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
Enter a budget in whole cents and two to ten decimal odds for all mutually exclusive outcomes. Currency is a display choice under Money unit; no exchange-rate conversion is performed. Select Calculate, then open Calculation details for the stake and payout table.
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 exact cents so they sum to the entered budget. Each modeled gross payout is rounded down to a cent before subtracting the full budget. The lowest modeled outcome profit can differ from the unrounded theoretical percentage, including becoming zero or negative. Actual settlement rules may differ. 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. Budgets must use whole cents. Cent allocation and the conservative payout rule are applied explicitly, while theoretical percentages describe the unrounded mathematical model.
Saving and Revising a Scenario
A successful calculation is saved in this browser and can be restored on the next visit. Editing an input marks the saved result as stale. Select Calculate to update it. Reset clears this calculator’s inputs and saved result. Other scripts on this site may access values saved in browser storage.
Sources
Betfair Help: stake-inclusive decimal odds. The allocation formula and modeled rounding assumptions are specified above.
