Kelly Criterion Calculator

The Kelly criterion is a mathematical formula for the optimal fraction of your capital to risk on each bet or trade. Developed by John L. Kelly Jr. at Bell Labs in 1956, it determines the stake that maximises the long-run geometric growth rate of your capital. The formula is: Kelly fraction = (b × p − q) / b, where p is your win probability, q = 1 − p, and b = average win / average loss (your payoff ratio). A positive fraction means stake that percentage of your bankroll; zero or negative means your edge is absent — do not bet.

Full Kelly maximises your long-run growth rate in theory, but it also produces the largest possible drawdowns along the way. A string of losses under full Kelly can wipe out a substantial portion of your capital very quickly — the strategy is mathematically optimal only if your inputs (win rate, payoff ratio) are perfectly accurate, which they never are in practice. Half-Kelly (staking half the full Kelly fraction) retains approximately 75% of the optimal growth rate while roughly halving the variance and drawdown risk. Most professional traders and portfolio managers recommend half-Kelly or even quarter-Kelly as their practical staking rule.

A negative Kelly fraction means your trading system has a negative edge — on average, you are expected to lose money per trade at the current win rate and payoff ratio. The Kelly formula’s recommendation in this case is to bet nothing (or, if possible, to take the other side of the trade). If you see a negative Kelly output, you need to either improve your win rate, improve your reward-to-risk ratio, or both, before risking capital.

The binary Kelly formula is: f* = (b × p − q) / b, equivalently f* = p − q/b, where: f* is the optimal fraction of capital to stake (as a decimal, multiply by 100 for the percentage); p is the probability of a winning trade (win rate / 100); q = 1 − p is the probability of a losing trade; b = average win / average loss is the payoff ratio (the net odds, also called reward-to-risk ratio). For example, a 55% win rate (p = 0.55) with a payoff of 1.5 (average win $300, average loss $200) gives f* = (1.5 × 0.55 − 0.45) / 1.5 = 0.375 / 1.5 = 0.25, meaning 25% of bankroll per trade.

Fixed-fractional position sizing (for example, the '2% rule') risks a fixed percentage of your account on every trade regardless of your edge. The Kelly criterion is dynamic: the recommended fraction is proportional to your actual edge — a higher edge earns a larger fraction, a lower edge a smaller one. In practice, both approaches say 'risk a fraction of your account per trade'; Kelly tells you the mathematically optimal fraction given your specific win rate and payoff ratio, while fixed-fraction is a simpler rule of thumb that applies a predetermined limit. Many traders use Kelly to benchmark whether their fixed fraction is too large or too small.

Yes. Kelly’s 1956 paper was actually framed in terms of information theory and signal transmission, not gambling — it applies to any repeated-bet scenario where a win probability and payoff ratio can be estimated. It has been applied by professional traders, hedge funds, and sports bettors. The main challenge in trading is accurately estimating p (win rate) and b (payoff ratio) from historical data — a small overestimate of either can lead to over-betting. As long as you have a reasonable sample of trades (at least 30–100) and can calculate your average win and loss, the Kelly formula applies.

Edge per R (edgePerR = p × payoffRatio − q) is the numerator of the Kelly formula before dividing by the payoff ratio b. In other words: Kelly fraction = edgePerR / payoffRatio. This reveals something important: you need both a positive edge AND a meaningful payoff ratio to justify a significant stake. A system with a large edge but a very low payoff (e.g. scalping with 0.1R payoff) can still have a large Kelly fraction because the edge is divided by a small b; conversely, a high payoff system with a thin edge will have a modest fraction.

At a minimum you need 30 trades — and ideally 100 or more — before the win rate and average win/loss figures from your history become statistically meaningful. With a small sample, a single large winner or loser can shift all three inputs dramatically, leading to a very different Kelly fraction. Many practitioners apply an additional safety haircut (for example, using 80% of the estimated edge as the input, or using the lower bound of a confidence interval on win rate) precisely because Kelly is highly sensitive to input estimation error.

Not directly. The Kelly fraction tells you what percentage of your bankroll to put at risk — it does not translate directly to a share count without knowing your stop-loss distance. To convert: first use the Kelly fraction to calculate the dollar amount at risk (kellyBet = fraction × accountSize); then divide that by the risk per share (entry price minus stop-loss price) to get the number of shares. The Position Size calculator automates this second step: once you know your Kelly (or half-Kelly) bet size, use it as the dollar risk input there.

Betting more than the full Kelly fraction is mathematically suboptimal: above 2× Kelly the expected geometric growth rate actually becomes negative, meaning you would be better off not betting at all. Between 1× and 2× Kelly, you are growing slower than Kelly while taking on more risk. Interestingly, 2× Kelly has the same long-run growth rate as not betting at all (0%), but with enormous variance. This is why Kelly should be treated as a hard upper ceiling — never a starting point to scale up from.

The main limitations are: (1) Input sensitivity — small errors in your estimated win rate or payoff ratio can dramatically change the recommended fraction, often in the direction of over-betting. (2) Estimation requires a large trade sample — fewer than 30–50 trades make the estimates unreliable. (3) It assumes the same fraction is staked on every trade (fixed-fractional with reinvestment), which means the actual bet size changes every trade as the bankroll grows or shrinks. (4) It assumes independence between trades and a stationary (unchanging) win rate and payoff — neither of which is guaranteed in live markets. (5) It ignores correlation across simultaneously open positions. For these reasons, half-Kelly (or less) is the standard practitioner recommendation.

Yes. The Kelly criterion was notably applied by Ed Thorp — the mathematician who beat blackjack (documented in Beat the Dealer) and later ran one of the first quantitative hedge funds, Princeton-Newport Partners. Thorp has written extensively about using fractional Kelly for portfolio management. Renaissance Technologies and other quantitative funds are widely believed to use Kelly-based position sizing. That said, most practitioners use fractional Kelly (typically 25–50% of full Kelly) to manage the practical risks of estimation error and drawdown.