Free calculator
Arbitrage calculator
Last reviewed August 2026
The calculator
| Outcome | Odds | Stake | Returns | Profit |
|---|---|---|---|---|
| Bet365 | 2.10 | 48.78 | 102.44 | +2.44 |
| Pinnacle | 2.00 | 51.22 | 102.44 | +2.44 |
The worst outcome is the figure that matters. Rounding stakes breaks the equal-return property, so the headline margin is what you would make with fractional stakes and this is what you actually make. Best case here is 2.44.
Nothing is sent anywhere — the arithmetic runs in your browser. It is the same code the GoldEdge scanner uses to price the arbitrages it finds across Pinnacle, Bet365, Betano and Stake.
How the maths works
An arbitrage — a surebet — exists when different bookmakers disagree enough about a market that you can back every outcome and still come out ahead. The test is one line of arithmetic.
Decimal odds convert to an implied probability by inverting them: 1 / odds. Add those across a complete set of outcomes and a normal market gives you more than 100% — the excess is the bookmakers' margin. When prices from different books are combined, that total occasionally lands below 100%, and the shortfall is yours.
invSum = Σ (1 / oi)
// guaranteed return per unit staked
margin = 1 / invSum − 1
// the equal-return split
stakei = total × (1 / oi) / invSum
That split is not a preference — it is the unique one that makes the return identical whichever outcome lands. Stake anything else and you have taken a position on the result, which is the thing arbitrage exists to avoid.
A worked example
Bet365 has Over 2.5 at 2.10; Pinnacle has Under 2.5 at 2.00. Between them those two outcomes cover every possible result.
| Outcome | Book | Odds | Implied | Stake | Returns |
|---|---|---|---|---|---|
| Over 2.5 | Bet365 | 2.10 | 47.62% | 48.78 | 102.44 |
| Under 2.5 | Pinnacle | 2.00 | 50.00% | 51.22 | 102.44 |
| Total | 97.62% | 100.00 | +2.44 |
The two prices cover 97.62% of certainty, so 1 / 0.9762 − 1 = 2.44%. Stake 100 in that proportion and both outcomes return 102.44. The 2.44 is yours regardless of how the match goes — which is why it is worth being pedantic about the guards below.
Where arbitrage goes wrong
Spotting a sum under 100% is the easy half. A false arbitrage costs you both stakes rather than one bad bet, so the checks matter more than the arithmetic does. Each of these has burned somebody:
- Different settlement rules. Pinnacle gives a tennis moneyline action once a set is complete; several other books void the bet if a player retires. Combine those two and a retirement leaves you with one live bet and one refund, not a locked position.
- Different lines. Over 2.5 at one book against Under 2.75 at another is not a covered market. Quarter lines are worse: half the stake pushes, which turns a guaranteed return into a coin flip on the remainder.
- An incomplete outcome set. Backing home and away in a football match ignores the draw. Backing a basketball moneyline priced for regulation time against one priced including overtime is the same error wearing a disguise.
- Stale prices.A book that has stopped updating looks exactly like a generous one. Real arbitrages are usually gone within minutes, so an old price on one leg is the most common reason a "surebet" cannot actually be placed.
- One leg placed. Get the first bet on and find the second gone and you are holding an ordinary bet you never wanted, usually at bad odds.
Bookmakers restrict arbitrage accounts
Arbing is not illegal, but it breaches most bookmakers' terms. Accounts that do it visibly — round stakes on obscure markets, always the outlying price, never a parlay — get limited or closed. That is the practical constraint on how long this works at any one book, and no software removes it.
Frequently asked questions
How do you calculate an arbitrage bet?
Add up the implied probability of every outcome, where implied probability is 1 divided by the decimal odds. If the total is below 1 (100%), an arbitrage exists. The guaranteed return is 1 divided by that total, minus 1. Each outcome's stake is the total stake multiplied by its implied probability divided by the total — that split is the only one that returns the same amount whichever outcome wins.
What is a good arbitrage percentage?
Most real arbitrages sit between 0.5% and 3%. Anything above roughly 10% is far more likely to be a stale price, a palpable error, a mismatched fixture or a difference in settlement rules than a genuine opportunity — GoldEdge discards those rather than showing them.
Why is my profit lower than the margin says?
Rounding. The equal-return split usually asks for stakes like 48.78 and 51.22; once you round to what a bookmaker will actually accept, the returns stop being equal and one outcome pays less than the others. This calculator reports that worst outcome, because it is the only figure genuinely guaranteed.
Can I use this calculator for a 3-way market?
Yes. Add a third outcome and enter all three prices. The arithmetic is identical for any number of mutually exclusive outcomes that between them cover every result — the important word is every: a 1X2 market needs all three, and leaving the draw out does not make it a two-way market.
Does this work for lay bets on an exchange?
Not directly. A lay is a bet on everything the selection is not, and its commission is charged on profit, so it has to be converted to an equivalent back price first — 1 + (1 − commission) / (lay − 1) — and staked as liability rather than as the entered amount. GoldEdge does that conversion automatically when an exchange leg is part of an arbitrage.
Is arbitrage betting legal?
It is not illegal anywhere that betting itself is legal — you are placing ordinary bets at advertised prices. It does breach most bookmakers' terms of service, though, and books routinely limit or close accounts they identify as arbing. That is a commercial risk rather than a legal one.
For research, not betting advice. Positive expected value is an edge across many bets, never a prediction about one. Bet only what you can afford to lose. 18+.