Kelly Criterion Calculator for Binary Options
The Kelly Criterion Formula
Original Kelly: f* = (bp − q) / b, where: b = the odds (payout-to-stake ratio); p = win probability; q = loss probability = 1 − p; f* = optimal fraction of capital to bet. For binary options with 85% payout: b = 0.85. With 60% win rate: f* = (0.85 × 0.6 − 0.4) / 0.85 = (0.51 − 0.4) / 0.85 = 0.13 = 13% of capital. The math says: bet 13% of your capital on each trade for maximum long-term growth rate.
Why You Should NOT Use Full Kelly
Even mathematically optimal Kelly produces severe psychological pain. At 13% per trade, you'll have drawdowns of 50%+ in normal variance, even with positive edge. Real traders abandon their strategy long before reaching the theoretical optimum because the drawdowns are unbearable. Solution: 'Fractional Kelly' — use 0.5× Kelly (Half Kelly) or 0.25× Kelly (Quarter Kelly). Half Kelly sacrifices about 25% of theoretical growth rate for about 50% reduction in drawdown. Quarter Kelly sacrifices 44% of growth for 75% drawdown reduction. Most professional traders use Quarter Kelly or less in practice.
| Kelly Fraction | Position Size (at 60% win rate, 85% payout) | Max Drawdown (typical) | Growth Rate vs Full Kelly |
|---|---|---|---|
| Full Kelly | 13% | 55% | 100% |
| Half Kelly | 6.5% | 30% | 75% |
| Quarter Kelly | 3.25% | 18% | 56% |
| 1% Standard Rule | 1% | 10% | 30% |
| 2% Standard Rule | 2% | 15% | 45% |
Kelly Sizing Table for Common Scenarios
| Win Rate | 85% Payout → Full Kelly | Half Kelly | Quarter Kelly |
|---|---|---|---|
| 55% | 5.9% | 2.9% | 1.5% |
| 57% | 8.5% | 4.2% | 2.1% |
| 60% | 13.0% | 6.5% | 3.3% |
| 63% | 17.6% | 8.8% | 4.4% |
| 65% | 20.6% | 10.3% | 5.2% |
| 70% | 29.4% | 14.7% | 7.4% |
When Kelly Says 'Don't Bet'
If your win rate × payout − loss rate < 0, Kelly returns a negative number, meaning the mathematically optimal bet is zero — i.e., don't trade this strategy at all. Example: at 50% win rate with 85% payout: Kelly = (0.85 × 0.5 − 0.5) / 0.85 = -0.088, negative. The math says: with a 50% win rate at 85% payout, you should not bet because the strategy has negative expected value. Don't override this. If your numbers come out negative, your strategy is losing money — fix the strategy or stop trading.
Practical Kelly Recommendations
- Recommendation 1 — Calculate Full Kelly for your strategy but apply Quarter Kelly in live trading
- Recommendation 2 — If Quarter Kelly exceeds 5%, cap at 5% maximum regardless of math (variance protection)
- Recommendation 3 — Recalculate Kelly every 100 trades using your most recent win rate (not lifetime average)
- Recommendation 4 — Reduce to half of your Kelly fraction during the first 100 live trades of a new strategy (extra safety while confirming edge)
- Recommendation 5 — Never use Kelly above 25% — at that level you're essentially gambling, regardless of theoretical math
Kelly Criterion FAQ
Is the standard '2% rule' just Quarter Kelly?
Approximately, for typical strategies. For a 58% win rate at 85% payout, Quarter Kelly is about 2.5% — close to the 2% rule. The standard 2% rule is essentially a simplified Quarter Kelly that doesn't require recalculation. Both achieve similar drawdown profiles. The advantage of explicit Kelly is it scales with your demonstrated edge: better strategies justify larger positions; weaker strategies require smaller.
Can I use Kelly with uncertain win rate?
Yes, but conservatively. If you estimate your win rate is '60% but could be 55-65%', use the LOWER bound (55%) for Kelly calculations. This protects against overestimating your edge. Win rate estimation has variance — being humble about uncertainty is essential.
Does Kelly account for emotional pressure?
No — Kelly is pure math. It doesn't know that you can't sleep when your account is down 30%. That's why we recommend fractional Kelly (Quarter Kelly at most). Full Kelly is mathematically optimal but psychologically destructive for most humans.
What if I have multiple strategies?
Run Kelly separately for each strategy with that strategy's win rate. Don't aggregate. Allocate the resulting position sizes proportionally if running them simultaneously. For example, Strategy A says 3% Kelly, Strategy B says 4% Kelly — when both signal, take half-size on each (1.5% A + 2% B = 3.5% total exposure). Don't compound by taking full Kelly on both.
Has anyone made money using Kelly long-term?
Yes — Edward Thorp (originator of Kelly's trading application) used a variant to generate consistent returns at his hedge fund Princeton Newport Partners (1969-1988, 19% annual return). Warren Buffett has stated his sizing decisions are 'Kelly-inspired'. Bill Gross of PIMCO discussed Kelly in his writings. The technique works in practice when applied with discipline and humility about edge estimation.
Why is Quarter Kelly recommended instead of Half?
Robustness to estimation errors. If you think your win rate is 60% but it's actually 56%, Full Kelly says 13% but optimal is 8% — you'd be over-betting by 60%. Quarter Kelly is forgiving: even if you overestimate edge by 30%, you're still close to actual optimal. This makes Quarter Kelly more robust than Half Kelly when edge estimates are uncertain (which they always are).
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