A traditional accumulator commonly combines outcomes from separate events. If the outcomes are reasonably independent, multiplying their probabilities produces the probability that every leg succeeds.
A bet builder combines markets from the same event. Those outcomes may be positively or negatively correlated. A home win and a home player scoring are connected, so multiplying two stand-alone probabilities as though they were independent can produce a misleading answer.
| Question | Accumulator | Bet builder |
|---|---|---|
| Where do the legs come from? | Often separate events | Usually one event |
| Can probabilities be multiplied? | Only when independence is a reasonable assumption | Usually not without modelling the joint outcome |
| How is value assessed? | Joint probability against combined price | Joint probability against the quoted builder price |
| Main mistake | Ignoring compounded margin | Ignoring correlation |
Worked illustration
Three independent estimates of 60%, 55% and 65% produce a joint probability of 21.45%. Fair decimal odds are therefore about 4.66. An offered price of 4.20 would have negative expected value under those assumptions.
For a correlated builder, suppose the complete combination is assessed at 40%. Fair decimal odds would be 2.50. An offered price of 2.25 would again be below the entered fair price. These figures are illustrations, not live odds or predictions.
The expected-value guide explains the calculation, while the price-comparison guide covers market and settlement matching.