Kelly criterion

The Kelly criterion answers one question: given an edge, what fraction of your bankroll maximises long-run growth? For a simple bet it's

f* = edge / odds = (bp - q) / b

where b is the net odds, p your win probability, and q = 1 - p.

Two things matter more than the formula:

• When the edge is zero, Kelly is zero. This is the part people skip. If your honest estimate of p doesn't beat the price, the maths tells you to stake nothing — see the crash-game write-up for a worked example where every target came out at f* = 0.
• Full Kelly is too violent. The variance is brutal; the drawdowns will shake you out. Most people who use it size at a fraction of Kelly (a quarter to a half) to trade a little growth for a lot of sleep.

Kelly is only as good as your probability estimate, which is why it sits downstream of honest measurement — the whole point of validate before automating. It also depends on a real edge existing in the first place, which is what signals like order flow imbalance try to find.

Related: expected value.