Calculation steps
- Copy the accepted decimal price for each leg from the receipt.
- Remove only legs that the final settlement marks void or push.
- Multiply the remaining prices.
- Multiply the combined price by the total stake.
- Subtract the stake to obtain net profit.
- Divide 1 by the combined price for the raw break-even probability implied by that price.
Worked three-leg calculation
| Leg | Accepted decimal price |
|---|---|
| 1 | 1.80 |
| 2 | 1.65 |
| 3 | 2.10 |
Combined price = 1.80 * 1.65 * 2.10 = 6.237
For a GBP 12 stake:
Gross return = 12 * 6.237 = GBP 74.844
If the operator displays currency to two decimal places, the shown return may be GBP 74.84 under its rounding method.
Net profit using the unrounded calculation = 74.844 - 12 = GBP 62.844
Raw break-even probability = 1 / 6.237 = 0.16033, or about 16.03%
OpenStax defines probability on a zero-to-one scale. The reciprocal is a price conversion, not proof that the bookmaker's complete market is margin-free or that the three events are independent.
Void-leg revision
If leg 2 at 1.65 is void and the accepted rules remove it:
Revised price = 1.80 * 2.10 = 3.78
Revised gross return = 12 * 3.78 = GBP 45.36
Revised net profit = 45.36 - 12 = GBP 33.36
Betfair's Sportsbook rules are one operator example covering multiples, voids, dead heats, cash out and product features. Use the actual receipt and rule edition for the bet being checked.
Calculation record
| Field | Why retain it |
|---|---|
| Accepted prices | Later market prices do not reproduce the contract |
| Total stake | System and each-way screens can display a per-line stake instead |
| Live-leg count | Voids can turn an accumulator into a shorter multiple |
| Displayed return | Allows rounding and cap checks |
| Rule version | Settlement behavior can change by product and date |
| Cash-out transactions | Early settlement changes the payoff |
Probability and value checks
If estimated leg probabilities are independent, their product gives joint probability. If they are dependent, OpenStax's independence condition is not met and a conditional or joint model is required.
Expected value must include every mutually exclusive net payoff, including loss, full win, void, half result, dead heat or capped return where relevant. OpenStax's expected-value method supplies the weighting principle; it does not validate the input probabilities.
Next step
Use Accumulator Odds Calculation for the next part of this topic.
Reconcile price precision and rounding
Calculate with the full accepted prices before rounding the displayed combined price. If a receipt stores 6.237 but the interface displays 6.24, multiplying the stake by 6.24 can differ from the operator's settlement engine. Preserve both values and compare the final cash return with the receipt rather than forcing an early rounded value.
Use these boundary checks:
- A one-leg multiple must reproduce that leg's price.
- A leg settled at decimal 1.00 must leave the other product unchanged.
- A zero stake must produce zero gross return.
- Net profit must equal gross return minus the total cash stake.
- Break-even probability must be between zero and one for any valid decimal price of at least 1.00.
Promotions need a separate payoff function. A free-bet stake may not be returned, an odds boost may apply only above a threshold, and insurance may create a refund state. Do not add those features to the ordinary multiplication formula unless their accepted terms are modelled explicitly.
Continue learning
- Next guide: Accumulator Tracking
- Related guide: Hedging an Accumulator
Assumptions and limitations
The examples use a straight decimal-odds accumulator. Currency rounding, deductions, maximum payouts, each-way terms, systems, free bets and promotional adjustments require additional states.
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