Kelly criterion calculator
Computes the optimal share of the deposit per trade by the Kelly formula for binary options, the growth rate of the deposit and the share at which growth falls to zero.
Optimal share
10.00%
That is $100.00 per trade
Deposit growth per trade
0.40%
Logarithmic, at full Kelly
Trades to double
172
If the win rate holds
Share where growth hits zero
19.8%
Above this stake the deposit stops growing at all
Full, half and quarter Kelly
| Variant | Share of deposit | Trade size | Growth per trade |
|---|---|---|---|
| Full Kelly | 10.00% | $100.00 | 0.403% |
| Half Kelly | 5.00% | $50.00 | 0.302% |
| Quarter Kelly | 2.50% | $25.00 | 0.175% |
Kelly assumes the probability is known exactly. In practice the win rate is estimated from past trades and almost always overstated — and staking above the optimum hurts the deposit more than staking below it. That is why real trading uses half or a quarter of the computed share.
The binary options formula: share = (win rate × (1 + payout) − 1) / payout. Full Kelly maximises the growth rate but allows deep drawdowns — that is the price of maximum speed, not a flaw in the method.
What the formula computes
The Kelly criterion answers the question of what share of the deposit to put on a trade so that capital grows as fast as possible over a long run. For binary options, where a win brings the payout and a loss takes the whole amount, the formula is:
Share = (win rate × (1 + payout) − 1) / payout
At a 60% win rate and an 80% payout that gives (0.6 × 1.8 − 1) / 0.8 = 10% of the deposit per trade.
The formula already reveals the main point: at the breakeven threshold the numerator turns to zero. At an 80% payout the threshold is 55.6%, and exactly there Kelly prescribes zero. Below the threshold the share goes negative — a mathematical way of saying "do not trade this".
How the share depends on win rate
An 80% payout, a breakeven threshold of 55.6%:
| Win rate | Kelly share | Amount on a $1,000 deposit |
|---|---|---|
| 56% | 1.0% | $10 |
| 58% | 5.5% | $55 |
| 60% | 10.0% | $100 |
| 65% | 21.3% | $213 |
| 70% | 32.5% | $325 |
The table explains why full Kelly is never used literally. Putting a fifth of the deposit on one trade means drawdowns of tens of percent as the normal mode of operation, not as an emergency. The formula optimises the growth rate and takes no interest whatsoever in whether you can live through it.
The point where growth falls to zero
The second important result: the growth of the deposit goes to zero at roughly double the optimal share. At a 60% win rate and an 80% payout the optimum is 10%, and at 20% of the deposit growth becomes nil — the edge is eaten entirely by the size of the stake.
This is asymmetric, and the asymmetry is the whole practical recommendation. Bet half the optimum and you lose about a quarter of your growth rate. Bet double and you lose all of it. So erring toward the smaller amount is the safer mistake.
How to use this
- As a check, not as an instruction. Compute your Kelly share and compare it with what you actually trade. If your risk per trade is several times the computed figure, you are oversizing by the math, not just by feel.
- Take a quarter. At a 60% win rate and an 80% payout, quarter Kelly gives 2.5% of the deposit — nearly right on top of the recommended 1–2% of the deposit. Two reference points reached by completely different routes converge on roughly the same number, and that is the best argument for both.
- Recalculate when your statistics change. The Kelly share moves sharply: two percentage points of win rate between 58% and 60% almost double the computed share.
FAQ
What is the Kelly criterion?
A formula for the optimal share of the deposit per trade. It maximises the growth rate of capital over a long run when the probability of a win is known. For binary options the share is (win rate × (1 + payout) − 1) / payout.
Why do practitioners take a half or a quarter of it?
Because the formula needs a precisely known probability, while a win rate is always estimated from past trades and almost always overstated. Overshooting the optimum hurts the deposit more than undershooting it: at double the optimal share the growth disappears entirely. Half or quarter Kelly give up a little speed but forgive an error in the estimate.
Why does the calculator show zero when the win rate sits at the breakeven threshold?
That is what the formula says, not a bug. At the threshold there is no edge, so the optimal trade size is zero. Below the threshold the formula returns a negative share — a mathematical way of saying this approach cannot be traded at any size.
Can Kelly be applied literally in binary options?
As a reference point, yes; as an instruction, no. At a 65% win rate and an 80% payout the formula prescribes 21% of the deposit per trade, and that guarantees drawdowns almost nobody can stomach. The practical lesson from Kelly is a different one: it shows the ceiling of sensible risk, not a recommended amount.
How does Kelly differ from a fixed percentage?
You pick a fixed percentage yourself from your own tolerance for risk, while Kelly derives the share from your statistics. Both figures are worth looking at: if your usual risk is several times the Kelly number, then mathematically you are oversizing, no matter how it feels.