Kelly Criterion Calculator

The Kelly criterion, developed by John Kelly at Bell Labs in 1956, calculates the fraction of your bankroll to risk on a bet or trade to maximise long run growth, given your edge. Bet less than Kelly and you grow more slowly; bet more and you grow more slowly too, with far larger drawdowns, and well above Kelly your bankroll can shrink even with a positive edge. Because real edges are uncertain, most practitioners use a fraction of Kelly. This calculator shows full Kelly, your chosen fraction and the expected growth per bet.

Calculator#

How it works#

Kelly fraction f* = p - (1 - p) / b
Expected log growth per bet = p × ln(1 + b × f) + (1 - p) × ln(1 - f)

Here p is the probability of winning, b is how much you win per unit risked, and f is the fraction of bankroll risked. A negative Kelly fraction means there is no edge, and the right bet is zero. See Kelly Criterion.

Kelly for prediction markets#

On a prediction market contract priced at $0.40 that pays $1 if correct, the payoff ratio is 0.60 divided by 0.40, or 1.5. If you believe the true probability is 50%, Kelly is 0.50 minus 0.50 divided by 1.5, about 16.7% of bankroll. If your estimate is wrong and the market's 40% is right, Kelly is zero. Small errors in probability estimates make large differences in Kelly sizing. See Reading Odds as Probabilities and Prediction Market Strategies and Risks.

Why fractional Kelly#

These growth figures follow from the standard approximation for small edges. Half Kelly sacrifices about a quarter of the growth for about half the volatility, a trade most traders gladly make, especially since estimates of edge are uncertain.

Kelly for trading#

Trading outcomes are not simple win or lose bets with fixed payoffs, but the idea still applies. Estimate win rate and payoff ratio from a large sample of trades, apply a conservative fraction and treat the result as a ceiling on risk per trade, not a target. Many traders find that their Kelly fraction, even halved, is well above the 1% to 2% risk per trade they actually use. See Position Sizing and Fixed Percentage vs Fixed Dollar Risk.

Common mistakes#

1. Overestimating your edge, which leads to oversized bets.
2. Using full Kelly with uncertain estimates.
3. Ignoring correlated bets taken at the same time.
4. Applying Kelly to small samples. See Statistical Significance in Trading.
5. Forgetting costs, which reduce the edge. See Expected Value.

Frequently asked questions#

What is the Kelly criterion?#

A formula that gives the fraction of your bankroll to risk on each bet or trade to maximise long term growth, based on win probability and payoff.

Why do traders use half Kelly?#

It keeps most of the growth while roughly halving volatility and protecting against overestimated edges.

What if the Kelly fraction is negative?#

It means the bet has no edge at the assumed odds, so the growth maximising bet size is zero.

Next, measure how assets move together with the Correlation and Beta Calculator.