Calculate arbitrage from your inputs, with a result breakdown and worked steps.
Arbitrage Formula and Method
Sum implied fractions = Σ(1 / odds)
Enter prices for every mutually exclusive outcome of one event and a total budget. The reciprocal total describes the market’s implied coverage. A value below one is necessary for a positive unrounded equal-return margin under the stated prices and ordinary cash settlement.
How to Use This Calculator
Select the result and any applicable method before entering the visible values. Check the selected record, unit and scoring conventions before calculating. Review the primary result and its breakdown, then open the calculation steps to see how the inputs were used.
Worked Example
With the example inputs in the table, the result is 5 USD. Only a reciprocal total below 100% gives a positive theoretical equal-return margin.
Unrounded stake on outcome i = budget / (odds i × reciprocal total) Round stakes to cents with largest-remainder allocation.
Input and Example Guide
| Input or category | Example or weight | Entry guidance |
|---|---|---|
| Money unit | U.S. dollars (USD) | Choose the convention that applies to your record. |
| Total stake budget (selected currency) | 100 | Use the stated unit; retain available precision. |
| Exhaustive outcome prices (decimal odds) | 2.1, 2.1 | Use matching entries separated by commas or spaces. |
Interpreting the Result
Stakes are allocated inversely to their prices, then apportioned in cents so they sum to the rounded budget. The smallest outcome profit after this rounding is emphasized; it can differ from the ideal percentage. Missing outcomes, unequal settlement, price movement and stake acceptance limits invalidate an apparent margin.
All outcomes must cover the same event exhaustively without overlap. Prices, acceptance limits, currency rounding, fees and settlement differences can erase the calculated margin.
Assumptions and Common Input Errors
Only a reciprocal total below 100% gives a positive theoretical equal-return margin. Keep the same currency and settlement conditions throughout a scenario. Displayed currency amounts are rounded to two decimals; calculations retain precision unless cent allocation is explicitly described.
Saving and Revising a Scenario
A successful calculation is saved in this browser and can be restored on the next visit. Editing an input clears the old result so it is not mistaken for an updated calculation. Reset returns the example inputs and clears the saved result.
Sources
Betfair Help, Decimal Odds and Stake-Inclusive Returns, reviewed 2026. Arithmetic and scenario assumptions are specified above.