kelly-criterionlisted

# Kelly Criterion — Optimal Bet Sizing The Kelly criterion is the mathematically optimal bet size that maximizes long-term geometric growth of capital. Developed by John Kelly at Bell Labs in 1956, it answers a precise question: given a known edge, what fraction of your bankroll should you risk to maximize the compounding rate? **Core insight**: Betting too small leaves growth on the table. Betting too large increases ruin risk and actually *reduces* long-term growth. Kelly finds the exact optimum between these extremes. **Practical insight**: You should almost never use full Kelly. Estimation error in your edge means full Kelly will overbets in practice. Use fractional Kelly (0.25x to 0.5x) for real trading. --- ## The Kelly Formula For a binary outcome (win or lose): ``` f* = (p * b - q) / b ``` Where: - `f*` = optimal fraction of bankroll to bet - `p` = probability of winning - `q` = probability of losing (1 - p) - `b` = payoff ratio (average win / average loss) **Equivalent forms**: ``` f* = p - q / b f* = p - (1 - p) / b f* = (p * b - (1 - p)) / b ``` **Edge** = `p * b - q` = expected value per unit risked. Kelly only makes sense when edge > 0. If edge is zero or negative, the optimal bet is zero — do not trade. ### Quick Reference | Win Rate | Payoff 1:1 | Payoff 1.5:1 | Payoff 2:1 | Payoff 3:1 | |----------|-----------|-------------|-----------|-----------| | 40% | -20% | -6.7% | 10% | 20% | | 45% | -10% | 3.3%