Ten selections at 1.20 each look like ten near-certainties. Put them together, and the numbers tell a very different story.
Every weekend, thousands of punters build the same ticket: a long accumulator stacked with heavy favourites. Each leg looks safe on its own. The combined odds look generous. And week after week, one leg lets the whole thing down.
That is not bad luck. It is arithmetic, and once you see it, you will never look at a long acca the same way again.
Step one: every price hides a percentage
Decimal odds are a probability in disguise. Divide 1 by the odds and you get the chance the bookmaker is implying:
- Odds of 2.00 imply 50%
- Odds of 1.50 imply 66.7%
- Odds of 1.20 imply 83.3%
A “banker” at 1.20 is the bookmaker saying the team wins roughly five times out of six. Good, but not certain. One time in six, it doesn’t.
Step two: the margin is built into every leg
Bookmakers do not offer fair odds. Add up the implied percentages for all outcomes of a match and the total is more than 100%. The extra is the bookmaker’s margin, also called the overround.
Take a typical 1X2 market priced 2.10 / 3.40 / 3.50. The implied chances add up to about 105.6%, so the margin is roughly 5.6%. Strip that out proportionally and the fair prices become about 2.22, 3.59 and 3.70. Every time you back a selection, you are accepting a slightly worse price than the fair one.
On a single bet, that cost is small. On an accumulator, it multiplies.
Step three: watch what happens across ten legs
The formula for how margin compounds in an acca is simple:
Combined margin = (1 + margin on leg 1) × (1 + margin on leg 2) × … − 1
It is set out, with worked examples, alongside the free accumulator tools at gamblingcalc.com. Plug in a 5% margin per leg and the effect is striking:
| Number of legs | Combined margin |
| 1 (single) | 5% |
| 5 | about 27.6% |
| 10 | about 62.9% |
A single bet gives the bookmaker a 5% edge. A ten-fold gives it close to 63%.
The banker acca, worked through
Let us put real numbers on the classic ticket: ten favourites at 1.20 each, assuming each price carries a 5% margin and is otherwise accurate.
- What the ticket pays. 1.20 multiplied ten times gives combined odds of about 6.19. A 1,000 stake returns 6,190.
- The real chance of each leg. Remove the 5% margin and each favourite wins about 79.4% of the time, not 83.3%.
- The real chance of all ten. 79.4% multiplied ten times comes to roughly 9.9%. The ticket lands about once in ten attempts.
- What it should pay. A fair price for a 9.9% chance is about 10.08. The bookmaker pays 6.19.
The result: on average, every 1,000 staked on this ticket comes back as about 614. You lose roughly 39% of your money over time. The same favourites backed as singles lose about 5%.
Same teams. Same opinion. Eight times the cost, purely because of how the bet was built.
So should you never play an acca?
Not necessarily. Accumulators are fun, they turn a small stake into a big possible return, and some bookmakers add acca boosts that claw back part of the margin. The point is to know the price you are paying for that excitement:
- Fewer legs, smaller cost. A treble carries about 15.8% combined margin at 5% per leg; a ten-fold carries about 63%.
- Shop for the best price on each leg. Going from a 5% to a 3% margin per leg cuts a ten-fold’s combined margin from about 63% to about 34%.
- Treat long accas as entertainment, not income. Set the stake you are happy to lose before the weekend starts.
The bookmaker is not hiding the maths. It is just counting on nobody doing it. Now you have.
