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Multiple conditions change the question
The probability of one outcome occurring is different from the probability that several outcomes all occur. An accumulator makes this distinction especially visible because every required condition usually needs to be satisfied.
Here we use hypothetical percentages to explore that mathematics. They are not forecasts, selections or recommendations.
Multiply only when the assumption fits
For independent events, the chance that all occur is the product of their individual probabilities. If each of four independent events has a 70% chance, the combined probability is:
| Required outcomes | Combined probability |
|---|---|
| 1 | 70.00% |
| 2 | 49.00% |
| 3 | 34.30% |
| 4 | 24.01% |
| 6 | 11.76% |
The inputs are assumed probabilities. They were not obtained by treating bookmaker prices as objective forecasts.
When outcomes are related
Independence means that knowing one outcome does not change the probability of another. In sport, that assumption can fail. A team scoring several goals and that team winning the same match are related outcomes.
The general rule is P(A and B) = P(A) × P(B given A). Multiplying P(A) and P(B) is valid only when independence applies. This is why a same-game combination cannot generally be analysed by blindly multiplying standalone percentages.
A larger price does not remove uncertainty
For a standard multiple, quoted decimal prices are commonly multiplied. But the resulting price is still not a measured probability of success, and settlement rules can affect how void or cancelled outcomes are treated.
The larger number can draw attention to the possible return while obscuring the additional conditions. A single unsuccessful required outcome can be enough for the combination to fail.
Read the assumptions alongside the result
Before interpreting any probability example, ask whether its events are independent, whether the input probabilities are justified and whether it describes all relevant outcomes. Precise arithmetic cannot repair an unreliable assumption.
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Sources & methodology
All prices and numerical examples are hypothetical; calculations are shown so they can be checked independently.
- This guide distinguishes quoted prices from true probabilities and states the assumptions behind each worked example.
- Mathematical method: reciprocal probability, odds-format identities and, where stated, the multiplication rule for independent events. These are derived in the worked examples above.
- Gambling Regulatory Authority of Ireland: Get Help — local support information.