Three-leg calculation
For illustrative accepted decimal prices 1.70, 1.80 and 1.90:
Combined price = 1.70 * 1.80 * 1.90 = 5.814
For a GBP 10 stake:
Gross return = 10 * 5.814 = GBP 58.14
Net profit = 58.14 - 10 = GBP 48.14
Betfair's current placement guide distinguishes a treble from a double and longer accumulator in the multiple section of the bet slip.
Settlement matrix
| Live outcomes | Ordinary result |
|---|---|
| Three wins | Treble wins |
| Two wins and one loss | Treble loses |
| One early loss | Treble loses regardless of later live outcomes |
| Two wins and one void | Reverts to a double if the rule removes the void leg |
| One win and two voids | Reverts to a single if the rule removes both void legs |
If the middle 1.80 leg is void:
Revised price = 1.70 * 1.90 = 3.23
Revised gross return on GBP 10 = GBP 32.30
The actual operator multiple rules decide voids, dead heats, deductions and maximum payouts.
Joint probability
If illustrative probabilities 0.60, 0.55 and 0.50 are independent:
Joint probability = 0.60 * 0.55 * 0.50 = 0.165, or 16.5%
That multiplication is invalid when one outcome changes another's chance. OpenStax's independence definition should be an explicit gate, not an assumption added after the return is calculated.
Compare structures
| Structure | Positions purchased | What can return after one loss? |
|---|---|---|
| Three singles | 3 | Other winning singles |
| One treble | 1 | Nothing from the treble |
| Trixie | 4 | A winning double can still return |
Use system bets for the line-count and stake consequences of the third structure.
Verify all eight win-loss paths
OpenStax's multiplication rule provides the probability basis for independent event paths, while Betfair's current multiple-bet rules provide one operator example of all-to-win settlement. A three-leg win-loss model has eight terminal paths before voids or partial settlements are added. Only WWW wins a straight treble; every other path loses it.
| Path | Straight treble result |
|---|---|
| WWW | Combined return |
| WWL, WLW, LWW | Loss |
| WLL, LWL, LLW, LLL | Loss |
For independent legs with different probabilities, assign each path its product probability and confirm that all eight probabilities sum to one. With dependent legs, estimate the joint paths directly or use ordered conditional probabilities. Do not silently use the product of three marginals.
A void introduces a different tree: confirm whether the affected leg becomes decimal 1.00, whether the remaining double is valid, and whether promotions or minimum-leg conditions survive. Record the operator's final revised price alongside your independently calculated value.
Continue learning
- Next guide: 1X2 Accumulators
- Related guide: Accumulator Calculator
- Definition: Treble Bet
Assumptions and limitations
Examples are illustrative and use a straight treble. They do not establish that any leg is correctly priced or independent. Promotions, each-way terms, cash out and free-bet settlement require separate rules.
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