The Kelly Criterion — and Why Pros Bet a Fraction

The formula

Kelly fraction f* = W − (1−W)/R, where W = win probability and R = win/loss ratio. Example: 40% wins at 3:1 → f* = 0.40 − 0.60/3 = 0.20 — Kelly says 20% of capital per trade maximizes long-run geometric growth. The math is correct; the input is not: your W and R are ESTIMATES with error bars.

Why full Kelly is a trap

Kelly assumes you KNOW the true odds. Overbetting Kelly (betting more than f*) guarantees ruin territory; and because your estimates are noisy, the "full Kelly" you compute is frequently an accidental overbet. The compounding curve is also brutal near the optimum: full Kelly suffers monstrous drawdowns (50%+ are normal) in exchange for maximal growth.

The professional answer

Bet a FRACTION of Kelly — quarter-Kelly to half-Kelly. Growth drops modestly; variance and estimation-error risk collapse. Combined with the 1% rule (which usually lands near a tenth of Kelly for realistic edges), it is the same lesson twice: survive first, optimize second. Kelly is a ceiling, not a target.

Sources

• Kelly CriterionInvestopedia
• The Kelly Criterion in Blackjack and the Stock MarketEdward Thorp