Kelly Criterion Calculator
The Kelly fraction for a given win rate and payoff — and, more usefully, how far the answer moves when the win rate you supplied turns out to be a few points wrong.
- Expectancy per trade
- 0.38R
- Kelly fraction
- 25.00%
- Half Kelly
- 12.50%
- Quarter Kelly
- 6.25%
- If win rate is 5 pts lower
- 16.67%
- If win rate is 5 pts higher
- 33.33%
f = (bp − q) ÷ b, where b is the reward/risk ratio, p the win rate and q = 1 − p. The last two rows are the point of this page: Kelly is extremely sensitive to a win rate you estimated. A few points of error moves the output a long way, and the formula assumes that estimate is exact and that outcomes are independent. Neither holds for discretionary trading. This is arithmetic, not a recommendation about how much to risk.
The formula
f = (b·p − q) ÷ b
b = reward/risk ratio
p = probability of winning
q = 1 − pIt maximises the long-run growth rate of a bankroll under a specific set of assumptions. Those assumptions are the interesting part.
What it assumes, and whether trading honours it
- You know p exactly. In trading, p is estimated from your own history — a limited sample, drawn from market conditions that have since changed.
- Outcomes are independent. Trades are not. Losses cluster, because the conditions that produce one produce the next.
- The payoff is fixed. Realised R varies with slippage, partial fills and early exits.
- You can bet the exact fraction. Lot sizes, minimum notionals and margin tiers all interfere.
None of this makes the formula useless. It means the output is a reference point derived from assumptions you should check, not an instruction.
The sensitivity is the point of this page
Change the uncertainty field and watch the two sensitivity rows. A few percentage points of error in the win rate move the fraction a long way, and at higher R it can cross zero entirely — the formula going from "bet a meaningful fraction" to "there is no edge here" on an input you could plausibly have got wrong.
If your estimate of p carries a few points of uncertainty, then so does the answer, and the answer's uncertainty is larger than the input's. That is the practical takeaway, and it is why the full-Kelly number is rarely the one people use.
Why the downside is penalised more
The growth-rate curve as a function of bet size is asymmetric around the optimum: relatively flat below it and steep above. Betting half the optimal fraction gives up some growth; betting twice it can produce negative expected growth despite a genuine edge. Since your estimate is uncertain in both directions, the asymmetry argues for erring low — which is the whole case for fractional Kelly.
Not advice
This page shows arithmetic and its sensitivity. It does not tell you what fraction of your capital to risk, and anyone offering that number without knowing your circumstances is guessing. If you use the output at all, use it as one input alongside a position size you have chosen for reasons you can state, and a drawdown you are prepared to recover from.
FAQ
What is the Kelly criterion?
A formula for the bet size that maximises the long-run growth rate of a bankroll, given a known probability of winning and a known payoff. For a bet paying b to 1 with win probability p, it is f = (bp − q) ÷ b, where q = 1 − p. It answers a precise mathematical question, and the gap between that question and trading is where the difficulties live.
Why is the output so sensitive to the win rate?
Because p appears in the numerator multiplied by b, so an error in p is amplified by the payoff ratio. At higher R, a few percentage points of error in the win rate move the recommended fraction substantially — and can flip it negative, meaning the formula says there is no edge at all. The sensitivity rows exist to make that visible rather than theoretical.
Why do people use half or quarter Kelly?
Because full Kelly assumes your inputs are exact, and they are estimates. Overestimating the edge leads to overbetting, and the growth curve is steeply penalised on that side while being relatively flat on the other — so erring small costs little and erring large costs a lot. Fractional Kelly is a response to input uncertainty, not a modification of the mathematics.
Can I use this to decide my position size?
It is one input among several and should not be the only one. Kelly assumes a known and stable edge, independent outcomes, and the ability to bet an exact fraction — none of which hold cleanly in discretionary trading, where the edge is estimated from a limited sample and outcomes correlate through market conditions. It is a useful reference point and a poor autopilot.