An accumulator rolls several bets into one. Every leg has to land, and the odds are multiplied together, so a handful of short prices can grow into a big one. That big number is exactly why accas are so popular.
The bookmaker’s margin gets multiplied as well, though. This guide shows how the margin stacks up leg by leg, how to measure it on your own bets, and why a single value leg rarely makes a whole acca worth backing.
Key points
- Every leg pays a little less than its fair price, and in an acca those shortfalls multiply.
- With a 5% book on every leg, a five-fold pays about 78.4% of its fair price, an effective margin of about 21.6%.
- To find an acca’s margin, multiply the book percentages of each leg’s market: 1.0434 × 1.0592 × 1.0447 = 1.155, so you receive 86.6% of the fair payout.
- One value leg alongside ordinary legs usually still leaves a negative-value price. Every leg needs to be value.
- More legs means fewer winners and longer runs without one, even at fair prices.
The margin on a single bet
Add up the implied probabilities of every outcome in a market and you get the book percentage. A fair book totals exactly 100%. Bookmakers price above that, and the extra is their margin.
Take a two-way market priced at 2.05 and 1.80. The implied chances are 1 ÷ 2.05 = 48.78% and 1 ÷ 1.80 = 55.56%, which together make 104.34%, a book of 1.0434.
Using the proportional method from our fair odds lesson (Lesson 3 out of 25 in the Masterclass), the fair price is the bookmaker’s price multiplied by the book: 2.05 × 1.0434 = 2.139. So the bookmaker is paying 1 ÷ 1.0434 = 95.8% of fair.
How the margin stacks up
In an acca you multiply the prices. If every leg pays 96% of fair, the acca pays 96% × 96% × 96% and so on, and the shortfall grows with each leg you add.
This is what happens when every leg comes from a market with a 5% book (a book of 1.05).
| Legs | Payout as % of fair | Effective margin | Combined book |
|---|---|---|---|
| 1 (single) | 95.2% | 4.8% | 105.0% |
| 2 (double) | 90.7% | 9.3% | 110.3% |
| 3 (treble) | 86.4% | 13.6% | 115.8% |
| 4 | 82.3% | 17.7% | 121.6% |
| 5 | 78.4% | 21.6% | 127.6% |
| 6 | 74.6% | 25.4% | 134.0% |
| 8 | 67.7% | 32.3% | 147.7% |
| 10 | 61.4% | 38.6% | 162.9% |
For five legs, the sum is 1 ÷ 1.05⁵ = 1 ÷ 1.276 = 0.784. The acca pays 78.4% of its fair price, so over the long run you would expect to give up about 21.6p of every £1 staked, assuming the bookmaker’s prices are otherwise accurate.
Two figures are worth keeping apart. The combined book (127.6% for five legs) shows how far the prices are inflated. The effective margin (21.6%) shows how much of your stake you would expect to give up, and that is the one that matters to your bankroll.
Worked example: pricing a treble
Suppose you want a treble across three different matches. The prices are made up for this example.
| Leg | Your pick | Other side | Book | Fair price | Fair chance |
|---|---|---|---|---|---|
| Match A: over 2.5 goals | 2.05 | 1.80 | 1.0434 | 2.139 | 46.75% |
| Match B: BTTS yes | 1.75 | 2.05 | 1.0592 | 1.854 | 53.94% |
| Match C: under 2.5 goals | 1.95 | 1.88 | 1.0447 | 2.037 | 49.09% |
- Acca price: 2.05 × 1.75 × 1.95 = 6.996, so a £10 treble returns £69.96 if all three land.
- Fair acca price: 2.139 × 1.854 × 2.037 = 8.078.
- Combined book: 1.0434 × 1.0592 × 1.0447 = 1.155.
- Payout as % of fair: 6.996 ÷ 8.078 = 86.6%, an effective margin of 13.4%.
- Chance all three land: 1 ÷ 8.078 = 12.4%.
- Expected value of £10: (0.1238 × £69.96) − £10 = −£1.34.
Compare £10 singles on the same three picks. Their expected values are −£0.42, −£0.56 and −£0.43, or −£1.41 in total on £30 staked, about −4.7% of the stake. The treble gives up about 13.4% of its stake. Same picks, same prices, nearly three times the margin per pound.
Value multiplies too, but so do mistakes
The maths cuts both ways. If every leg genuinely is 3% above fair, a treble is 1.03³ = 1.0927, about +9.3% expected value, which is why some value bettors do use multiples.
The catch is “genuinely”. Your fair prices are estimates, and if each one is slightly too generous, the error multiplies exactly as the margin does.
And one strong leg can’t carry the others. Say leg one is 5% above fair but the other two are ordinary prices from 5% books. The acca pays 1.05 × (1 ÷ 1.05) × (1 ÷ 1.05) = 0.952 of fair, about −4.8% expected value, even though one leg was value.
A simple rule: only add a leg you would happily back as a single at that price. If it isn’t value on its own, it makes the acca worse.
Fewer winners, longer gaps
Even a fair acca behaves very differently from singles. Our treble lands about 12.4% of the time, so the chance of ten in a row without it landing is 0.876¹⁰ = 26.7%, and even twenty in a row happens 7.1% of the time.
That is ordinary variance, not a sign something is wrong. It does mean stakes need to be small and a few weeks of results tell you very little. Our betting variance lesson (Lesson 13 out of 25 in the Masterclass) goes into more detail.
Acca boosts
Some bookmakers offer acca boosts that add a percentage to your winnings. Exactly how a boost is calculated depends on the bookmaker’s terms, so check them, but you can test any boost with the same sums.
In our treble, the profit on £10 is £59.96. A 10% boost on that profit takes it to £65.96, a return of £75.96. The expected value becomes (0.1238 × £75.96) − £10 = −£0.60: better, but still negative. On these prices, a boost on profit would need to be about 18% before the treble had any positive value.
When the simple sums don’t apply
- Linked legs. Multiplying chances only works when legs are independent. Selections from the same match are often linked, such as a team winning and over 2.5 goals, so don’t multiply those chances together.
- Bigger margins in some markets. Smaller leagues and markets with lots of outcomes often carry bigger books, and one leg like that can add a lot to the total.
- Different rules. What happens to a void or postponed leg depends on the bookmaker’s rules, so check them before you bet.
FAQ
How do I work out the margin on my acca?
Find the book percentage for each leg’s market by adding up 1 ÷ odds for every outcome. Multiply the books together, then 1 ÷ that figure is your payout as a share of fair. Take it away from 1 for the effective margin.
Is an accumulator ever value?
Only when the acca price is longer than your fair price for it, which in practice usually means every leg is value on its own. The size of the payout is never a reason to expect a winner.
How many legs is too many?
There is no magic number, but the table shows the trend: with 5% books, a ten-fold pays only 61.4% of fair, and every extra ordinary leg makes the price worse.
Are singles always better than accas?
On the same prices, singles carry less margin per pound and have far smaller swings. In maths terms an acca only makes sense when every leg beats its fair price.
Can I check this in a spreadsheet?
Yes. Put each leg’s book in a column and multiply them with PRODUCT(). Then 1/PRODUCT(…) gives the payout as a share of fair.
Related lessons: Fair odds: how to take the margin out of a market (Lesson 3 out of 25 in the Masterclass), Expected value betting: how to work out EV (Lesson 4 out of 25 in the Masterclass), Odds shopping: what the best price is really worth (Lesson 6 out of 25 in the Masterclass), Betting variance (Lesson 13 out of 25 in the Masterclass). Check your own legs with the fair odds calculator and the expected value calculator, or see which matches the Value Predictor flags.
18+ only. Betting should stay fun. Set a budget before you start, only bet what you can comfortably afford, and take a break whenever you need one. For free, confidential support, visit BeGambleAware.org or call the National Gambling Helpline on 0808 8020 133.