A trader has a strategy with 55% win rate and 1.5:1 reward-to-risk ratio. What fraction of capital should be risked per trade?

Step 1 — Kelly formula: f* = (bp − q) / b, where b = reward/risk = 1.5, p = 0.55, q = 0.45.

Step 2 — Calculate: f* = (1.5 × 0.55 − 0.45) / 1.5 = (0.825 − 0.45) / 1.5 = 0.375 / 1.5 = 0.25 or 25%.

Step 3 — Apply fractional Kelly: Full Kelly is mathematically optimal for growth but produces brutal drawdowns (often 50%+). Most professionals use quarter-Kelly to half-Kelly. Quarter-Kelly here = 6.25% per trade.

Step 4 — Sanity check: On a $100,000 account, quarter-Kelly risks $6,250 per trade. If the strategy hits a 6-trade losing streak (probability ≈ 0.45⁶ ≈ 0.83%, happens roughly once per 120 trades), the loss is ~$37,500 — a 37.5% drawdown. Full Kelly would have lost ~$82,000 (82%).

Takeaway: The gap between full and fractional Kelly is the gap between theoretical optimality and psychological survivability.