Kelly Criterion
Mathematically optimal bet-sizing rule for any wager with a known edge. Given an estimated win probability and the offered odds, returns the fraction of bankroll to stake.
The Kelly criterion is a formula derived by John L. Kelly Jr. in 1956 that maximizes the long-run geometric growth of a bankroll subject to repeated wagering. The output, expressed as a fraction of bankroll, is the size of bet at which expected log-wealth is highest. Bet less than Kelly and capital compounds more slowly than the optimum. Bet more and growth is paradoxically slower while ruin risk rises sharply.
- It is the unique sizing rule that maximizes long-run wealth growth when probability estimates are accurate.
- It punishes overestimation severely, which is why every serious operator uses a fractional Kelly (typically half or quarter) rather than full.
- It applies universally: sports, prediction markets, options, any binary-outcome wager with known odds.
- Sportsbook risk teams and prediction market makers price assuming sharp counterparties size with Kelly. Knowing the rule is table stakes for institutional play.
f* = (b·p − q) / bf* is the fraction of bankroll to stake. b is the net decimal odds (decimal − 1). p is your estimated win probability. q is 1 − p. If f* is negative, the bet is unprofitable in expectation and the correct action is to not bet.
Bankroll $1,000. American odds -110 (decimal 1.909). Your estimated win probability 55%. Then b = 0.909, p = 0.55, q = 0.45. f* = (0.909 × 0.55 − 0.45) / 0.909 = 0.055, or 5.5% of bankroll. At half Kelly that becomes 2.75%, or $27.50.
- Treating gut estimates as calibrated probabilities. Kelly amplifies estimation error, so feeding it a 60% gut feeling on a true coin flip destroys bankrolls fast.
- Using full Kelly without applying an empirical CLV haircut. Live odds never match backtested odds exactly; the standard correction is a 10-25% haircut measured against actual closing-line slippage.
- Resizing the position at every micro-update. Kelly is derived for repeated independent bets; partial-fill resizing on a single position breaks the math.
Compute it yourself.
We built a free calculator that implements the formula above. Plug in your numbers and see the math.
Open Kelly Stake CalculatorWhy use half Kelly instead of full?
Full Kelly is optimal only if your probability estimate is exactly correct. In practice every estimate carries error, and the loss function around the optimum is asymmetric: overestimation punishes you much harder than underestimation. Half Kelly trades a small amount of expected growth for dramatically lower drawdown variance and ruin risk. Quarter Kelly is conservative and common for newer models still building calibration history.
When does Kelly recommend not betting?
When your estimated probability is below what the offered odds imply. The formula returns a negative fraction in that case, which is interpreted as 'do not bet' rather than 'bet against.' Negative Kelly is also the natural test for whether a bet has any edge at all: if it does not, no sizing rule can make it profitable.
Does Kelly work for parlays and correlated bets?
Naive Kelly assumes independence between sequential bets. For uncorrelated parlays the leg multiplication still applies, but for same-game or correlated parlays you need a joint-distribution model. Most retail parlay calculators get this wrong, which is part of why parlays are the highest-margin product at any sportsbook.
Who actually uses Kelly in practice?
Sharp sports bettors, options market makers, prediction market participants, and quantitative hedge funds all size at fractional Kelly or related variants. Retail bettors almost never do, which is one reason why retail and sharp bankroll trajectories diverge so dramatically over time.