Combined price and return
For decimal prices d1 through dn:
Combined odds = d1 x d2 x ... x dn
Three legs at 1.80, 2.00 and 2.20 give 1.80 x 2.00 x 2.20 = 7.92. A 10-unit stake has a potential gross return of 10 x 7.92 = 79.20 units and potential profit of 79.20 - 10 = 69.20 units.
Raw break-even probability
The reciprocal of the combined price is 1 / 7.92 x 100 = 12.63%. Multiplying the three raw reciprocals gives the same result:
(1 / 1.80) x (1 / 2.00) x (1 / 2.20) x 100 = 12.63%.
That multiplication describes joint probability only when the leg probabilities are independent. OpenStax distinguishes independent from dependent events. Same-match legs, shared team news and common weather can create dependence, so multiplying standalone probabilities can be wrong.
Void and push treatment
DraftKings' market rules are one operator example of how voids and pushes affect multiples. If the 2.00 leg is settled at 1.00, the revised combined price is 1.80 x 1.00 x 2.20 = 3.96. A 10-unit stake then returns 10 x 3.96 = 39.60 units.
How another leg changes the bet
| Active legs at 1.80 | Combined price | Raw reciprocal |
|---|---|---|
| 1 | 1.80 | 55.56% |
| 2 | 3.24 | 30.86% |
| 3 | 5.832 | 17.15% |
| 4 | 10.4976 | 9.53% |
The larger possible return comes with a smaller joint break-even percentage. It does not show whether any leg or the combined bet has positive expected value.
Trace how each leg changes the multiple
The combined price can be built one leg at a time. Starting with a 10-unit stake, two legs at 1.50 and 2.00 produce combined decimal odds of 3.00 and gross return of 30 units. Adding a third leg at 1.20 raises the combined price to 3.60 and gross return to 36 units. The added leg contributes only 6 units to the winning return in this example, but it also creates another condition that must settle as a win.
A contribution table makes the trade-off visible:
| Stage | Active prices | Combined odds | Gross return on 10 units |
|---|---|---|---|
| One leg | 1.50 | 1.50 | 15.00 |
| Two legs | 1.50 x 2.00 | 3.00 | 30.00 |
| Three legs | 1.50 x 2.00 x 1.20 | 3.60 | 36.00 |
Check dependence before multiplying probabilities
Multiplying decimal payoffs is a settlement calculation. Multiplying estimated win probabilities is justified only for independent events, or by using conditional probabilities for dependent events. Two selections from the same match can share scoring, team-news or game-state drivers. The combined odds may still be displayed, but a probability assessment that assumes independence can be misleading.
Before accepting a calculated return, verify the permitted combination, each market's settlement period, treatment of void legs and whether the operator reprices related selections.
Related resources
Compare the concise accumulator definition or use expected value to evaluate an explicit probability estimate.
Continue learning
- Next guide: Ante-Post Odds
- Related guide: Best Odds Guaranteed
Assumptions and limitations
Calculations assume all prices are accepted and no boost, cap, deduction or commission applies. Raw reciprocals contain any embedded margin. The table repeats one illustrative independent price and is not a performance forecast. If betting is affecting finances or wellbeing, the NHS support guide lists practical help.
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