What is the Kelly criterion?

A formula from information theory (John Kelly, 1956) for the share of a bankroll to stake on a bet with a known edge so that the bankroll grows fastest over many bets. With decimal odds o and win probability p: f = (p x o - 1) / (o - 1).

Why use half or quarter Kelly?

Full Kelly assumes your probability is exactly right. Real estimates are not, and an estimate that is too high gives stakes that are too big, with deep drawdowns. A fraction of Kelly gives up some growth for much smaller swings.

What if Kelly says zero?

Then the odds imply a higher probability than your estimate: by your own numbers the bet has no edge, and Kelly says not to place it.

Does Kelly apply to surebets?

Not directly. A surebet has no outcome risk if every leg stands, so the question there is how much of your bankroll each book holds and the risk of a leg being voided or limited, not the Kelly fraction.

Kelly criterion calculator

Your odds, your probability, your bankroll: see your edge and the stake the Kelly formula gives, at full, half, quarter or a tenth of Kelly.

Odds (decimal)

Your probability (%)

Bankroll

Fraction

Your edge

10.00%

Full Kelly

8.33%

Stake

20.83

Expected value of this stake: +2.08, if your 50.0% is right. Implied probability of the odds: 45.45%.

Kelly is only as good as your probability. An estimate a few points too high turns into stakes that are too big, which is why most people use a fraction of it.

The formula

With decimal odds o, your probability of winning p and b = o - 1:

f* = (b × p - (1 - p)) / b = (p × o - 1) / (o - 1)

f* is the share of the bankroll to stake. The top of the fraction, p × o - 1, is your edge: what you expect back per unit staked, minus the unit. No edge, no stake.

Simulated: odds 2.20, your probability 50%. Edge = 0.50 × 2.20 - 1 = 10%. Full Kelly = 0.10 / 1.20 = 8.33% of the bankroll. Quarter Kelly on a 1,000 bankroll: 20.83.

Where the probability comes from

Kelly needs a probability that is better than the odds' own. Some bettors use a model; many use a sharp book's price with the margin taken out (the no-vig calculator does that) and compare it with a softer book's odds. Either way, the answer is only as good as the estimate.

Why most people use a fraction

Full Kelly maximises long-run growth if your edge is real and exactly known. It also produces large swings: a run of losses can take a big share of the bankroll. Overestimate your probability by a few points and full Kelly overstakes. Half Kelly keeps about three quarters of the growth with far smaller swings, which is why fractional Kelly is the common choice.

Whatever the formula says, only stake money you can afford to lose. Results vary and no stake size removes the risk of a bet.

Prices that are still there

A calculator is only as good as the odds you type into it. Arbistoteles scans 10 crypto sportsbooks prematch and re-reads every leg of a surebet at its book before it shows as confirmed. The free account shows up to 3 live confirmed surebets of 0.99% or less.

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Questions

What is the Kelly criterion?: A formula from information theory (John Kelly, 1956) for the share of a bankroll to stake on a bet with a known edge so that the bankroll grows fastest over many bets. With decimal odds o and win probability p: f = (p x o - 1) / (o - 1).
Why use half or quarter Kelly?: Full Kelly assumes your probability is exactly right. Real estimates are not, and an estimate that is too high gives stakes that are too big, with deep drawdowns. A fraction of Kelly gives up some growth for much smaller swings.
What if Kelly says zero?: Then the odds imply a higher probability than your estimate: by your own numbers the bet has no edge, and Kelly says not to place it.
Does Kelly apply to surebets?: Not directly. A surebet has no outcome risk if every leg stands, so the question there is how much of your bankroll each book holds and the risk of a leg being voided or limited, not the Kelly fraction.

Other free tools

Arithmetic on the numbers you type, nothing saved. It says nothing about whether a bet will win. 18+. If gambling stops being fun, stop.