Free tool
Kelly criterion calculator
A stake sized to the edge and the price, with the fraction and cap we use ourselves.
Any format.
The money set aside for betting, all of it.
We cap at 2%. Set 100 for no cap.
- Full Kelly
- 10.00%
- of bankroll
- After the fraction
- 2.50%
- of bankroll
- After the cap
- 2.00%
- of bankroll
- Stake
- 20.00
- on a bankroll of 1000
Full Kelly assumes your probability is exactly right. It never is, and over-staking an estimated edge is how a genuinely good bettor goes broke, so the fraction and the cap matter more than the formula.
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How the formula works
Kelly asks: given an edge, what fraction of the bankroll grows it fastest over many bets? Stake too little and growth is slow; stake too much and the losing runs wipe out more than the winning ones add. The answer is the edge divided by the profit per unit: (p × b − q) ÷ b, where p is the probability, q is 1 − p and b is the decimal price minus one.
At evens with a 55% chance that is (0.55 − 0.45) ÷ 1 = 10% of the bankroll. At 3.00 with a 40% chance it is (0.8 − 0.6) ÷ 2 = 10% too — the same fraction, because the edge and the price scale together.
Why nobody sensible uses full Kelly
The formula is exact only when the probability is. If you think a chance is 55% and it is really 50%, full Kelly stakes 10% of the bankroll on a bet with no edge; do that for a season and the drawdown is brutal. Fractional Kelly — staking a half or a quarter of the formula’s answer — keeps most of the growth and sheds most of the variance, and it is what every serious record you can find actually uses.
This site stakes a quarter of Kelly on a notional 100-unit bankroll, capped at 2 units. The cap and the fraction matter more than the formula: they are what protect the record on the days the model is confidently wrong.
Questions
- What is the Kelly criterion?
- A formula for the fraction of a bankroll to stake that maximises its long-run growth rate: (probability × (price − 1) − (1 − probability)) ÷ (price − 1). It stakes more when the edge is larger and the price shorter, and nothing at all without an edge.
- Why use a fraction of Kelly?
- Full Kelly assumes the probability is exactly right. Real probabilities are estimates, and over-estimating an edge while staking full Kelly produces large drawdowns and can lose the bankroll. Half or quarter Kelly gives up a little growth for much less variance; this site stakes a quarter.
- Why cap the stake?
- Because a large modelled edge is more often a model error than a market error. A cap — 2% of the bankroll here — limits the damage of the times the model is confidently wrong.
- What is a unit?
- A fixed fraction of the bankroll used to express stakes, so records are comparable. This site’s stakes are in units of a notional 100-unit bankroll, so a 2-unit stake is 2% of it.
The same numbers on real fixtures
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A calculator turns your numbers into other numbers. It does not know whether your numbers are right, and no arithmetic makes an outcome certain. Never stake money you cannot afford to lose.