kelly-criterion
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:
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