🎯 Kelly Criterion Calculator

The Kelly criterion finds the bet fraction f* that maximizes long-run growth given win rate (p) and payoff ratio (b, reward relative to risk). f* = (bp − q) / b (q = 1−p). At a 60% win rate and payoff ratio of 1, f* = (1×0.6 − 0.4) / 1 = 0.2 (20%) — theoretically optimal to bet 20% of your bankroll each time.

The Kelly formula assumes you know your true win rate and payoff exactly. In practice these are estimates, and full-Kelly betting produces very high bankroll volatility that is psychologically hard to sustain. Many practitioners use half-Kelly (f*/2) or quarter-Kelly to cut volatility while keeping most of the growth.

If f* comes out at or below zero, the bet has negative expected value — mathematically, you should not bet at all. This happens with low win rates or a poor payoff ratio (small wins, large losses), and sizing up in that situation only raises your risk of ruin.