Trading term

What is Kelly criterion?

The Kelly criterion is a formula for the bet size that maximises the long-run growth of capital, given your edge and your payoff. For a 40% win rate paying 2:1 it says risk 10% — and most traders deliberately bet less.

For a payoff of b to 1 with win probability p, Kelly says stake the fraction f = (bp − q) ÷ b, where q is the probability of losing. With p = 0.40, q = 0.60 and b = 2, that gives (0.8 − 0.6) ÷ 2 = 0.10, or 10% of capital per trade. Bet that fraction repeatedly and capital compounds faster than at any other constant fraction.

The shape of the growth curve is the part worth internalising. Growth rises to the Kelly peak and then falls away sharply — betting twice Kelly produces almost no growth at all, and betting three times it is reliably ruinous. The penalty for over-betting is far worse than the penalty for under-betting, which is why practitioners commonly use half-Kelly: it retains roughly three-quarters of the growth rate with substantially smaller swings.

In trading the honest caveat is that Kelly needs your true edge as an input, and nobody knows theirs precisely. An overestimated win rate produces an oversized bet in exactly the direction that does the most damage — which is why full Kelly is a theoretical ceiling rather than a recommendation.

There is an optimum, and it's finite
LONG-RUN GROWTH →0½ Kelly5%Kelly10%2× Kelly20%peak growth≈ zero growthcapital shrinksThe curve is asymmetric: under-betting costs a little, over-betting costs everything.Half-Kelly keeps ~76% of the growth with far shallower drawdowns — which is why most people use it.

Growth peaks at 10% of capital for this edge, then collapses — 2× Kelly earns almost nothing. Under-betting costs a little; over-betting costs everything.

For example

A system wins 40% of the time with winners twice the size of losers. Kelly says 10% of capital per trade. Half-Kelly — 5% — keeps about 76% of the growth rate with far shallower drawdowns. Betting 20% earns almost nothing despite the same edge, and 30% loses money.

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Why it matters to you

Kelly makes explicit something most traders never quantify: that there is an optimum bet size, that it is finite, and that exceeding it destroys returns even when the edge is real. Understanding that curve is what stops a profitable strategy from being ruined by the sizing decision on top of it.

Full Kelly is a ceiling, not a target

Kelly assumes you know your edge exactly and that outcomes are independent — neither holds in trading. Overestimate your win rate slightly and full Kelly becomes over-betting, where the growth curve is steepest downward. Its drawdowns are also brutal even when correct. Most professionals use a half or a quarter of it.

Frequently asked questions

What is the Kelly criterion?

It's a formula for the position size that maximises long-run capital growth: f = (bp − q) ÷ b, where b is the payoff ratio, p the win probability and q the loss probability. It gives the fraction of capital to risk per trade.

How do you calculate Kelly for trading?

Take your payoff ratio b (average win divided by average loss), your win rate p and loss rate q. For a 40% win rate at 2:1, f = (2 × 0.4 − 0.6) ÷ 2 = 0.10 — risk 10% of capital per trade.

Why do traders use half-Kelly?

Because the growth curve is asymmetric. Half-Kelly retains roughly three-quarters of the growth rate with much smaller drawdowns, and it provides a margin of safety against overestimating your own edge — the error that makes full Kelly dangerous.

What happens if you bet more than Kelly?

Growth falls rapidly. At twice the Kelly fraction, long-run growth drops to near zero despite the edge being unchanged; beyond that it turns negative and capital declines even with a genuinely profitable system.

Related terms

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