Parlays and accumulators: the margin compounds too
Combining selections multiplies the odds — and multiplies the bookmaker margin with them. A four-fold at 5% margin per leg carries roughly 19% margin in total. The arithmetic of why accumulators are the most profitable product on a bookmaker's shelf.
A parlay (accumulator) requires every selection to win. The odds multiply, which is why a modest set of favourites can pay long odds — and the bookmaker's margin multiplies with them. At a typical 5% margin per leg, a four-fold carries roughly 19% margin against you, compared with 5% on any one of its legs bet alone.
How does the margin compound in a parlay?
If each leg is priced with margin m, the combined margin across n legs is:
combined margin = 1 − (1 − m)^nAt m = 5%: two legs 9.8%, four legs 18.5%, eight legs 33.7%.| Legs | Margin at 3% per leg | Margin at 5% per leg | Margin at 7% per leg |
|---|---|---|---|
| 1 | 3.0% | 5.0% | 7.0% |
| 2 | 5.9% | 9.8% | 13.5% |
| 4 | 11.5% | 18.5% | 25.2% |
| 6 | 16.7% | 26.5% | 35.0% |
| 10 | 26.3% | 40.1% | 51.6% |
A ten-fold at 7% per leg gives away more than half the stake in margin before any judgement about the sport is involved. This is why accumulators are promoted so heavily and why bonus offers cluster around them.
How often do parlays land?
For independent legs, the probability of all winning is the product of the individual probabilities:
| Legs, each 60% likely | Probability all win | Expect one winner every |
|---|---|---|
| 2 | 36.0% | 3 attempts |
| 3 | 21.6% | 5 attempts |
| 4 | 13.0% | 8 attempts |
| 6 | 4.7% | 21 attempts |
| 10 | 0.6% | 166 attempts |
Long dry spells on accumulators are the arithmetic working as designed, not a run of bad luck. Anyone sizing their bankroll for accumulator play should read maximum drawdown first: the losing runs are far longer than intuition suggests.
The one case where combining helps
Multiplying probabilities is valid only for independent events. Legs from the same match never are: if a team wins comfortably, over 2.5 goals and that team to score first are both more likely than their standalone prices suggest.
Positive correlation makes a combination worth more than the product of its parts. Bookmakers know this, which is why same-match combinations are either blocked outright or priced through a dedicated engine that accounts for the correlation.
This is a hard rule in our own engine: a combined market is never priced by multiplying the marginals. Only a joint probability taken from the same underlying distribution is allowed. Multiplying the parts would systematically misprice every correlated pair — and would do it in the direction that makes the bet look attractive.
If you play them anyway
- Fewer legs. Each additional leg costs you the margin of that leg, permanently.
- Compare the combined price against building the same position from singles. Frequently the singles pay more.
- Treat bonus offers as what they are: the price of the promotion is inside the odds you are being offered.
- Size for the strike rate, not the payout. A 4.7% hit rate means the stake must be small enough to survive twenty misses.
Check any of this against our record
Every signal CONSENSUS publishes carries the bookmaker odds fixed before the event starts and the settled result afterwards — including the drawdowns and the losing runs. The running total is on the front page and every entry is in the log.