Arbitrage & value
Arbitrage calculator
An arbitrage exists when the best available prices on every outcome of a market, taken together, imply a total probability below 100%. Stake each outcome in proportion to its implied probability and every result returns the same amount — so the position settles the same way regardless of who wins.
This calculator gives you the stake for each leg, the combined market percentage, and the return you are guaranteed once stakes are rounded to whole cents. It reports the worst outcome, not the best: if rounding or the prices themselves leave a losing result, it says so rather than showing you the most flattering leg.
Inputs
Result
- Stake on outcome 1 (at 2.10)Returns €105.44 if it wins
- €50.21
- Stake on outcome 2 (at 4.00)Returns €105.44 if it wins
- €26.36
- Stake on outcome 3 (at 4.50)Returns €105.44 if it wins
- €23.43
- Combined market percentageBelow 100% — an arbitrage exists at these prices
- 94.84%
- Edge
- +5.44%
- Locked-in return (if all legs match)5.44% of the €100.00 staked
- €5.44
Figures assume both legs are matched at the prices shown. Prices move, stakes can be limited or rejected, and an unmatched leg leaves an open position. Check the maximum stake at each venue before you place the first leg.
How this is calculated
stake_i = total x (1 / odds_i) / sum(1 / odds_j)
Each outcome is staked in proportion to its implied probability, which makes every leg return the same amount. The market percentage is sum(1 / odds_j): below 1 the total return exceeds the total stake, which is the arbitrage. Because stakes must be whole cents, the calculator allocates the rounding remainder to the legs with the largest discarded fraction, so the total staked matches what you asked for exactly.
Worked example
A three-way football market where the best price on each outcome sits at a different bookmaker.
- 01Best prices: 2.10 on the home win, 4.00 on the draw, 4.50 on the away win.
- 02Implied probabilities: 1/2.10 = 0.4762, 1/4.00 = 0.2500, 1/4.50 = 0.2222. Total 0.9484, i.e. a 94.84% market.
- 03Because the market is under 100%, an arbitrage exists. The edge is 1/0.9484 - 1 = 5.44%.
- 04Staking EUR 100 in proportion: EUR 50.21 at 2.10, EUR 26.36 at 4.00, EUR 23.43 at 4.50.
- 05Every outcome returns about EUR 105.44, for a guaranteed EUR 5.44 on a EUR 100 outlay.
Questions
Why does the calculator show the worst outcome rather than the best?
Because that is the only figure you are guaranteed. Rounding stakes to whole cents makes the legs return slightly different amounts, and a hand-edited stake can make them differ a lot. Reporting anything other than the minimum would show a profit you might not receive.
Do I need all the outcomes for this to work?
Yes. The maths only holds if the prices cover every result of the market. Two prices from a three-way football market will often sum to under 100% and look like an arbitrage when they are not — the draw is simply missing.
Why is my real return lower than the calculator says?
Common causes are the second leg being matched at a shorter price than quoted, a stake being partially matched or limited, commission at an exchange, or one leg being voided while the other stands. The figure here is the arithmetic of the prices you enter, not a forecast of execution.
Related calculators
These calculators are information tools. They describe the arithmetic of the prices you enter — they are not advice, and they do not predict outcomes. Betting involves risk. 18+ only. If gambling is causing you harm, support is available from Peluuri.