Probability

Kelly Criterion

The bet size that maximises the long-run growth rate of a bankroll.

For odds of b to 1 with win probability p: f = (bp - q)/b, where q = 1 - p.

The asymmetry that matters. Half Kelly gives about 75% of the optimal growth rate. Twice Kelly gives a growth rate of exactly zero - you have a real edge and make nothing. Beyond that, a winning strategy becomes a losing one.

That is why practitioners use fractional Kelly. If you overestimate your edge by a factor of two, full Kelly on your estimate is twice Kelly on reality.

Also: uncertainty about your edge argues for a smaller bet, not a larger one.

Full guide

The Kelly Criterion, Explained

How the Kelly criterion sizes bets to maximise long-run growth, the formula, a worked example, and why traders use fractional Kelly.

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