Staking
Kelly criterion calculator
The Kelly criterion answers the question expected value does not: given that a price is favourable, how much of your bankroll should go on it. It returns the fraction that maximises the long-run growth rate of the bankroll — bet more than that and growth falls, bet enough more and the bankroll trends to zero even on bets with an edge.
Almost nobody should bet full Kelly. The formula is optimal only if the probability estimate is exactly right, and the penalty for error is asymmetric: overbetting compounds losses far faster than underbetting sacrifices growth. Practitioners use a half or a quarter of the figure, which is why this calculator defaults to half.
Inputs
The single input that determines the answer. Overstating it by a few points can double the recommended stake.
Result
- Recommended stake5.00% of bankroll at 0.5x Kelly
- €50.00
- Full Kelly fractionThe theoretical maximum. Treat it as a ceiling, not a target.
- 10.00%
- Applied fraction
- 5.00%
Kelly assumes the probability estimate is correct and that the bankroll is money you can afford to lose entirely. It also assumes you can keep betting: a bankroll that has to fund anything else is not a Kelly bankroll. Stakes are rounded down, never up.
How this is calculated
f* = (p x o - 1) / (o - 1)
p is the estimated probability and o the decimal odds. The numerator is the edge — how much more than break-even the price pays — and the denominator is the net return per unit staked if the bet wins. Dividing one by the other gives the fraction of bankroll that maximises the expected logarithm of wealth, which is equivalent to maximising the long-run growth rate. When p x o = 1 the numerator is zero and the criterion stakes nothing; when it is negative the formula returns a negative fraction, which this calculator clamps to zero rather than suggesting you lay the bet.
Worked example
A EUR 1,000 bankroll, a price of 3.00, and an estimated true probability of 40%.
- 01Edge: p x o - 1 = 0.40 x 3.00 - 1 = 0.20.
- 02Net return per unit if it wins: o - 1 = 2.00.
- 03Full Kelly fraction: 0.20 / 2.00 = 0.10, i.e. 10% of bankroll — EUR 100.
- 04At half Kelly the fraction is 5%, giving a stake of EUR 50.
- 05Now suppose the true probability was really 36% rather than 40%. The actual edge is 0.36 x 3.00 - 1 = 0.08, so true full Kelly was 4% — and the EUR 100 full-Kelly stake was two and a half times too large.
- 06That sensitivity is the argument for fractional Kelly: half Kelly on a wrong estimate is still roughly the right size, while full Kelly on a wrong estimate is not.
Questions
Why does the calculator default to half Kelly rather than full?
Because full Kelly is only optimal if your probability is exact, and it never is. Halving the fraction gives up roughly a quarter of the theoretical growth rate but cuts the volatility of the bankroll by about half, and it makes the strategy robust to the estimation error that is always present.
What happens if I overestimate my edge?
You overbet, and the cost compounds. Staking at twice the true Kelly fraction gives zero long-run growth even though every individual bet has a genuine edge; staking above that, the bankroll trends to zero. This is why the failure mode of Kelly is not "slightly worse returns" but ruin.
Why is the recommended stake rounded down?
Because every rounding decision in this direction is safe and the opposite is not. Staking one cent under the criterion costs a negligible amount of growth; staking over it moves you towards the overbetting regime.
Should I use Kelly on a bankroll I need for something else?
No. Kelly assumes the bankroll can absorb a long losing run without being topped up or drawn down for other purposes. If the money has another job, the fractions the formula produces are far too large for the real constraint you are under.
Related calculators
These calculators are information tools. They describe the arithmetic of the prices you enter — they are not advice, and they do not predict outcomes. Betting involves risk. 18+ only. If gambling is causing you harm, support is available from Peluuri.