The Kelly criterion answers a deceptively simple question: given an edge, how much of your bankroll should you commit to this bet? It is the only widely used sizing rule with a clean mathematical property — the fraction it returns maximizes the long-run growth rate of your bankroll. That is why it appears everywhere from sports-betting blogs to hedge-fund risk decks, and why it is worth understanding before you use it: the formula is easy, and the mistakes around it are not.
Kelly does not predict whether you will win. It takes your edge as a given — your win probability and your average win and loss — and tells you the stake that grows a repeated bankroll fastest over time. No edge means no size, not a smaller size. The criterion was worked out by John L. Kelly at Bell Labs in 1956 (building on earlier ideas of F. Y. Edgeworth) and became widely known through Edward Thorp, who used a version of it to beat blackjack before turning to market timing.
The Kelly formula
For a repeated bet that either wins an average amount W or loses an average amount L, the full-Kelly fraction is:
f* = (b·p − q) / b, equivalently f* = p − q/b
- p — probability of winning the bet, 0 < p < 1 (0.60 for a 60% win rate)
- q — probability of losing, q = 1 − p
- b — the win/loss ratio, b = W / L (average win divided by average loss)
Four steps to compute it:
- Estimate p from a long history of the exact same bet or strategy — the more samples, the more you can trust it (see the estimation section below).
- From that same history, measure the average win W and the average loss L, then b = W / L. In fixed-odds betting, b is the decimal odds minus 1: at decimal odds of 2.0, b = 1 (even money); at 2.5, b = 1.5.
- Plug into f* = (b·p − q) / b. The result is the fraction of your current bankroll to stake on each instance of the bet.
- Apply your fractional multiplier — most people 50% or 25% — to get the stake you actually place.
Worked example
Suppose a strategy wins 60% of the time, with an average win of $150 and an average loss of $100, on a $10,000 account:
- b = 150 / 100 = 1.5, q = 1 − 0.60 = 0.40
- f* = (1.5 × 0.60 − 0.40) / 1.5 = 0.50 / 1.5 ≈ 33.3% of the bankroll
- Full Kelly stake: 33.3% × $10,000 ≈ $3,333; half Kelly ≈ $1,667; quarter Kelly ≈ $833
Two sanity checks worth internalizing. At even money (b = 1) the formula collapses to f* = 2p − 1, so a 55% win rate supports a 10% stake — and a 45% win rate gives −10%, which is the formula telling you to not bet at all. A negative Kelly is information, not an error: the price you are paid does not cover your odds.
What full Kelly actually does to a bankroll
Full Kelly maximizes the per-bet log-growth rate g = p·ln(1 + b·f) − q·ln(1 − f). The catch is what that maximization buys you in the short run. With even-money bets, a full-Kelly bankroll has roughly a 50% chance of falling to half its peak at some point, and about a 1-in-4 chance of falling to a quarter of its peak. Those are not tail risks; they are the normal texture of full Kelly. Most people who watch their bankroll do that to themselves stop long before the math does.
There is a second, subtler problem: you do not know the true p and b. Kelly is maximally aggressive exactly at the point where its inputs are right — and its inputs are estimates. If your real win rate is 55% but you believe it is 60%, your "full Kelly" stake is already an overbet. And overbetting is asymmetric in the worst way: bet less than Kelly and you simply grow more slowly; bet more — 2× Kelly, even on a slightly overestimated edge — and the expected log-growth of your bankroll turns negative, so the bankroll trends to zero over time. Underbetting is a cost; overbetting is a slow ruin. That asymmetry is the entire case for fractional Kelly.
Why most people use half Kelly (or less)
The standard trade-off, in the small-edge regime where most real edges live: betting half of Kelly retains about 75% of the long-run growth while cutting per-bet variance to roughly a quarter. Quarter Kelly keeps a little under half the growth with about a sixteenth of the variance. The growth-versus-risk curve is steep at first and then flattens — which is why the practical menu is quarter, half and full, with half as the default for almost everyone.
Our Kelly calculator defaults to half Kelly for exactly this reason. It shows, for your specific numbers, the stake and the per-bet log-growth rate at 25%, 50%, 75% and 100% of Kelly side by side, so you can see the trade-off in your own units instead of an abstraction. If the Kelly fraction comes out zero or negative, it tells you directly: do not place the bet.
How to estimate p, W and L without fooling yourself
Most Kelly failures are estimation failures, not formula failures. A few habits that keep the numbers honest:
- Sample size first. A 60% win rate over 20 bets has a 95% confidence interval of roughly 40% to 80%. Use at least a hundred closed bets or trades — several hundred for anything you will size seriously — and treat the low end of the interval as your planning case.
- Same market, same rules. p and W/L must come from the exact strategy you intend to run: same instrument, same timeframe, same entry and exit rules, including fees and slippage. A backtest that cherry-picks its best period flatters Kelly more than any input error does.
- Expect the edge to drift. Market edges decay and betting lines move. Re-estimate p and b on a rolling window and re-size whenever the numbers change. Kelly is a policy, not a setting you make once.
- Check the price before the probability. In betting, convert the offered odds to an implied probability first — your p must beat it before any Kelly stake exists. The Odds Converter and the Implied Probability calculator on this site do exactly that.
Using the Kelly calculator
The Kelly Criterion calculator takes four inputs — win rate (in %), account size, average win and average loss — plus a fractional-Kelly selector (25 / 50 / 75 / 100, defaulting to 50). It returns:
- Optimal bet — the stake for your chosen fraction, in currency
- Kelly % — the full-Kelly fraction the formula returns
- Expected value — p·W − q·L per full bet
- Growth rate — the per-bet log-growth g for the selected fraction
- Win/loss ratio — b = W/L, the payoff structure of the bet
- A fraction comparison table — stake and growth rate at quarter, half, three-quarter and full Kelly, so the volatility trade-off is visible at a glance
Everything runs in your browser; nothing is submitted. If you work in fixed stop-loss terms rather than win/loss terms, the Position Sizing calculator is the companion tool: it sizes a position from account risk % and stop distance, which is the right framework when your "average loss" is defined by your stop rather than by history.
Kelly vs other sizing approaches
Kelly is optimal under strict assumptions — a repeated, independent bet with known p and b, an infinite horizon, and log-utility over wealth. Real markets violate every one of those, so practitioners blend it with simpler rules:
- Fixed fractional risk (risk 1–2% of the account per trade, sized off the stop): robust to estimation error and easy to justify, but it never scales the stake with the size of your edge.
- Kelly as a cap, not a target: size by fixed risk, then take the minimum of that and (say) half Kelly. You get Kelly's protection against overbetting without its sensitivity to a noisy p.
- Volatility targeting (size inversely to realized vol): the portfolio-world cousin of fractional Kelly; useful when your "bet" is a continuously managed position rather than a discrete one.
A sensible working rule: compute Kelly on your best, conservative estimate of the edge; never stake more than half of it; and let a fixed-risk rule be the floor you check against. Once the sized strategy is running, the Sharpe ratio is the right yardstick for how it is performing — and the odds-conversion guide shows the odds → implied probability → Kelly pipeline that betting-side applications usually start from.