The mathematical condition
For mutually exclusive, exhaustive outcomes with decimal odds o₁, o₂, and optionally o₃, add their reciprocals: S = 1/o₁ + 1/o₂ (+ 1/o₃). If S is below 1, the quoted prices support a positive theoretical margin before costs. If S is 1 or higher, that set of odds does not produce positive arbitrage.
For a total stake B, the continuous stake allocation is sᵢ = B × (1/oᵢ) / S. Each winning payout is then B/S. The profit rate before costs is (1/S − 1) × 100%. This rate is a calculated return, not the probability that the bets will be accepted.
Two-outcome example: 2.15 and 2.20
This is an invented teaching example, not a live offer. Imagine a market where exactly one of A and B wins, and both operators use the same settlement rules. With a total stake of 1,000 units and no extra costs, the rounded stakes are 505.75 on A at 2.15 and 494.25 on B at 2.20.
If A wins, the gross payout is 1,087.3625 before currency rounding. If B wins, it is 1,087.35. Using the smaller payout gives 87.35 in calculated net profit before costs. The total stake is 1,000, not 1,000 on each selection.
| Outcome | Decimal odds | Stake | Gross payout if it wins |
|---|---|---|---|
| A | 2.15 | 505.75 | 1,087.36 |
| B | 2.20 | 494.25 | 1,087.35 |
Football: the draw must also be covered
In a regular-time 1X2 market, the outcomes are home win, draw and away win. At illustrative odds of 2.10, 4.20 and 4.20, a 1,000-unit stake is split 500, 250 and 250. Each outcome pays 1,050, producing 50 before costs.
Do not replace the draw with an unrelated two-way winner market. A market including extra time or a different match period can settle differently. Double-chance selections overlap: a home win can satisfy both 1X and 12. The simple reciprocal formula and the public calculator on this site assume exclusive outcomes, so they must not be used directly for overlapping double-chance prices.
Check whether the calculation is achievable
The public calculator lets you practice without opening an account. For an actual opportunity, enter the prices currently offered by each operator and compare the whole combination again if one changes.
- Same event, period and settlement rules on every row, including extra time, abandonment and voiding.
- Every required stake must be accepted in full at the entered odds; a partial acceptance breaks the assumed allocation.
- Use only operator products available to your residence and current physical location. The website language does not establish eligibility.
- Include known costs, conversion and rounding. Exchange commission and available liquidity require a separate appropriate calculation.
- Treat a saved or frozen card as an observation. It does not reserve odds or funds.
What to look at in ArbiScan
Read the odds timestamp, market type, start time, stake on each row and calculated minimum net result. Set residence and playing location separately before selecting operator products. An unverified availability label means information is missing; it is not approval.
The public homepage and portfolio can show observed calculations and simulations. They are different from accepted bets and an actual settled result. In the portfolio, compare estimated profit with recorded settlement rather than treating the estimate as earned money.
Common questions
Can I use one bookmaker? The formula depends on the combined available prices, not the number of brands. It cannot create a margin when the sum is 1 or higher, and one operator may not permit or accept all required selections.
Does a green result mean I cannot lose? It means the inputs produce a positive minimum calculated payout under the stated assumptions. Changed odds, missing acceptance, different rules or costs can turn the real result negative. ArbiScan is intended for adults, 18+; learn with hypothetical amounts before making any decision.
Why not split the stake equally?
In a fictional 1X2 example with odds 2.10 / 4.20 / 4.20 and a budget of 1,000, the allocation is 500 / 250 / 250. Each of the three outcomes returns 1,050, giving 50 before costs. Equal stakes produce different returns. All three outcomes must be covered under identical settlement rules.