Kelly Criterion
Optimal bet sizing formula that maximizes long-term compound growth.
The Kelly Criterion determines the optimal fraction of capital to risk on a bet (or investment) to maximize long-term wealth growth. Formula: f* = (p×b − q) / b, where p = win probability, q = loss probability, b = win/loss ratio. Example: A bet with 60% win chance and 1:1 payoff → Kelly = (0.6×1 − 0.4)/1 = 20% of bankroll. Insight: Never go all-in (Kelly is always <100% for realistic probabilities). Overbetting reduces growth; underbetting is suboptimal. In finance: Rarely used at full Kelly (too volatile). Practitioners use fractional Kelly (e.g., half-Kelly) for smoother equity curves. Criticism: Assumes you know p and b precisely (impossible in markets), ignores leverage constraints and path dependency.
Formula