Appendix A · A.3
Accumulator margin table
What an accumulator really costs, by number of legs, at three representative per-leg overrounds.
For n legs each priced to a common per-leg overround v, the effective tax on the whole slip is 1 − 1/(1 + v)ⁿ. The table gives that tax, as a percentage of the expected stake, at three representative per-leg overrounds (a Pinnacle-tight 3 per cent, a typical soft-book match-odds 5 per cent, and an 8 per cent prop-heavy leg) across two to twelve legs.
| Legs | 3% per leg | 5% per leg | 8% per leg |
|---|---|---|---|
| 2 | 5.74% | 9.30% | 14.27% |
| 3 | 8.49% | 13.62% | 20.62% |
| 4 | 11.15% | 17.73% | 26.50% |
| 5 | 13.74% | 21.65% | 31.94% |
| 6 | 16.25% | 25.38% | 36.98% |
| 7 | 18.69% | 28.93% | 41.65% |
| 8 | 21.06% | 32.32% | 45.97% |
| 9 | 23.36% | 35.54% | 49.98% |
| 10 | 25.59% | 38.61% | 53.68% |
| 11 | 27.76% | 41.53% | 57.11% |
| 12 | 29.86% | 44.32% | 60.29% |
Read the middle column against the ten-leg row and there is Chapter 10's headline figure again: a ten-fold built from ordinary 5 per cent markets hands the house 38.61 per cent of the expected pound, more than the toll on eight singles combined charged as one bet. Nothing in this table changes if the legs come from different sports, different bookmakers or different days; the tax is a property of the multiplication, not the football.
This is reference lifted from the book. The chapters are where the arithmetic gets built and argued for.
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