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Kelly calculator

How much should you stake on a bet you think is underpriced? Enter your bankroll, the odds and your honest estimate of the chance it wins.

Not sure of the probability? Take the margin out of a sharp price with the no-vig calculator.

Result

Edge (EV)
–
Break-even
–
EV per 100
–
FractionOf bankrollStakeExpected profit
Full Kelly–––
½ Kelly–––
¼ Kelly–––
⅛ Kelly–––

Expected value first, then stake size

A bet is worth making when the odds pay more than the true chance of winning deserves. That gap is the edge, or expected value:

EV per unit staked = p × odds − 1

At odds of 2.10 with a 50% chance, EV = 0.5 × 2.10 − 1 = +0.05. On average you make 5 cents per euro staked. On any single bet you either win €1.10 per euro or lose the euro; the 5 cents only shows up over hundreds of bets.

How Kelly turns an edge into a stake

f = (b × p − q) / b, b = odds − 1, q = 1 − p

Same example: b = 1.10, so f = (1.10 × 0.5 − 0.5) / 1.10 = 4.55%. With a €1,000 bankroll, full Kelly is €45.45, half Kelly €22.73, quarter Kelly €11.36 and eighth Kelly €5.68. Re-calculate from your current bankroll as it grows or shrinks, so stakes shrink during losing runs.

Why fractions

Full Kelly is only optimal if your probability is exactly right. Real estimates are noisy, and overbetting hurts much more than underbetting: staking twice the Kelly amount brings expected growth down to roughly zero. Fractional Kelly gives up a little growth for a lot less volatility, which is why the ArbVantage dashboard lets you choose a Kelly fraction and cap any single stake at a percentage of your bankroll.

FAQ

Kelly and EV questions

What is the Kelly criterion?
A formula for sizing bets when you have an edge. It gives the fraction of your bankroll that maximises long-term growth: f = (b × p − q) / b, where b is the decimal odds minus 1, p is your probability of winning and q = 1 − p. Bet more than that and you grow more slowly while taking more risk; bet much more and you can go broke even with an edge.
Why do most people bet a fraction of Kelly?
Because full Kelly assumes your win probability is exactly right, and it never is. If you overestimate your edge, full Kelly overbets, and the swings are brutal even when you're right: drawdowns of half your bankroll are normal. Half Kelly keeps about three quarters of the growth with much smaller swings. Quarter Kelly and below are common for value betting.
Where does the win probability come from?
From a price you trust more than the bookmaker's. Value bettors usually take a sharp market such as Pinnacle or Betfair, remove the margin with the no-vig calculator, and use that fair probability. A probability you made up gives you a stake you made up.
Why does the calculator say not to bet?
Kelly is zero or negative when your probability is at or below the break-even probability for the odds (1 / odds). At 2.10 you need to win more than 47.62% of the time just to break even. Without an edge, the growth-maximising stake is nothing.
What does expected value mean here?
Expected value (EV) is the average profit per bet if you could place the same bet many times: p × odds − 1 per unit staked. +5% means €5 profit on average per €100 staked. Any single bet still wins or loses in full, so EV only shows up over a large number of bets.
Should I use Kelly for sure bets?
No. A sure bet has a fixed result once every leg is placed, so there is no win probability to size against: stake as much as your bookmaker limits and bankroll allow. Kelly is for single bets with a positive but uncertain edge, such as value bets.

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Get the edge and the stake on every value bet

ArbVantage compares 25+ bookmakers against margin-free sharp prices and shows each value bet with its edge and a suggested stake at your Kelly fraction and bankroll. Free for 7 days.

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