Kelly Criterion Stake Calculator
Enter your bankroll, the odds you're taking and the true chance of the bet (as fair odds or a win %). The tool sizes the stake with the Kelly criterion, with full, half or quarter Kelly.
Fill in the fields above to see the result.
The Kelly criterion answers the question that arrives right after you find value: how much to stake. Its answer is the fraction of your bankroll that grows the money fastest over the long run without ever going broke.
How the math works
f* = (p × b − (1 − p)) ÷ b
Where p is the true probability by your estimate and b is the net profit per unit, that is, odds − 1. The result is the slice of bankroll to stake.
Notice what the formula does: it divides your edge by the size of the prize. A big edge at short odds asks for a big stake, because the risk of ruin is low. The same edge at long odds asks for less, because the losing runs will be longer.
When f* comes out negative, there is no positive fraction to stake. The price is against you.
Worked example
A 1,000 bankroll and odds of 2.10, varying only the true probability you assign:
| Your true prob | Fair odds | f* | Full Kelly | Half Kelly | Quarter Kelly |
|---|---|---|---|---|---|
| 55.0% | 1.818 | 14.09% | 140.91 | 70.45 | 35.23 |
| 50.0% | 2.000 | 4.55% | 45.45 | 22.73 | 11.36 |
| 48.0% | 2.083 | 0.73% | 7.27 | 3.64 | 1.82 |
| 45.0% | 2.222 | −5.00% | no bet |
This table is why Kelly frightens people the first time they use it. Moving your estimate five points, from 50% to 55%, triples the stake. The size it tells you to bet is extremely sensitive to a number you guessed.
Which is why almost nobody stakes full Kelly. A half or a quarter of the fraction delivers most of the growth with a fraction of the swing, and it forgives your p being somewhat wrong, which it normally is.
Where it misleads
**Full Kelly assumes your p is correct.** It is not. The formula was derived for known probabilities, as in a deck of cards. In sport you are estimating, and overstating your edge by 20% makes Kelly recommend far more than the true optimum.
It does not know you have other bets open. Kelly sizes one bet in isolation. With five correlated positions on the same Sunday, your real exposure is well above the sum of the f* values.
The bankroll in the formula is the real bankroll. If you recompute against a number that does not reflect what you could lose without changing your life, the protection disappears.
FAQ
Which Kelly fraction should I use?
Between a quarter and a half is where nearly everyone doing this seriously sits. The less confidence you have in your probability estimate, the smaller the fraction.
Is Kelly suitable for beginners?
Yes, at a low fraction. If you do not yet have a record that validates your p, use quarter Kelly or a flat stake until you have a few hundred logged bets to check whether your estimate holds up.
Why is the result sometimes negative?
Because the odds sit below the fair odds your probability implies. Negative Kelly is the formula telling you the correct bet is no bet.
To check whether value exists before sizing, use the EV calculator, and to get a defensible p, the no-vig calculator. The bankroll and staking guide covers the whole subject. Betting is entertainment for adults 18 and over and carries a risk of loss.