ARMFThe Kelly criterion: a share calculator
The calculator works out the share of capital by the Kelly criterion that maximises long-term growth and shows what happens when you deviate from it. The practical value is not in the number itself — almost nobody trades it — but in the shape of the curve: it explains why erring on the smaller side is safer.
Kelly criterion trading calculator: the calculation
The curve shows the average logarithmic growth of capital at different shares of risk. The maximum falls on full Kelly; to the right of it growth falls quickly and at a doubled share becomes negative.
How the Kelly share of capital is calculated
| Value | Formula | In the example |
|---|---|---|
| Expectancy per trade | win rate × R/R − (1 − win rate) | +0.35 R |
| Full Kelly | expectancy ÷ R/R | 17.5 % |
| Your share | full Kelly × the chosen share | 4.38 % |
| Money risk | deposit × your share | $438 |
| Average growth | the logarithmic rate: the shares of wins and losses under ln | per trade |
The example inputs: 45 % winners, a target twice as far as the stop, an account of $10,000, taking a quarter of Kelly. The last row is the logarithmic growth rate: the value the Kelly formula maximises. It also explains the shape of the curve on the chart.
What the curve shows
The chart is the dependence of average capital growth on the share of risk. It has three parts, and all three are practically useful.
Hence the practical rule: a working risk of 0.5–2 % per trade is usually between a fifth and a twentieth of full Kelly. That is deep in the left part of the curve — where the loss of growth rate is small and the resilience to an error in the parameters is at its maximum.
How to use the Kelly share on a forex account
The number from the calculator almost never becomes your risk per trade. It has two other roles, and both are more useful.
Related calculations. The chosen risk percentage is checked with the losing streak calculator — it shows what drawdown the expected streak will give. And the size of the edge Kelly is calculated from is estimated by the distance simulation.
Frequently asked questions
Can you trade at full Kelly?
Technically yes, in practice almost nobody does. The formula assumes exactly known probabilities, and any error in the win rate estimate shifts the actual share to the right along the curve — into the zone where growth falls.
What does a negative result show?
That the system has no edge: the expectancy is negative and the optimal bet is zero. No share of capital gives positive growth in such a game.
Which fraction of Kelly should be chosen?
The common options are a half and a quarter. But it is more practical to go the other way round: choose the risk from the acceptable drawdown and use Kelly as a check that the chosen value does not exceed a sensible boundary.
What does the curve on the chart show?
The average logarithmic growth of capital at different shares of risk. The maximum falls on full Kelly; to the right of it growth falls quickly and at a doubled share becomes negative.
Why can growth be negative with a winning system?
Because of compounding: too large a share of risk makes drawdowns so deep that the subsequent percentages are counted from a much reduced account. The average result of a trade is positive while the capital shrinks.
How do you convert the Kelly share into lots?
Through the position size calculator: the share gives the money risk, and the size is calculated from it and the stop distance. The Kelly formula itself knows nothing about size.
Can Kelly be applied with a fixed lot?
No, it assumes the bet is recalculated from current capital. With a fixed size the share of risk changes by itself as the account grows or falls, and the optimum is not met.
Can Kelly be applied to several simultaneous positions?
The formula is derived for one sequential bet. With several open positions the share is divided between them — otherwise the total bet exceeds the calculated one by as many times as there are open trades.
Does the Kelly share depend on the account size?
No, it is expressed as a percentage of capital. The deposit is needed only to convert the share into a money risk amount.
What if the win rate is known imprecisely?
That is exactly why a fraction of Kelly is taken rather than the full value. An error of a few percentage points in the win rate estimate shifts the actual bet to the right along the curve — into the zone where growth falls.
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