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🎲 Kelly Criterion Calculator
Kelly maximises long-run growth on parameters you know exactly. You do not know them exactly, which is why the fraction people use is a fraction of Kelly.
💡 Kelly Translation
Kelly tells you the optimal bet size to maximize long-term growth. But it assumes you can handle 30-50% drawdowns. You can't. Use Quarter Kelly.
Kelly Criterion: Optimal Position Sizing (In Theory)
The Kelly Criterion is a mathematical formula developed by John Kelly in 1956 to determine optimal bet sizing. It's used by professional gamblers, hedge funds, and quant traders.
📐 The Formula
Kelly % = (Win Rate × Avg R:R - Loss Rate) / Avg R:R
Where:
- Win Rate = % of trades that win
- Loss Rate = % of trades that lose (1 - Win Rate)
- Avg R:R = Average Win / Average Loss
Example Calculation
Strategy Stats:
- Win Rate: 55%
- Avg Win: $300
- Avg Loss: $150
- R:R = $300/$150 = 2:1
Kelly % = (0.55 × 2 - 0.45) / 2 = (1.10 - 0.45) / 2 = 0.325 = 32.5%
The formula says bet 32.5% of your account on EVERY trade.
🚨 The Problem
Full Kelly maximizes long-term growth but produces BRUTAL drawdowns (30-50%). One losing streak and you're psychologically destroyed.
No retail trader can handle full Kelly volatility.
Why Full Kelly Will Destroy You
Kelly Criterion is mathematically optimal for long-term growth. It's also psychologically impossible for humans.
Simulation: Full Kelly vs Quarter Kelly
Strategy: 55% win rate, 2:1 R:R, 100 trades
🔴 Full Kelly (32.5% per trade)
Starting balance: $10,000
- Trade 1: Risk $3,250, lose → $6,750
- Trade 2: Risk $2,194, lose → $4,556
- Trade 3: Risk $1,481, lose → $3,075
- Trade 4: Risk $1,000, lose → $2,075
Down 79% after 4 losses in a row
Even though your edge is real, you're psychologically destroyed and quit.
✅ Quarter Kelly (8% per trade)
Starting balance: $10,000
- Trade 1: Risk $800, lose → $9,200
- Trade 2: Risk $736, lose → $8,464
- Trade 3: Risk $677, lose → $7,787
- Trade 4: Risk $623, lose → $7,164
Down 28% after 4 losses
Painful but survivable. You keep trading and recover.
💎 The Lesson
Full Kelly optimizes for dollars, not psychology.
It doesn't care if you can sleep at night. It doesn't care if you quit after a drawdown. Quarter Kelly sacrifices some upside for survivability.
Dead equity earns 0%. Fractional Kelly keeps you alive.
Fractional Kelly: What Pros Actually Use
Professional traders don't use full Kelly. They use fractional Kelly: a percentage of what the formula recommends.
| Kelly Fraction | Max Drawdown | Growth Rate | Who Uses It |
|---|---|---|---|
| Full Kelly (100%) | 40-60% | Maximum | Gamblers, degenerates |
| Half Kelly (50%) | 25-35% | ~75% of max | Aggressive hedge funds |
| Quarter Kelly (25%) | 15-20% | ~50% of max | Professional traders ✓ |
| Eighth Kelly (12.5%) | 8-12% | ~25% of max | Conservative institutional |
Recommended: Quarter Kelly
Take the Kelly % and divide by 4. This gives you:
- ✅ 50% of the growth rate
- ✅ 15-20% max drawdowns (survivable)
- ✅ Psychological comfort to keep trading
- ✅ Room for estimation errors in your stats
Example: Full Kelly says 32%? Use 8% per trade.
⚠️ Important Caveat
Kelly assumes your stats (win rate, R:R) are EXACT. They're not. Markets change. Your edge decays. Using fractional Kelly gives you a margin of safety for when your stats are wrong.
Practical Application
Step 1: Calculate your win rate and average R:R from last 50-100 trades
Step 2: Run the Kelly formula
Step 3: Divide by 4 (Quarter Kelly)
Step 4: Compare to your current risk per trade (1-2%)
Step 5: Use the SMALLER of the two
Pro Tip: If Quarter Kelly says 8% but you normally risk 2%, stick with 2%. Kelly gives you a ceiling, not a floor.