Education · Kelly criterion

The Kelly criterion

The Kelly criterion is a formula for sizing a position based on your estimated edge and the available net return (odds). It maximizes long-run growth — but it is aggressive, and most people use a fraction of it.

The formula

Edge over net return

f* = ( b·p − q ) / b

f* fraction of bankroll to allocateb net return (odds): profit per unit allocatedp your probability of YESq probability of NO (1 − p)

Worked example

Putting in numbers

Suppose a market pays a net return of b = 1.0 (even money), you estimate the true probability at p = 0.60, so q = 0.40.

Net return (odds) b1.0

Your probability p0.60

Opposite q = 1 − p0.40

f* = (1.0 × 0.60 − 0.40) / 1.00.20

Full Kelly suggests20% of bankroll

Use with care

Why most use fractional Kelly

Full Kelly assumes your probability estimate is exactly right. In reality it rarely is, and 20% on a single position is a lot of variance.

Half or quarter Kelly

Many participants allocate ½ or ¼ of the Kelly figure to cut volatility while keeping most of the growth.

Garbage in, garbage out

Kelly is only as good as your probability estimate. Overconfidence leads to oversizing.

Account for correlation

Several related positions act like one big one — size them together, not in isolation.

Cap your unit

Combine Kelly with a hard cap (e.g. never more than 3–5% on one market).

Kelly is a sizing tool, not a forecast. If your edge is negative, Kelly says allocate nothing — and that is often the most valuable answer it gives.