The Kelly criterion: how much to stake once you've found an edge

Kelly gives a mathematically optimal stake from your edge and the price. It is also famously too aggressive to use in full, and understanding why is more useful than the formula.

5 min read

Finding a good price tells you what to bet on. It says nothing about how much. Stake too little and an edge earns almost nothing; stake too much and a normal losing run takes you out entirely. The Kelly criterion is the formula that answers the question properly.

The formula

Where p is your estimated chance of winning, q is 1 − p, and b is the decimal odds minus 1 — the profit per dollar staked.

Say you rate something a 55% chance and the price is $2.00, so b = 1.00:

On a $2,000 bankroll that is a $200 bet. If your 55% estimate is right, that is the stake that grows the bankroll fastest over time. If the formula returns zero or a negative number, it is telling you there is no edge and the correct stake is nothing.

Why nobody sensible uses full Kelly

Kelly maximises long-run growth, which is not the same as being comfortable to live through. A full-Kelly bettor swings violently: drawdowns of 50% or more are entirely normal, not a sign anything has gone wrong. Most people stop betting during one, which converts a theoretical optimum into a real loss.

The deeper problem is that Kelly assumes p is correct. It never is — it is an estimate, usually derived from no-vig fair odds that carry their own error. Overestimate your edge by a little and full Kelly overstakes by a lot, because the formula scales directly with the number you got wrong.

Fractional Kelly

The standard fix is to stake a fixed fraction of what Kelly says — half, quarter or less. Quarter Kelly on the example above turns a $200 bet into $50.

FractionStake on the exampleCharacter
Full$200Theoretically optimal, brutal in practice
Half$100Most of the growth, much less swing
Quarter$50Common default; forgiving of a wrong estimate

Quarter Kelly gives up surprisingly little long-run growth for a large reduction in volatility, and — more importantly — it stays sensible when your probability estimate is off. It is what EdgeBoard's EV Finder shows for that reason.

Things worth being honest about

This is the maths behind the EV Finder, which does it for you across 11 Australian bookmakers.