kelly Criterion Calculator

Calculate the mathematically optimal bet size based on your estimated edge. Includes full, half, and quarter Kelly with bankroll evolution table.

Inputs
£
%
Enter bankroll, win probability, and decimal odds above to see Kelly sizing.
Responsible Gambling Notice The Kelly Criterion assumes you have a genuine, consistent edge over the bookmaker — which is extremely rare. Most bettors overestimate their probability estimates, leading to overbetting and rapid bankroll erosion. Never bet more than you can afford to lose. If gambling is causing harm, visit GamCare (gamcare.org.uk) or the National Problem Gambling Helpline (1-800-522-4700).

What Is the Kelly Criterion?

The Kelly Criterion, developed by John L. Kelly Jr. in 1956, is a formula for calculating the optimal fraction of a bankroll to bet in order to maximise long-run wealth growth. It maximises the expected logarithm of wealth, which is equivalent to maximising the geometric growth rate.

f* = (b × p − q) / b

where:
b = decimal odds − 1 (net profit per unit)
p = estimated win probability
q = 1 − p (loss probability)

Why Practitioners Use Fractional Kelly

Full Kelly is mathematically optimal but extremely aggressive. A 50% loss in bankroll (which full Kelly can produce even with an edge) requires a 100% gain to recover. Most professional bettors use half Kelly or quarter Kelly to reduce variance at the cost of slightly slower bankroll growth. Half Kelly reduces variance by ~75% while retaining ~75% of the growth rate.

The Edge Is Everything

Kelly sizing is only valid when you genuinely have an edge — your estimated probability must exceed the implied probability embedded in the odds. Overestimating your edge leads to overbetting. Underestimating leads to underbetting. Accurately estimating probabilities is the hardest part of sports betting.

Limitations

Kelly assumes independent, identically distributed bets with known probabilities — none of which hold perfectly in practice. Correlated bets (e.g. multiple bets on the same match) require adjusted Kelly. Also, fractional Kelly does not mean "bet less on every bet" — it means bet a fixed fraction of whatever your optimal Kelly stake would be.