Overview

The Kelly Criterion is a bankroll-sizing formula derived by John Kelly at Bell Labs in 1956. It calculates the fraction of your bankroll to wager on a positive-EV bet to maximize long-run logarithmic growth. Bet too little and you under-grow; bet too much and you risk ruin even on winning propositions. Kelly is the mathematically optimal middle ground — assuming your edge estimate is accurate.

The Formula

Formula: f* = (bp − q) / b

Where f* is the fraction of bankroll to bet, b is decimal odds minus 1 (the net payout per unit staked), p is your estimated win probability, and q = 1 − p.

When To Use It

Use Kelly when you have a defensible edge estimate — for example, a +EV alert from a sharp model, a known soft line, or a quantified prop projection. Most professional bettors use Fractional Kelly (half or quarter Kelly) to dampen variance and protect against estimation error in the win-probability input.

Worked Example

Example 1: A line is posted at +110 (decimal 2.1). Your model says the true win probability is 52%. f* = (2.1 × 0.52 − 1) / 1.1 = 0.092 / 1.1 = 8.4% of bankroll. On a $10,000 bankroll, full Kelly = $836. Half Kelly = $418, which is what most pros would actually bet.

Example 2: A −200 favorite (decimal 1.5) that you project to win 70% of the time. f* = (1.5 × 0.70 − 1) / 0.5 = 0.05 / 0.5 = 10% of bankroll. Quarter Kelly on a $5,000 roll = $125. The formula returns negative numbers when the bet is −EV, which is your signal to pass.

Common Mistakes

• Trusting your win-probability estimate too much — small errors blow up at full Kelly.
• Ignoring correlation between bets when stacking multiple Kelly stakes the same day.
• Recomputing bankroll after every win, not after a fixed period — leads to over-betting on heaters.
• Using market-implied probability as your input, which always returns f* = 0.