Kelly criterion calculator
Enter a win probability and payout and it gives the stake with the highest long-run growth. Half and quarter Kelly are shown too.
Given how often you win and what you win when you do, this is the share of your money to stake for the fastest long-run growth. John Kelly derived it at Bell Labs in 1956 while working on signal noise. It is only optimal if you know the probability and the payout exactly, which is why people usually stake half or a quarter of it.
Your numbers
What you enter is saved in this browser, so it is still here next time
1 means you win what you staked
100 means the whole stake is gone
What Kelly says to stake
Full Kelly
10.0% · ₩1,000,000
Fractional Kelly
- Half Kelly (1/2)
- 5.0% · ₩500,000
- Quarter Kelly (1/4)
- 2.5% · ₩250,000
On a single bet
- Expected gain
- 10.00%
- Expected growth at the Kelly stake
- 0.50%
Almost nobody stakes full Kelly. It is optimal only if you know the odds and the payout exactly, and nobody does. Being even slightly generous about your chance of winning throws the answer off badly — and always in the direction of betting too much. Half or quarter Kelly gives up a little expected growth for a great deal less swing.
John Kelly derived this in 1956 while working on noise in telephone lines. It gives the stake that maximises long-run growth when the same bet repeats — it does nothing for any single outcome. If the odds and payout you enter are wrong, so is the answer. For reference, not a recommendation to invest.
Make a link with these numbers
Opening the link fills this screen with the same values. Useful for going through it with a partner, or for comparing two sets of conditions.
A 55% win rate paying 1× gives a full Kelly of 10%
The formula is f = (b·p − a·q) ÷ (a·b): p is the chance of winning, q is 1 − p, b is the multiple paid on a win, a is the share lost on a loss. With the defaults — 55%, 1×, 100% lost — the numerator is 0.55 − 0.45 = 0.10 and the denominator is 1, so 10%, or ₩1m of ₩10m. The "expected gain" is that numerator, 0.10; "expected growth" is the per-bet log growth at the full Kelly stake, 0.55 × ln(1.1) + 0.45 × ln(0.9) = 0.50%.
Three points of optimism about the win rate turn growth negative
If the true win rate is 52% but 55% was entered, the screen gives 10% while the true Kelly at 52% is 4%. Staking 10% repeatedly, expected growth per bet is 0.52 × ln(1.1) + 0.48 × ln(0.9) = −0.10% — the money shrinks. Half and quarter Kelly give up a little growth for a lot more margin against a wrong win rate, which is why the three are shown together.
It says nothing about a single outcome or about several bets at once
Kelly maximises long-run growth only when the same conditions repeat many times. "Expected growth" is per bet, not per year — 0.50% repeated 100 times is 1.005^100 = 1.65×. Several bets at once, outcomes that are not a clean win or loss, and win rates that drift over time all sit outside the formula's assumptions.
Common questions
QShould I stake full Kelly?
It is hard to recommend. Kelly is optimal only if you know the win probability and the payout exactly, and nobody does. Being slightly generous about your win rate throws the answer off badly, and always in the direction of staking too much. Half Kelly keeps about three quarters of the expected growth and halves the swings.
QWhat if the expected value is zero or below?
Kelly answers: do not bet. If the win probability times the payout is less than what you stand to lose, repeating the bet loses money over time.
QCan I use it for stocks?
People do, but the assumptions do not hold. A stock does not resolve into win or lose, and the win probability is unknown. This calculator takes a probability and a payout that you supply — if those are wrong, so is the answer.
QIs expected growth shown for half and quarter Kelly too?
Only for full Kelly. The same formula with a smaller fraction gives it: at the defaults, full Kelly 10% grows 0.50% per bet, half Kelly 5% grows 0.38% and quarter Kelly 2.5% grows 0.22%.
QWhat does a result of 100% mean?
The formula came out above 1. At 60%, 0.5× paid and 30% lost, 0.18 ÷ 0.15 = 120%; staking more than you have means nothing, so it is capped at 100%.