Kelly criterion calculator

What the Kelly criterion is

The Kelly criterion is a formula from information theory, published by John Kelly in 1956, for sizing repeated bets. It answers one narrow question: if you know the odds and the payoff, what fraction of your bankroll should you stake each time to make it grow as fast as possible over the long run?

The answer is a balance. Stake too little and the account grows slowly. Stake too much and the losses, which are proportionally larger on a bigger stake, drag growth down, and past a certain point the account shrinks even though every bet has a positive expectation. Kelly finds the peak between those two.

In trading terms, the "stake" is the amount you lose if the stop is hit, so the Kelly fraction is a risk per trade percentage, the same number you would feed into the position size calculator. It is not the size of the position or the margin used.

The formula

For a strategy that wins with probability W, pays R times the amount risked when it wins and loses the amount risked when it loses:

Kelly fraction f* = W − (1 − W) ÷ R

An equivalent form is f* = (W × R − (1 − W)) ÷ R: the edge per unit risked, divided by the payoff. That form makes the logic plain. No edge, no bet. A bigger edge, a bigger stake. A larger payoff for the same edge means more variance per trade, so a smaller stake.

The calculator also shows the long-run growth per trade at several multiples of Kelly, from the expected logarithm of the account's growth: W × ln(1 + R × f) + (1 − W) × ln(1 − f). The peak of that curve is at f*, and it falls away on both sides. Read the table to see how little growth you give up at half Kelly compared with how much volatility you avoid.

Get W and R from a large record of trades, not a hunch. The win rate calculator gives both, plus a range for how far your true win rate could sit from the measured one.

A worked example

Hypothetical numbers, matching the calculator's defaults: a 55% win rate, a payoff ratio of 1.5 and a $10,000 account.

1. Full Kelly: 0.55 − 0.45 ÷ 1.5 = 0.55 − 0.30 = 25% of the account per trade.
2. Half Kelly: 12.5%, or $1,250 at risk on a $10,000 account.
3. Quarter Kelly: 6.25%, or $625.

The growth table for these numbers shows about +4.675% per trade at full Kelly, +3.503% at half Kelly and +2.045% at quarter Kelly. Half Kelly keeps three quarters of the growth at half the risk. At 1.5 times Kelly growth is already back down to +3.454%, and at twice Kelly (50% per trade) it is negative: −0.412% per trade, despite a winning strategy.

Now suppose the true win rate is 50%, not 55%. That is well within the error of a few hundred trades. Kelly for 50% and 1.5 is 0.50 − 0.50 ÷ 1.5 = 16.7%. Full Kelly sized on the 55% estimate (25%) would be one and a half times the true Kelly, already on the falling side of the curve. That is the practical case for fractional Kelly in one line.

Kelly with more typical trading numbers

The default example uses a generous edge to make the curve easy to see. Real trading records are usually thinner. Take a hypothetical strategy that wins 45% of the time with a payoff of 1.8:

• Edge per unit risked: 0.45 × 1.8 − 0.55 = +0.26.
• Full Kelly: 0.45 − 0.55 ÷ 1.8 = 14.44% of the account per trade.
• Quarter Kelly: 3.61%, or $361.11 on a $10,000 account.

Even a quarter of Kelly here is above the 0.5% to 2% most traders risk. That is normal, and it is not a sign that 2% is too timid. It reflects how much uncertainty sits in a 45% estimate and how hard a 14% stake is to live with: five losses in a row at full Kelly would remove more than half the account.

The useful reading is the other way round. If you already risk 1% per trade and your full Kelly comes out at 14%, you are far inside the safe side of the curve and have room for your estimates to be wrong. If your full Kelly comes out at 2% and you risk 2%, you are betting at full Kelly on a number you cannot know precisely.

Why traders use a fraction of Kelly, if they use it at all

The inputs are noisy. Kelly assumes you know your win rate and payoff exactly. In practice they are estimates from a finite sample, they drift as markets change, and a backtest usually flatters them. Because over-betting costs much more than under-betting, cutting the stake to a half or a quarter is cheap insurance against an optimistic estimate.

Full Kelly is a rough ride. Even with a perfectly known edge, full Kelly regularly produces drawdowns of half the account. Few people can keep following a method through that, and many trading accounts and prop firm rules would be closed long before.

Trades are not independent coin flips. Kelly assumes each bet is separate. Open positions on correlated pairs, such as EUR/USD and GBP/USD, are closer to one bigger bet, and outcomes can cluster in some market conditions.

Use it as a ceiling, not a target. A sensible way to use the number is as an upper limit: if your fixed risk per trade is above quarter Kelly, it is probably too high. Most retail risk frameworks settle on 0.5% to 2% per trade, which is well below Kelly for typical edges. The risk of ruin calculator shows what different risk levels do to the chance of a deep drawdown, and the risk management guide covers daily and weekly loss limits.

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