The Kelly Criterion is the mathematically optimal formula for stake sizing. Used by professional gamblers, investors, and quantitative bettors, it tells you exactly how much to stake when you have an edge — and protects you from over-betting.
Developed by mathematician John L. Kelly Jr. in 1956, the Kelly Criterion is a formula that determines the fraction of your bankroll you should stake on a bet to maximise long-term growth. The formula is:
Kelly % = (b × p − q) ÷ b
b = decimal odds − 1 (net profit per unit staked)
p = probability of winning (your estimate)
q = probability of losing = 1 − p
The result is the percentage of your current bankroll to stake. A positive Kelly percentage means bet; a negative means do not bet — there is no edge.
You believe a team has a 55% chance of winning (p = 0.55). The bookmaker offers odds of 2.10 (b = 2.10 − 1 = 1.10).
b = 1.10 p = 0.55 q = 0.45
Kelly = (1.10 × 0.55 − 0.45) ÷ 1.10
Kelly = (0.605 − 0.45) ÷ 1.10
Kelly = 0.155 ÷ 1.10
Kelly = 14.1% of bankroll
With a £1,000 bankroll, full Kelly recommends staking £141. That is a significant percentage — which is why most bettors use fractional Kelly in practice.
Full Kelly maximises expected bankroll growth but produces high short-term variance. A string of losses can severely damage your bankroll even if your edge is genuine. Most professional bettors use half-Kelly (50% of the Kelly stake) or quarter-Kelly for two key reasons:
In practice, any stake between quarter-Kelly and full Kelly is considered sensible for bettors with high-confidence edges. Below quarter-Kelly, the growth rate becomes very slow relative to the actual edge.
Flat staking means betting the same amount on every bet regardless of the edge. Kelly staking means your stake varies with the perceived edge and current bankroll.
Flat staking is simpler and more predictable. Kelly staking, applied correctly, produces faster bankroll growth when your edge estimates are accurate. The risk with Kelly is that overconfident probability estimates — a common trap — lead to systematic over-staking.
A practical approach: use flat staking for most bets and apply Kelly only to high-confidence selections where your edge is well-established.
Kelly only works if your probability estimates are accurate. If you believe a team has a 60% win probability but the true probability is 48%, Kelly will recommend over-staking on a losing bet. The formula amplifies both edges and errors in equal measure.
This is why Kelly should only be used by bettors who have a systematic, tested method for estimating probabilities — not for casual bets based on intuition.
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula for calculating the optimal fraction of your bankroll to stake on a value bet. It maximises long-term bankroll growth given your estimated edge and the offered odds.
What is fractional Kelly betting?
Fractional Kelly means staking a proportion of the full Kelly amount — commonly half-Kelly (50%) or quarter-Kelly (25%). This reduces variance significantly and is safer when your edge estimates carry uncertainty.
Should beginners use Kelly staking?
Kelly staking requires accurate probability estimates to work correctly. Beginners are usually better served by consistent flat staking while building a track record. Once you have 200+ bets of data and a reliable edge, Kelly can be introduced gradually.
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