What is the Kelly Criterion?
The Kelly Criterion is a formula for optimal bet sizing. Given the odds and your estimated chance of winning, it tells you what fraction of your bankroll to stake to grow it as fast as possible over the long run — without risking going broke. It was devised by John Kelly in 1956 and is used in both sports betting and investing.
The key insight: bet too much and one bad run wipes you out; bet too little and you leave growth on the table. Kelly finds the mathematically ideal middle — but only when you genuinely have an edge.
How to use the calculator
Enter the odds
The decimal odds on offer.
Your win probability
The true chance you give it, as a %.
Add your bankroll
Turns the % into an actual stake.
Pick a fraction
Half or quarter Kelly is safer.
The Kelly formula
f = (b × p − q) ÷ b
- b = decimal odds − 1 (your net winnings per unit staked)
- p = your probability of winning
- q = 1 − p (your probability of losing)
- f = the fraction of your bankroll to stake
If f comes out zero or negative, you have no edge — your win probability doesn't beat the odds' implied probability (1 ÷ decimal odds), so Kelly says don't bet.
Worked example
Odds of 2.50, and you estimate a 45% chance of winning:
- b = 2.50 − 1 = 1.5, p = 0.45, q = 0.55
- f = (1.5 × 0.45 − 0.55) ÷ 1.5 = (0.675 − 0.55) ÷ 1.5 = 8.3% (full Kelly)
- On a €1,000 bankroll that's an €83 stake — or €42 at half Kelly.
The implied probability of 2.50 is 40%, so your 45% estimate sits 5 points above the market — a positive expected value of +12.5% per unit staked, which is why Kelly returns a positive stake. Drop your estimate to 40% (no edge) and the stake becomes zero.
Why most bettors use fractional Kelly
Full Kelly is optimal if your probability estimate is exact — but it never is. Overestimate your edge even slightly and full Kelly over-stakes, producing wild swings and deep drawdowns. Half Kelly keeps most of the long-term growth with far less than half the volatility, and quarter Kelly is gentler still. That trade-off — a little growth for a lot less risk — is why experienced bettors and investors rarely bet full Kelly.
Kelly also depends on having a real edge in the first place. To check whether the odds offer value, compare your probability with the odds converter's implied probability, and if you're chasing a guaranteed profit instead, see arbitrage betting.
Learn more about arbitrage betting
New to this? Read our full guide on what is arbitrage betting, or see the arbitrage betting formula explained step by step with worked examples. Odds in a different format? Use our odds converter to switch between decimal, fractional, American and implied probability.
Frequently asked questions
- What is the Kelly Criterion?
- The Kelly Criterion is a formula that calculates the optimal fraction of your bankroll to stake on a bet, based on the odds and your estimated probability of winning. It maximises long-term bankroll growth while avoiding ruin. It is used in both sports betting and investing.
- What is the Kelly formula?
- f = (bp - q) / b, where b is the decimal odds minus 1 (net odds), p is your probability of winning, and q is 1 - p. The result f is the fraction of your bankroll to stake. If f is zero or negative, you have no edge and should not bet.
- Why use half or quarter Kelly?
- Full Kelly is mathematically optimal but very aggressive, and it assumes your probability estimate is exact — which it never is. Half or quarter Kelly stakes proportionally less, dramatically reducing bankroll swings and the damage from over-estimating your edge, at a small cost to growth. Most experienced bettors use fractional Kelly.
- What happens if I have no edge?
- If your win probability is not higher than the odds' implied probability (1 / decimal odds), the Kelly fraction is zero or negative — meaning the maths says do not bet. Staking on a negative-edge bet loses money over time whatever your staking plan.
- Is the Kelly Criterion good for betting?
- It is the theoretically optimal staking method when you genuinely have an edge and can estimate probabilities well. Its weakness is that it depends entirely on the accuracy of your probability estimate — overestimate your edge and full Kelly over-stakes badly. That is why fractional Kelly is the practical choice.
- Does Kelly work for investing too?
- Yes. The same formula sizes positions for any repeated bet with known odds and probabilities, which is why it is used in trading and portfolio management as well as sports betting.