Kelly Criterion Calculator

The Kelly Criterion is a mathematical formula for calculating the optimal fraction of your capital to risk on each trade or bet, maximizing the long-term geometric growth rate of your account. It was developed by John L. Kelly Jr. at Bell Labs in 1956, originally for telephone signal transmission, and later applied to gambling and investing.

The full Kelly formula:

Kelly % = W − (L / R)

Simplified equivalent:

Kelly % = (Win Rate × Average Win − Loss Rate × Average Loss) / Average Win

Variable definitions:

• W = Win probability (as a decimal, e.g., 0.55 for 55% win rate)
• L = Loss probability = 1 − W
• R = Win/Loss ratio = Average winning trade size / Average losing trade size

Worked example: A strategy wins 55% of trades (W = 0.55). Average win = $150. Average loss = $100. R = $150 / $100 = 1.5

Kelly % = 0.55 − (0.45 / 1.5) = 0.55 − 0.30 = 0.25 (25% of account per trade)

This means risking 25% of your account on each trade maximizes long-term geometric growth.

Risked, not invested, and the difference is enormous. Kelly gives you the fraction of your bankroll to put at stake. In a coin-flip bet the two are the same thing, because losing means losing the whole wager. In trading they are not: you exit at a stop, so what is at stake is the distance from entry to stop, not the position size. On a $10,000 account, 25% Kelly means risking $2,500. If your stop is 5% below entry, that is a $50,000 position, which is five times the account. If your stop is 25% away, it is a $10,000 position. Same Kelly, wildly different trade.

Read Kelly as “put 25% of the account into the position” and you will risk a twentieth of what the formula intended. Read it as “risk 25% of the account per trade” and you have it right, which is also why the number frightens people once they understand it.

Full Kelly vs. Fractional Kelly in practice:

Why most professionals use fractional Kelly: Full Kelly is theoretically optimal only if your probability estimates are perfectly accurate. In real trading, win rates and payoff ratios fluctuate, and any estimation error pushes full Kelly straight into over-betting territory. Half Kelly sacrifices roughly 25% of long-term growth but cuts volatility dramatically.

The asymmetry is what settles the argument. Bet under Kelly and you give up a little growth. Bet over it and growth falls away fast, and at twice Kelly the long-run growth rate is zero no matter how good the edge is. Since nobody knows their true win rate to the decimal, and every estimate is drawn from a limited sample, betting half of what you calculated is the cheap insurance against having calculated it too high.

When Kelly is negative or zero: A Kelly percentage of 0% or negative means the strategy has no positive edge, so the expected value is zero or worse. Do not take this trade at all. Fix the strategy before risking capital. The break-even point sits at a win rate of 1 ÷ (1 + R), so at a 1.5 payoff ratio you need to win 40% of the time before Kelly turns positive at all.

Important caveats:

• Kelly assumes you can bet fractional amounts (not always possible with whole shares)
• It assumes returns are independent (real markets have serial correlation)
• Kelly is a long-run formula: over short periods, even a high-Kelly strategy can show losses
• Never bet more than Kelly recommends, even if you feel confident: this is mathematically provable