How it works
The Kelly criterion answers one question precisely: what fraction of a bankroll maximizes long-run geometric growth when you know the true odds? Its formula divides your edge by your odds — f* = W − (1−W)/R, where W is win probability and R the average-win-to-average-loss ratio — and punishes both timidity and bravado asymmetrically: betting half of Kelly captures three-quarters of the growth at half the volatility, while betting double Kelly guarantees ruin regardless of the edge. Enter a 55% win rate with 3%-wins against 2%-losses and full Kelly solves to 25% of the bankroll per idea — a figure nobody sane trades, which is exactly the lesson. Real probabilities are estimates, estimation error biases the optimum downward, and variance along the way is brutal, so practitioners standardize on half or quarter Kelly: here 12.5%, or $3,125 at risk on a $25,000 book. The survival table then stress-tests that choice through consecutive losses — routine at any realistic win rate, since five-loss streaks appear regularly inside a few hundred trades — showing fractional-Kelly drawdowns that dent rather than destroy. Treat every output as conditional on your inputs being true; the criterion's mathematics is exact, but its appetite for confidence should scare you appropriately.
Formula
f* = W − (1−W)/R, R = avg win ÷ avg loss | Risk $ = bankroll × f* × multiplier | Expectancy = risk$ × (W×R − (1−W))
Tips
- Use half-Kelly or less — full Kelly assumes your probabilities are exact, and they aren't.
- Estimate win rate from at least fifty real trades; smaller samples flatter everyone.
- Check the streak table before sizing: five-to-eight loss runs are normal weather, not disaster.
- Kelly assumes independent sequential bets — correlated positions violate it silently.
- No positive fraction appears? The system has negative expectancy — sizing cannot fix that.
Frequently asked questions
- What is the Kelly criterion in simple terms?
- A formula for the bet size that maximizes long-run growth: f* = W − (1−W)/R, where W is win probability and R the win-loss payoff ratio. With a 55% win rate and 1.5-to-1 payoffs, it says risk 25% of the bankroll — theoretically optimal, practically terrifying.
- Why do traders use half Kelly instead of full Kelly?
- Because full Kelly's inputs are estimates, and overestimating the edge turns 'growth-optimal' into ruin-fast. Half Kelly sacrifices about a quarter of theoretical growth while cutting volatility dramatically and forgiving estimation error — the standard compromise among practitioners who survive long enough to publish.
- What is risk of ruin in trading?
- The probability of drawing down to a level you cannot recover from. Fixed-fractional sizing makes mathematical ruin essentially impossible — losses shrink the bet size as the account shrinks — but deep drawdowns still occur: at 12.5% risk per idea, ten straight losses here still leaves about 26% of the starting bankroll.
- How do I calculate my win rate and payoff ratio?
- From a logged sample of trades: wins divided by total trades, average profit on winners divided by average loss on losers. Fifty trades minimum for rough stability; hundred-plus preferred. Most self-assessed systems collapse once honestly measured — which is itself valuable information.
- Does the Kelly criterion work for stock investing?
- Loosely. Long-term investors adapt its spirit — size positions by conviction and edge, avoid bets that could destroy the franchise — but Kelly's precision assumes known repeated odds that markets rarely offer. Fractional Kelly thinking guides sizing; literal Kelly application belongs to games with measurable probabilities.