Kelly Criterion

Also called: Kelly

A formula that calculates the bet size which maximises long-run growth given your edge and odds.

Kelly answers ‘what fraction of bankroll should I bet?’ For binary outcomes: f* = (bp − q) / b where b is net odds, p is win probability, q = 1 − p.

Full Kelly is theoretically optimal but extremely volatile — most traders use half-Kelly or quarter-Kelly for emotional sustainability.

60% win rate, 2:1 R:R. Kelly fraction = (2 × 0.60 − 0.40) / 2 = 40% of account per trade — far too aggressive in practice.

f* = (b × p − q) / b
p = win probability, q = loss probability (1 − p), b = net odds (R:R)

Kelly assumes your win-rate estimate is exact. Even small over-estimation of edge leads to catastrophic over-betting.

Definition