Kelly criterion calculator
The stake that maximises long-run growth, the edge it depends on, and the fractional version that most people who use Kelly in practice actually stake.
| Edge on this bet | 12.50% |
|---|---|
| Full Kelly stake | 8.33% of bankroll |
| Full Kelly amount | $416.67 |
| Fractional Kelly amount | $104.17 |
| Implied probability of the price | 40.00% |
Positive expectation at your estimate: you think the true chance is 45.0% and the price implies 40.0%. Full Kelly is correct only if that estimate is correct, and it is brutally volatile when it is not.
What Kelly optimises, and what it ignores
Kelly maximises the expected logarithm of wealth, which over a long enough run maximises growth rate. It is provably optimal for that specific objective, and it is optimal for nothing else. It does not minimise risk, it does not smooth returns, and it has no view on whether you can tolerate the drawdowns it produces.
The formula needs your estimated probability of winning, not the probability implied by the price. If you feed it the implied probability, it returns a stake of zero, correctly, because a bet at fair odds has no edge. Everything Kelly outputs is therefore only as good as an estimate you supplied yourself.
That dependency is the whole difficulty. Overestimating your edge by a small margin causes Kelly to overstake by a large one, and the resulting drawdowns compound against you. Kelly is unforgiving in exactly the direction most people are wrong.
Why almost nobody stakes full Kelly
Full Kelly produces drawdowns that are far deeper than most people expect. A full-Kelly bettor with a genuine edge should still expect to see their bankroll halve at some point, and to spend long stretches below previous highs. The growth rate is optimal, the path to it is violent.
Half Kelly gives up roughly a quarter of the growth rate for substantially less variance. Quarter Kelly, the default here, gives up more growth again and is what many professional bettors and fund managers actually use, precisely because it tolerates a wrong edge estimate without ruin.
Fractional Kelly also hedges against the thing the formula cannot model: that your probability estimate is itself uncertain. If you are confident to within a couple of percentage points instead of exactly, staking a fraction is not timidity, it is the correct response to estimation error.
Kelly in a casino, and why it returns zero
Enter any casino game honestly and Kelly returns no bet, because every casino game carries a negative edge by construction. There is no stake size that turns a negative expectation into growth, and no staking system changes that. Kelly is the clearest way to see why.
This is the useful thing the calculator does for a casino player and not a bettor. Martingale, Fibonacci, d’Alembert and every other progression redistribute when losses arrive without altering their expected total. Kelly, asked the same question, simply declines to bet.
Where Kelly earns its keep is sports betting, prediction markets and anywhere else you can plausibly hold a better estimate than the price. Its answer in a casino is not a limitation of the formula, it is the formula being correct.