Kelly Criterion Calculator
The bet size that maximises growth for your edge, and the cost of over-betting.
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- Free preview: the full Kelly fraction in full, with the first rows of each table (up to 3) and a watermarked chart; every other figure is hidden.
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Expected growth at each bet size
Growth rises to its peak at the Kelly fraction, falls back to zero further on and is negative beyond.
Full, half and quarter Kelly
The chance of ever falling this far
From the start, at each fraction of Kelly (continuous approximation, x^(2/c − 1)).
If your win rate is a little off
How this was calculated
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For education only, not investment advice: no tool here tells you what to buy, sell or hold. Results use only the figures you enter, the files you load (read in your browser, never uploaded) and the published rules each page names. Check them against your broker's or exchange's own figures, and consider a licensed or registered adviser for advice on your situation.
About the Kelly Criterion Calculator
The Kelly criterion gives the share of your equity to risk on each trade that makes equity grow fastest over many trades, if your win rate and payoff are what you say they are. This calculator works it out from your own figures, then shows what matters more in practice: the growth at full, half and quarter Kelly (half Kelly keeps about three quarters of the growth), the growth curve that falls to zero and below once you bet about twice the Kelly fraction, the chance of ever falling to a share of your starting equity at each fraction, and how far the answer moves if your win rate is a few points off.
Use your win rate and payoff (the discrete formula, for a trade that wins b times what it risks or loses what it risks), or an expected return above the risk-free rate and a volatility (the continuous formula for a portfolio held continuously). When the formula says more than 100% of equity, it is asking for borrowed money, and the page says so.
It describes what your inputs imply under the model; it is not a recommendation of any bet size. Nothing you type leaves your browser.
How to use it
- Choose the discrete formula (win rate and payoff) or the continuous one (expected excess return and volatility).
- Enter your win rate and your average win ÷ average loss (or the two averages); or the expected return above the risk-free rate and the volatility, both a year.
- Optionally add a fraction of Kelly of your own, your equity to see amounts, and an uncertainty on the win rate (± points).
- Read the Kelly fraction, the growth at each fraction, the curve and the drawdown odds.
- Copy the summary or download the tables as CSV — with a pass, or after unlocking this result.
Examples
Win rate 55%, payoff 1
f* = 10% · growth a trade 0.0050084 at full Kelly, 0.0037526 at half (about 75%), 0.0021879 at quarter, −0.0001377 at twice Kelly
Win rate 40%, payoff 2
f* = 10% · growth 0.0097123 a trade
Win rate 60%, payoff 1.5
f* = 33.33% · growth 0.0810930 at full Kelly, −0.0235566 at twice Kelly
Expected return 8% a year above the risk-free rate, volatility 20%
f* = 0.08 ÷ 0.2² = 2.0: 200% of equity, borrowed money
Common uses
- See the risk per trade the Kelly formula gives for your edge, and how much less half or quarter Kelly risks.
- Check whether your current risk per trade is past the point where growth turns negative.
- See how quickly the answer changes when your win rate is a few points lower than you think.
- Compare an expected return and volatility with the leverage the continuous formula implies.
The formulas
- Discrete: a trade wins b times the amount risked with probability p, or loses it. **f* = p − (1 − p) ÷ b, the share of equity to risk, and the expected log growth a trade at a fraction f is g(f) = p·ln(1 + b·f) + (1 − p)·ln(1 − f)**. g is largest at f*, falls back to zero at a point fc above f* (often about 2f*) and is negative beyond it.
- Continuous (a portfolio held continuously, lognormal returns): **f* = μ ÷ σ² with μ the expected (average, not compound) return above the risk-free rate and σ the volatility; growth above the risk-free rate g(f) = f·μ − f²·σ² ÷ 2**, zero at exactly 2f*.
- Drawdowns: betting c × the Kelly fraction, the chance of ever falling to a share x of the starting equity is x^(2/c − 1) in the continuous approximation (Thorp’s formula with the risk-free rate at zero; 1 from c = 2 up): 50% to lose half at full Kelly, 12.5% at half, 0.78% at quarter. For discrete bets the page also gives Lundberg’s bound for your own bets, which at full Kelly is exactly x.
- Sources: Kelly, “A New Interpretation of Information Rate” (Bell System Technical Journal); Thorp, “The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market”; MacLean, Thorp and Ziemba, The Kelly Capital Growth Investment Criterion.
Reading the results
- The Kelly fraction is the share of equity you would lose if the trade loses (your risk per trade), not the size of the position. In the continuous formula it is the share of equity held.
- Growth is the expected change of log equity a trade (a year in the continuous formula): it is what compounds. Half Kelly gives up about a quarter of it and takes far smaller drawdowns.
- The curve: past the zero-growth point, a bigger bet makes equity shrink over time even though each trade has a positive average.
- The band: the Kelly fraction of a win rate a few points lower, and what betting your full Kelly fraction would do if that lower rate were the true one.
What it leaves out
- Uncertainty in your figures: the formula takes your win rate and payoff as exact; estimated from a few trades they rarely are, and an overestimated edge turns the full Kelly fraction into over-betting.
- Trades that are not two-outcome bets: real results vary in size; the risk of ruin calculator can resample your own results.
- Several positions at once, correlation between them, costs and taxes (put costs into your averages: the expectancy calculator does).
- Leverage limits of your broker and the risk of losing more than you put in.
Limitations
- The formula assumes independent trades with the same odds every time.
- The drawdown chances are the continuous approximation; for discrete bets the page adds a bound for your own bets.
- Growth figures describe the model, not your future results.
- A win rate between 0% and 100% (exclusive), and a payoff above zero, are needed.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
What do I get without a pass?
Without a pass, Kelly Criterion Calculator shows the full Kelly fraction in full, with the first rows of each table (up to 3) and a watermarked chart; every other figure is hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
What is the Kelly criterion formula?
For a bet that wins b times its stake with probability p and loses the stake otherwise, the Kelly fraction is f* = p − (1 − p) ÷ b of your equity. A 55% win rate at even money gives 0.55 − 0.45 = 10%.
Why do traders use half Kelly?
Because the growth curve is flat near the top: half Kelly keeps about three quarters of the growth but makes deep drawdowns much less likely (the chance of ever losing half falls from 50% to 12.5% in the continuous approximation), and it leaves room for an edge that is smaller than you think.
What happens if I bet more than Kelly?
Growth falls, and past a point (about twice the Kelly fraction) it turns negative: equity shrinks over time even though the average trade makes money. At 55% and even money, betting 20% a trade has an expected log growth of −0.0001377 a trade.
Is the Kelly fraction my position size?
No: in the discrete formula it is the share of equity you lose if the trade loses, your risk per trade. The position size calculator turns a risk per trade into shares, lots or contracts for your stop.
Why does the continuous formula give more than 100%?
Because μ ÷ σ² is large for a steady return: 8% above the risk-free rate at 20% volatility gives 200%, which means borrowing as much again as you have. Real returns have fatter tails and changing volatility, so the page marks it as leverage.
What does the uncertainty band show?
The Kelly fraction at your win rate minus and plus the points you choose, and the growth you would get if the lower rate were true while you bet the Kelly fraction of the rate you entered: often negative, which is the strongest case for betting a fraction of Kelly.