Kelly Criterion Calculator

The math

Given a true win probability p and decimal odds d (so net payoff per unit staked is b = d − 1), the Kelly fraction is:

f* = (b·p − (1−p)) / b

When f* ≤ 0 the bet is −EV and the optimal stake is zero. When f* > 0 it's the fraction of bankroll that maximizes the expected logarithm of bankroll over repeat plays.

Why fractional Kelly

Full Kelly is optimal only under perfect knowledge of p. In reality, your probability estimate has error — your model might say 55% when the true rate is 51% or 58%. Over-betting compounds estimation error: if you bet 5% of bankroll thinking edge is 3% but it's only 1%, you'll lose money in expectation. Fractional Kelly (multiplier between 0.10 and 0.50) shrinks the stake toward zero, sacrificing a sliver of long-run growth for dramatically lower drawdown variance.

Empirical research and survey results from pro sports bettors converge on quarter Kelly (0.25) as the practical sweet spot — enough growth to matter, enough cushion to survive your model being wrong by a percentage point.

Common pitfalls

• Stale-bankroll Kelly. Recompute Kelly with your current bankroll after every meaningful bet. The whole point of the formula is to compound; holding a stale "bet size" defeats it.
• Implied probability from the same book as edge estimate. If you back into p by devigging the same book you're betting at, you'll always compute zero edge. Your p needs to come from a separate model — your own, a market consensus across sharper books, a closing-line proxy.
• Cross-correlated bets. Kelly assumes independent wagers. If you Kelly six correlated NFL spread bets on the same Sunday, you're effectively making one big bet six times — your real bankroll variance is much higher than the formula suggests.