Kelly Criterion Calculator

The Kelly criterion answers one question exactly: what fraction of a bankroll maximises its long-run growth rate for a given edge. Bet more than Kelly and growth falls while risk climbs. Bet twice Kelly and expected growth is zero, whatever the edge.

It is the correct answer to a question with a brutal assumption attached — that your probability is right. Most of what follows is about that assumption.

The Formula

In decimal terms, with p as your win probability and d as the decimal price:

f = (p × d − 1) ÷ (d − 1)

Worked example. A price of +120 is 2.20 in decimal, and you rate the outcome at 50%.

f = (0.50 × 2.20 − 1) ÷ 1.20 = 0.10 ÷ 1.20 = 8.33% of the bankroll

On a $5,000 bankroll, full Kelly is $416.67. At half Kelly it is $208.33, which is 4.17% of the bankroll, or a little over four units for a bettor whose unit is 1%.

The numerator is the edge: p × d is what the bet returns per dollar in expectation, so subtracting 1 leaves the profit. The denominator scales it by how much you can lose relative to what you can win, which is why the same edge on a longshot warrants a much smaller stake than on a favourite.

Why Fractional Kelly Is The Practical Answer

Full Kelly is optimal only if your probability estimate is exact. Overestimate your edge and you are automatically overbetting, and the penalty is not symmetrical — the growth curve falls away much faster above the optimum than below it.

Half Kelly keeps about three quarters of the growth rate for roughly half the volatility. Quarter Kelly keeps a bit under half the growth for a quarter of the volatility. Given that no bettor's probabilities are exact, giving up some theoretical growth to buy a margin for error is not timidity, it is the correct response to uncertainty about your own inputs.

Full Kelly on a genuine 2% edge also produces drawdowns most people cannot sit through. Losing half the bankroll is a routine event under full Kelly with a real edge, and the bettor who stops betting at that point never collects the growth the formula promised.

When The Answer Is Absurd, The Input Is Wrong

Kelly is a useful liar detector. If it tells you to stake 30% of the bankroll, the honest conclusion is not that you have found a spectacular bet.

A 30% Kelly fraction at standard prices implies you believe you have found something like a fifteen-point edge on a market that hundreds of professionals also price. That happens in a mispriced stale line, occasionally, and in a spreadsheet error, constantly. Check the second explanation first.

The calculator says nothing at all when there is no edge: at a price whose implied probability exceeds your own estimate, the Kelly stake is zero. There is no fractional version of a bad bet. This is the property that makes Kelly worth running even for bettors who then size flat — it refuses bets rather than shrinking them.

Kelly Versus Flat Staking

Most disciplined bettors size flat, in units of 1–2% of bankroll, and they are not making a mistake.

Flat staking needs no probability estimate at all, which removes the input Kelly is most sensitive to. It is simple enough to execute consistently at volume, it makes a record legible — a 3-unit week means something — and it removes the temptation to talk yourself into a bigger number on a bet you like.

The reasonable middle ground, and what our own card uses, is flat sizing with a small number of discrete tiers — one unit standard, two units for a stronger edge — with the tiers set by the Kelly fraction rather than by conviction. That keeps the arithmetic honest without pretending the probabilities are precise to a decimal place.

Whichever you choose, the bankroll projection calculator shows what it does to a season, and variance and drawdowns covers the swings each approach produces.

Frequently Asked Questions