How it works
Kelly Fraction = (Win Probability × Win Amount − Loss Probability × Loss Amount) / Win Amount. Simplified for a binary outcome: f = (p × b − q) / b, where p is win probability, q is loss probability (1 − p), and b is the ratio of win amount to loss amount. The result is the fraction of bankroll to wager. Negative output means no edge; do not bet.
Example
Your strategy has 55 percent win rate and a 2:1 average win-to-loss ratio. Kelly fraction = (0.55 × 2 − 0.45) / 2 = 0.325 or 32.5 percent. The math says to risk 32.5 percent of capital on each bet for maximum long-term growth. Most practitioners use fractional Kelly (half or quarter Kelly) because the full Kelly assumes perfect knowledge of probability and payoff, which traders rarely have.
Why it matters
Kelly is mathematically optimal for compounding when inputs are known precisely. In practice, both win rate and payoff ratio are estimated from past data and may be biased upward. Trading at full Kelly amplifies estimation error into ruin risk. Sizing at half Kelly retains most of the geometric growth advantage with substantially lower drawdown. Use Kelly as a ceiling, not a target.
