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Next: is there a positive edge at all?
If the expected value is zero or negative, the Kelly fraction is zero. Check the average trade first.
What is included
- The calculator, with your own numbers
- The formula written out
- A worked example you can reproduce
- Where grid, martingale and DCA bots break the maths
Who it is for
- People running or testing a trading bot
- Anyone sizing a position or checking costs
- Readers learning how the numbers work
- Not advice, and not for placing trades
Key facts
- The Kelly fraction f* = p - (1 - p) / b, where p is the win rate and b is the average win divided by the average loss.
- It is the fraction of the balance that maximises long-run growth if p and b are known exactly and the bets repeat independently. Neither holds in real trading.
- f* is zero or negative when there is no positive edge. Then the formula says to bet nothing.
- A small error in the inputs moves f* a lot, and full Kelly is very bumpy even when the inputs are exact.
- This page shows the arithmetic and never recommends a fraction. Half and quarter Kelly are shown only because many people discuss them.
How the calculator works
Kelly sizing asks one question: what fraction of the balance, bet repeatedly, makes it grow fastest in the long run? For a bet that wins b times what it risks with probability p, the answer is:
Growth per bet = p x ln(1 + f x b) + (1 - p) x ln(1 - f)
Half Kelly = f* / 2, quarter Kelly = f* / 4
Here p is the win rate as a fraction, b is the average win divided by the average loss, and f is the share of the balance lost on a losing bet. If f* is zero or negative the formula gives no positive size, because the average bet has no edge.
A worked example
Take a made-up strategy that wins 40 percent of the time and wins twice what it loses. f* = 0.40 - 0.60 / 2 = 0.10, so full Kelly is 10 percent, half Kelly is 5 percent and quarter Kelly is 2.5 percent. If those inputs were exact and the bets independent, betting 10 percent would grow the balance by about 0.97 percent per bet on average, calculated by us on 27 Oct 2026, exact for those inputs.
Why the inputs make it fragile
The result swings with small input changes. Hold the payoff at 2 and move the win rate, and the fraction changes by 7.5 points for every 5 points of win rate. You never know the true win rate, only an estimate from past trades, and the range around a 30 trade estimate is very wide (see the win rate calculator).
Full Kelly is very volatile, even when the inputs are right
Kelly maximises growth. It does not minimise the pain on the way. We ran a seeded simulation of the 40 percent, payoff 2 strategy above, with exact inputs: 500 bets, 20,000 runs, each bet risking a fixed share of the current balance. The table shows the share of runs that fell at some point by at least 30 or 50 percent from their own peak.
| Fraction risked per bet | Fell 30% from a peak | Fell 50% from a peak |
|---|---|---|
| Full Kelly (10%) | 100% | 100% |
| Half Kelly (5%) | 100% | 84% |
| Quarter Kelly (2.5%) | 76% | 9% |
Approximation from a simulation with a fixed seed, calculated by us on 27 Oct 2026. Percentages are rounded. It uses exact inputs and independent bets, which real trading rarely has. It shows the size of the swings, not what any real strategy will do.
Where bots break the maths
- The inputs are estimates. A bot backtest gives a win rate and payoff that were fitted to the data. Both are usually better in the test than in live trading, and Kelly is most sensitive in exactly those inputs.
- Bets are not independent. Grid, martingale and recovery bots take positions that overlap and depend on each other, so a "bet" is not a clean win or loss.
- Payoffs are not two-point. Real losses can be larger than the average, especially a bot with a large rare loss. A payoff ratio built from an average hides the tail the formula needs.
- Size is set by the bot, not you. A martingale ladder increases size after losses, which is the opposite of Kelly, where the fraction is of the current balance and shrinks as the balance falls.
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FAQ
Frequently Asked Questions
What does the Kelly criterion do?
It finds the fraction of a balance to risk on each repeated bet to maximise long-run growth, when the win probability and payoff are known exactly. It is a theory result, not a rule for a live account.
Why is the formula negative sometimes?
When win rate times payoff is lower than the loss rate, the average bet loses money and the best fraction is zero. The calculator shows the raw value and a floor of zero.
Why do people use half or quarter Kelly?
Because the inputs are uncertain and full Kelly is volatile. A smaller fraction lowers the swings at the cost of slower growth. The page shows them for comparison, not as a recommendation.
How do I get the payoff ratio?
Divide the average winning trade by the average losing trade, both after costs. A $150 average win and a $100 average loss is 1.5.
Does Kelly work for a grid or martingale bot?
Not directly. Those bots have many small wins and rare large losses that depend on each other, so a single win rate and payoff do not describe them.
Are the numbers on this page real?
Example numbers are made up to show how the maths works, and the page says so. A figure only counts as exact when the page says it was calculated on a stated date. Nothing you enter in a calculator leaves your browser.
Can I use this to decide whether to run a bot?
It can show whether a bot's numbers hold together and how much an account can lose. It cannot say what the market will do, and it is not advice. Use it to ask better questions, then read the terms of your own broker or exchange.
Is this financial advice?
No. It is a calculator and general education. It does not consider your situation, and it never recommends a fraction or a size.
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