Accumulator Calculator

The section above says the overround compounds. That is true, and on its own it is not a number you can act on. Two identities turn it into one, and they point in opposite directions: the cost of an accumulator rises fast with every leg, while the standard of selection it demands does not move at all.

The take compounds geometrically

Suppose each leg is priced so that a unit staked on it returns 0.95 on average — a 5% take, around the middle of the range for a well-priced football match market. Because the legs multiply, so do the takes: an N-fold returns (1 − 0.05)^N per unit staked. The result is not a gentle slope.

A five-fold gives up more than four times what a single gives up. The useful way to hold it: every leg you add multiplies your expected return by 0.95, and it costs that same 5% whether the leg you added is priced at 1.20 or at 12.00. The odds of the extra leg change the shape of the payout, not the price of adding it. How much of any individual price is take in the first place is what the margin calculator measures.

The strike rate you need does not move

Now the identity that runs the other way, and it is the one almost nobody states. Take N legs, each at decimal odds O, each with a real chance p of winning, independent of one another. The acca pays O^N and lands with probability p^N, so it breaks even when (p × O)^N= 1 — which is true exactly when p × O = 1, that is p = 1 ÷ O. The N has cancelled. The per-leg strike rate needed to break even on a fourteen-fold is the same as on a single: 50% at odds of 2.00, 33.3% at 3.00, 20% at 5.00.

An accumulator therefore does not ask you to be a better judge of football than a single does. It asks you to pay the take more times, and it converts a steady outcome into a rare one. Those two things are the whole of the difference, and neither of them is about picking winners.

What a boost has to be worth to matter

Which gives the acca boost above a number instead of an adjective. Take five legs, each offered at 2.00 with that same 5% take, so each has a true chance of 47.5%. The profit boost needed simply to bring the bet back to break-even is 30.2%. At four legs it is 24.3%; at six legs, 36.6%. The requirement climbs with every leg, because the thing it has to cancel climbs with every leg.

Set that against the boost ladder your operator actually publishes, which is the only comparison that matters. A boost well below the figure in this paragraph is not worthless — it genuinely reduces the cost — but it does not turn a compounded take into an even bet, and it is usually offered on the leg counts where the take has grown the most.

Why the combination bets exist at all

One last property, and it is the one that explains the rest of the family. An accumulator is a single line: with five selections it needs all five, and four winners out of five pay exactly nothing. Every other multiple in common use is a way of buying out of that. A Lucky 15 covers all fifteen combinations of four selections and returns something from a single winner; an each-way bet buys a second, easier outcome on the same selection. Same opinions, different exposure, different price. Which of them fits is a question about how you want to be wrong, and the accumulator guide works through the settlement rules behind each.

What these figures assume

Every number above is arithmetic, not a forecast, and it holds only under the stated conditions: legs priced at the same take, results independent of one another, and no correlation between selections. Real accumulators frequently break the last of these — two markets from the same match are not independent, and bookmakers price them accordingly. Take figures vary by market and by operator, and 5% is used here as a round illustration rather than a claim about any book. The break-even identity is exact and does not depend on the take at all.

The calculator above prices one straight accumulator. Two searches come up again and again that need a different count: "doubles" from a list of selections, and the each-way acca. Both are easy to work out by hand once you know how many lines you are buying.

A double is a two-fold acca; "doubles" is every pair

A single double is simply an accumulator with two legs: enter two prices above and the result is the double. Asking for "doubles" on a list of selections is a different bet: the bookmaker makes every possible pair into its own double, each with its own stake. The number of lines grows quickly.

To settle every pair and every trio on one slip at once, with void legs and each-way place terms, use the Doubles and Trebles Calculator.

A worked example shows why people take doubles instead of one long acca. Four selections, each at 2.00 (evens), cost £6 as six £1 doubles, or £6 as a single four-fold. Every winning double returns £1 × 2.00 × 2.00 = £4.

• All four win: the six doubles return £24; the four-fold returns £6 × 16.00 = £96.
• Three win: three doubles land and return £12, a £6 profit; the four-fold returns nothing.
• Two win: one double lands and returns £4, a £2 loss; the four-fold returns nothing.
• One or none win: both return nothing.

Doubles give up most of the upside to get paid on three winners out of four. The margin does not go away: every double carries the take of both of its legs, so each line costs the Double row of the take table above (9.75% of its stake at a 5% take per leg), paid on all six lines. Trixies, Patents and Lucky 15s build on the same idea with trebles, singles and bigger folds; the Lucky 15 calculator works those out line by line.

Each-way accumulator: two accas for double the stake

An each-way acca is a win acca plus a place acca. The place price of each leg is 1 + (fractional odds × place terms). Take a £5 each-way treble, £10 in total, on horses at 4/1, 5/1 and 2/1, with place terms of 1/4, 1/5 and 1/4:

• Win acca: 5.00 × 6.00 × 3.00 = 90.00, so £5 returns £450 if all three win.
• Place acca: (1 + 4/4) × (1 + 5/5) × (1 + 2/4) = 2.00 × 2.00 × 1.50 = 6.00, so £5 returns £30 if all three at least place.
• All three win: £450 + £30 = £480. All three placed but not all won: £30, a £20 profit on the £10 stake. Any leg unplaced: nothing.

To check one with the calculator, run it twice: once with the win prices and once with the place prices, each at half the total stake. Place terms vary by race and by operator, so take them from the bet slip, and the each-way calculator shows how they are applied to a single selection.