The Kelly Criterion
How the Kelly formula sizes bets to your edge, why most pros use a fraction of it, and how to apply it without over-betting.
The Kelly Criterion is a formula that tells you what fraction of your bankroll to bet to maximize long-term growth, given your edge and the odds. It's the mathematically optimal staking method - and also a great way to blow up if used carelessly.
The formula
Kelly fraction = (bp − q) ÷ b, where b is the decimal odds minus 1 (your profit per $1), p is your estimated win probability, and q is 1 − p. The result is the share of your bankroll to stake.
A worked example
You find a bet at +120 (b = 1.2) that a fair line says wins 50% of the time (p = 0.5, q = 0.5). Kelly = (1.2 × 0.5 − 0.5) ÷ 1.2 = (0.6 − 0.5) ÷ 1.2 = 8.3% of bankroll. Full Kelly would have you bet 8.3% here - aggressive.
Why almost everyone uses fractional Kelly
Full Kelly assumes your probability estimate is exactly right. In reality, your fair line is an estimate, and overestimating your edge leads to painful over-betting. Most professionals bet a quarter to a half of Kelly, which sacrifices a little growth for dramatically lower risk of ruin and smoother swings.
- Full Kelly - maximum growth, brutal variance, unforgiving of estimation error.
- Half Kelly - ~75% of the growth with far less volatility. A common professional choice.
- Quarter Kelly - conservative, smooth, forgiving. Popular with +EV bettors betting soft numbers.
Kelly in practice
Our Kelly Criterion Calculator shows the exact Full, Half, and Quarter Kelly percentage for any wager based on your estimated edge. Treat Full Kelly as an upper bound and scale it down—betting Half or Quarter Kelly is safer and still captures most of the long-term growth.
Put theory into practice with SharpWire quantitative tools
Verify situational angles, strip bookmaker vig to find true fair-value probabilities, and uncover mathematical edges on the live board.
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