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Kelly criterion calculator — the mathematically optimal bet size

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Short answer

The Kelly fraction f* = W − (1 − W) ÷ R, where W is win rate and R is the ratio of average win to average loss, is the fraction of capital that maximises long-run compound growth. A strategy winning 40% of the time with wins twice the size of losses gives f* = 0.40 − 0.60/2 = 10% of capital per trade. In practice traders bet half-Kelly or less: the formula assumes your statistics are exact, and betting above true Kelly destroys capital faster than betting below it.

Full Kelly fraction

Half Kelly (practical)

Expectancy per trade

Reference: full Kelly fraction by win rate and win/loss ratio

f* = W − (1 − W) ÷ R. "—" means no positive edge at those statistics. Practitioners typically bet half of these figures or less.

Win rateR = 1R = 1.5R = 2R = 3
35%2.5%13.3%
40%0%10%20%
45%8.3%17.5%26.7%
50%16.7%25%33.3%
55%10%25%32.5%40%
60%20%33.3%40%46.7%

The Kelly criterion answers a precise question: given a repeatable bet with known odds, what fraction of capital maximises the growth rate of wealth over many repetitions? Bet less and you grow slower than possible; bet more and volatility eats the extra — far enough past Kelly, growth turns negative even though every individual bet has positive expectancy. It is the mathematical ceiling on aggression.

Enter your strategy’s win rate, average win and average loss below. The calculator returns full Kelly, half Kelly, and your strategy’s edge — and if Kelly comes out negative, the strategy has no edge to size.

What the formula says, and what it assumes

f* = W − (1−W)/R compresses a strategy into two statistics: how often it wins and how big wins are relative to losses. The output is exquisitely sensitive to both — a win rate of 55% versus 50% at R = 1 moves Kelly from 10% of capital to zero. And the formula assumes those statistics are exact, stationary and independent trade to trade, none of which is true of a real strategy estimated from a finite, regime-dependent sample.

That sensitivity is the practical danger: a backtest’s win rate is an estimate with error bars, and betting full Kelly on an overestimated edge means betting past true Kelly — the region where more risk produces less growth. Overbetting is punished more severely than underbetting to the same degree, which is the asymmetry behind every professional’s discount.

Half-Kelly: the professional convention

Betting half the Kelly fraction sacrifices only a quarter of the theoretical growth rate while roughly halving the volatility of the equity curve — one of the best trades in finance. Most quantitative traders operate at half-Kelly or below, and many cap the result at a fixed ceiling (2–5% of capital) regardless of what the formula permits, because the formula’s inputs are always less certain than they look.

Kelly also assumes you can tolerate its ride: full-Kelly betting routinely visits 50%+ drawdowns on the way to its optimal growth. If a drawdown that deep would end your trading — financially or psychologically — then full Kelly was never your optimum. Read the Kelly output as a ceiling to stay well under, not a target to reach; and confront any Kelly-derived sizing with a Monte Carlo simulation of the strategy’s actual trade sequence before trusting it with capital.

These calculators are free, run entirely in your browser, and store nothing. They produce estimates for NSE trades based on published rates and standard formulas — not investment advice, and not a substitute for your broker’s contract note. INDfolio AI builds algo trading software; the honest connection is that our backtests apply this same cost arithmetic to every simulated trade.

FAQ

Frequently asked questions

What win rate and win/loss numbers should I use?

Measured ones — from a backtest over several years with honest costs, or a live track record of meaningful length. Estimates from memory or from a handful of trades carry error bars wide enough to make the output meaningless. The statistics INDfolio AI reports on every backtest (win rate, average win, average loss) are exactly this calculator’s inputs.

What does a negative Kelly fraction mean?

That the strategy has negative expectancy — at those statistics, no position size makes it grow capital, and the growth-optimal allocation is zero. Fix the strategy, not the sizing.

Why do traders bet half-Kelly instead of full Kelly?

Three reasons: input statistics are estimates, and overbetting past true Kelly reduces growth; full-Kelly equity curves suffer drawdowns most humans abandon; and real trades are not independent — clustered losses in a regime hit harder than the formula assumes. Half-Kelly keeps ~75% of the growth at ~half the volatility.

Is Kelly sizing compatible with the 1–2% risk rule?

They usually agree in spirit: for typical retail strategy statistics, half-Kelly lands near a few percent of capital at risk per trade. When Kelly suggests far more than 2%, treat that as information about how sensitive your edge estimate is, not as permission — the fixed-fractional rule is the floor of prudence, Kelly the ceiling of aggression.

Put your risk rules into a system that enforces them.

INDfolio AI sizes positions, caps daily losses and squares off automatically — the same discipline these calculators teach, enforced in the cloud. Free to start.

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