Kelly criterion

A formula that sizes your position — the fraction of capital to risk — for the fastest long-run growth, based on your win rate and your reward-to-risk odds; most traders bet only a fraction of it because full Kelly swings hard.

The Kelly criterion is a position-sizing formula that tells you what fraction of your capital to risk on a bet to maximise long-run compound growth. It weighs two things: your edge — how often you win and how much you make versus lose — and the odds. In its simplest form the fraction is your edge divided by the odds, so a bigger edge or better payoff justifies a larger bet, while a thin edge calls for a small one. Bet more than Kelly and growth actually slows while ruin risk climbs; bet less and you grow steadily but slower.

In options this is a discipline, not a plug-in number. To use it you need honest inputs — a realistic win rate and an average win-to-loss ratio from your own history — and defined-risk trades where the maximum loss is knowable. A trade with a 70% probability of profit that risks 200 dollars to make 100 has a positive but modest Kelly fraction, telling you to commit only a slice of the account, not to load up because the win rate looks high.

The common mistake is using full Kelly with over-optimistic inputs. Full Kelly is brutally volatile and a slightly overstated edge tips you into over-betting and deep drawdowns, so almost everyone trades half-Kelly or quarter-Kelly, which keeps most of the growth for a fraction of the swings. And it only makes sense on edges you can actually estimate — feed it a fantasy win rate and it will happily size you into ruin.

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Educational use only. Quotes are delayed ~15 minutes and nothing here is financial advice. Options trading involves substantial risk of loss.