What is the Kelly criterion formula?

Kelly stake as a share of bankroll = (b x p - q) / b, where b is the decimal odds minus 1, p the win probability and q = 1 - p. At 2.20 with a 50% chance: (1.2 x 0.5 - 0.5) / 1.2 = 8.33% of bankroll.

Why use half or quarter Kelly?

Full Kelly assumes your win probability is exactly right. In practice it rarely is, and overestimating the edge makes full Kelly stake too much. A fraction of Kelly gives up a little growth for much smaller swings, which is why quarter Kelly is the default here.

Why does the calculator say no bet?

Kelly only stakes when the bet has positive expected value. If the odds are at or below fair for the probability you entered, the formula comes out at zero or below, and the right stake is nothing.

Should I recalculate after every bet?

Kelly sizes each bet as a share of your current bankroll, so the stake shrinks after losses and grows after wins. Use the bankroll you have now, and only money you can afford to lose.

Kelly criterion calculator

Work out how much of your bankroll a bet with an edge is worth. Enter the odds, your bankroll and the true win probability to see the full, half or quarter Kelly stake. Free, no account, decimal, American and fractional odds.

Kelly stake

Your odds

Bankroll

True win probability from

Sharp odds, your side

Sharp odds, other side

Fair probability after removing the margin: 47.48%

Kelly fraction

Stake: 9.28
Of bankroll: 0.93%
Full Kelly: 3.71%
Expected value: +4.45%

Kelly is only as good as the probability you give it. An overestimated edge makes it overbet, which is why most bettors use a fraction of it. Results still swing widely from bet to bet.

How it works

The Kelly criterion stakes a share of your bankroll in proportion to your edge:

f = (b x p - q) / b

b is the net odds: decimal odds minus 1.
p is the win probability and q = 1 - p.
f is the share of bankroll to stake. Zero or below means there is no edge and no bet.

The fraction switch multiplies f by 1, 0.5 or 0.25. The win probability comes from the same three sources as the EV calculator: a sharp market with the margin removed by the logarithmic method, a fair price, or your own estimate.

Use it with care

Kelly maximises long-run growth only when the probability is right, and it is sensitive to errors: overstate a 2% edge as 4% and full Kelly stakes twice what it should. Even with a real edge, bankrolls swing a long way before the long run arrives. That is why fractional Kelly is common, and why the stake here is a ceiling, not a target. Set limits that suit you, and see responsible gambling for tools that help.

Kelly needs a price with an edge to begin with. The free value bets page lists prices above the fair line across bookmakers, and the CLV calculator and Pinnacle closing odds lookup show afterwards whether you beat the closing price, the best check that your probabilities hold up.

More betting calculators

Calculators show arithmetic, not predictions. No result here guarantees a profit, and betting always carries the risk of losing your stake. Bet only what you can afford to lose; help and limits are on the responsible gambling page.

Frequently asked questions

What is the Kelly criterion formula?: Kelly stake as a share of bankroll = (b x p - q) / b, where b is the decimal odds minus 1, p the win probability and q = 1 - p. At 2.20 with a 50% chance: (1.2 x 0.5 - 0.5) / 1.2 = 8.33% of bankroll.
Why use half or quarter Kelly?: Full Kelly assumes your win probability is exactly right. In practice it rarely is, and overestimating the edge makes full Kelly stake too much. A fraction of Kelly gives up a little growth for much smaller swings, which is why quarter Kelly is the default here.
Why does the calculator say no bet?: Kelly only stakes when the bet has positive expected value. If the odds are at or below fair for the probability you entered, the formula comes out at zero or below, and the right stake is nothing.
Should I recalculate after every bet?: Kelly sizes each bet as a share of your current bankroll, so the stake shrinks after losses and grows after wins. Use the bankroll you have now, and only money you can afford to lose.