System bets: how a 2/3 and a 3/4 work and what they pay
A system bet is several accumulators built from the same selections. A 2 from 3 is three doubles and a 3 from 4 is four trebles, so one miss does not wipe out the whole stake. British bookmakers also sell ready-made versions with their own names, such as the Trixie, the Yankee and the Lucky 15. We show how many combinations each system has, how to work out the payout and what came out of a simulation of 3.2 million coupons on odds from 125,000 matches: how often a system pays something, how much of £100 is left compared with accas and singles, and what a £10 weekly acca costs over 10 years.
Key takeaways
- 1
A system bet is several accumulators built from the same selections, so a 3 from 4 is 4 trebles and a 3 from 8 is already 56.
- 2
On four favourites a 2/4 system paid something 85% of the time, and an accumulator 15%.
- 3
The average return depends on how many selections one combination has, as on favourites singles returned £94 of every £100, doubles £89, trebles £84 and a six-leg acca £71.
- 4
A 3/4 system at odds of 1.50–1.80 with one miss pays £40.80 to £48.96 for a £40 stake, so one miss only just gets the stake back.
- 5
Bettors staking £10 a week on a six-leg acca at 2.00 lost £1,635 of £5,200 over 10 years on average, five times the £314 lost on singles.
Singles, accumulators and system bets
A bet slip lets you bet in three ways:
| bet | what you back | when it wins |
|---|---|---|
| single | one selection | when that selection wins |
| accumulator (acca) | several selections on one slip, with the odds multiplied | when all of them win |
| system k from n | every acca of k selections from the n you pick | when at least k selections win |
So a system is not a separate market but a way of splitting the stake. The bookmaker builds all the combinations itself, and each one settles like an ordinary accumulator: it wins only if all its selections win. In the UK the same idea also goes by full-cover bets or permutations ("perms").
How many combinations a system has
The number of combinations is the number of ways to choose k selections out of n: n! / (k! × (n − k)!). In practice a table is enough:
| selections on the slip | doubles | trebles | four-folds | five-folds |
|---|---|---|---|---|
| 3 | 3 | – | – | – |
| 4 | 6 | 4 | – | – |
| 5 | 10 | 10 | 5 | – |
| 6 | 15 | 20 | 15 | 6 |
| 7 | 21 | 35 | 35 | 21 |
| 8 | 28 | 56 | 70 | 56 |
A 3 from 8 is 56 trebles. If you choose k equal to n, you get one bet, a plain acca. To win anything you need at least k winners, because only then does the first combination come in.
The bookmaker either splits your stake across the combinations or multiplies the stake of one combination by their number, depending on what you enter on the slip. Check before you confirm: £10 on a 3 from 8 can mean £10 or £560.
Trixie, Patent, Yankee and Lucky 15
British bookmakers sell full-cover bets under their own names, each several system sizes on one slip:
- Trixie: 3 selections, the three doubles and the treble, 4 bets (2/3 and 3/3),
- Patent: a Trixie plus the three singles, 7 bets,
- Yankee: 4 selections, the six doubles, four trebles and the four-fold, 11 bets (2/4, 3/4 and 4/4),
- Lucky 15: a Yankee plus the four singles, 15 bets.
Bigger ones follow the same pattern, every double and upwards: on 5 selections a Super Yankee (also called a Canadian, 26 bets), on 6 a Heinz (57), on 7 a Super Heinz (120) and on 8 a Goliath (247). The stake on these bets is per bet, so a £1 Yankee costs £11 and a £1 Lucky 15 costs £15. Each bet inside settles like any other combination, so everything below about the margin applies to each of them separately.
How to work out the payout: a 3/4 system step by step
Four selections at odds of 1.50 (A), 1.60 (B), 1.70 (C) and 1.80 (D), a 3/4 system at £10 per combination, so £40 in total:
| combination | odds | payout if it wins |
|---|---|---|
| A + B + C | 4.08 | £40.80 |
| A + B + D | 4.32 | £43.20 |
| A + C + D | 4.59 | £45.90 |
| B + C + D | 4.896 | £48.96 |
- All four win: all four combinations come in, £178.86 in total, a profit of £138.86.
- One miss: one combination comes in, £40.80 to £48.96. At odds this low that is barely the stake back, a profit of £0.80 to £8.96.
- Two misses or more: £0.
A £40 acca on the same four selections (odds of 7.344) would pay £293.76, but only if all four win. The system gives up part of that win so that one miss does not wipe out the slip.
You can load this slip with one click from the examples of the system bet calculator (3/4): change the odds, the system and the stake, mark the result of each match and you see the payout for every number of winners straight away. Pick 2/4, 3/4 and 4/4 Acca together and you have a Yankee; the 2/3 + 3/3 example is a Trixie.
What a system pays: our simulation
We built 3.2 million random coupons of 3–6 selections and split each one into singles, every system and an acca, with a £100 stake shared equally across the combinations. The selections come from 124,772 matches in 29 leagues from 2012–2026, with Pinnacle's closing odds (the bookmaker whose prices the industry treats as the benchmark) converted to a 7.65% margin, a typical margin of three recreational bookmakers we track. Each selection comes from a different match. Two kinds of pick:
- favourites: the match favourite at odds of 1.30–1.70 (1.52 on average, won 62.5% of the time),
- "around 2.00" selections: any 1X2 result at odds of 1.80–2.20 (2.00 on average, won 47.0% of the time).
Four favourites, £100 per coupon:
| bet | pays something | average return of £100 |
|---|---|---|
| 4 singles | 98.1% | £94.40 |
| 2/4 system | 84.8% | £89.20 |
| 3/4 system | 51.9% | £84.30 |
| acca | 15.3% | £79.70 |
Four "around 2.00" selections, £100 per coupon:
| bet | pays something | average return of £100 |
|---|---|---|
| 4 singles | 92.1% | £93.90 |
| 2/4 system | 64.1% | £88.10 |
| 3/4 system | 26.9% | £82.70 |
| acca | 4.9% | £78.00 |
A system pays something more often, but at odds around 2.00 that does not mean it gets the stake back more often: in both systems you need three winners out of four not to lose. Two winners at 2.00 give one winning double in a 2/4 system, £66.67 (£100 / 6 × 2.00 × 2.00), which is less than the stake. The same two winners played as singles return £100 (2 × £25 × 2.00), the stake back.
The return depends on the size of the combination
The average return of £100 does not depend on how many selections you put on the coupon, only on how many one combination has. A 3/4, a 3/5 and a 3/6 are all trebles, and each returned as much as a plain treble:
| selections per combination | favourites | "around 2.00" |
|---|---|---|
| 1 (singles) | £94.40 | £93.90 |
| 2 | £89.10 | £88.20 |
| 3 | £84.10 | £82.80 |
| 4 | £79.50 | £78.10 |
| 5 | £75.00 | £73.50 |
| 6 (six-leg acca) | £70.80 | £68.80 |
This is the same margin that multiplies on an accumulator: each combination is a separate bet, so you pay the margin in it as many times as it has selections. Hence three conclusions:
- A system is not cheaper than singles. Singles on the same selections return the most, because the margin works on them only once.
- A system is cheaper than an acca on the same selections. A 2/4 is made of doubles, so it returns as much as doubles, not as much as a four-fold.
- The number of selections on the coupon does not change the average, only the spread. A 3/6 returns as much as a 3/4 on average, but with 20 combinations it ends at zero less often: on favourites it paid something 85% of the time, a 3/4 52%.
A Yankee or a Lucky 15 is no different: it returns the average of the doubles, trebles and the four-fold inside it (and, in a Lucky 15, the singles), so it sits between singles and a four-fold.
System bets with a banker
Some bookmakers let you mark a selection as a banker: it goes into every combination, so it has to win. A 2/3 with one banker is three trebles: the banker plus each pair from the other three. On average it returns as much as a treble, in our simulation £84.10 of every £100, and on favourites it paid something about 43% of the time, against 52% for a plain 3/4. So a banker is not a safety net but an extra condition: if it loses, the whole slip loses. The word "banker" guarantees nothing either: a favourite at 1.50 fails to win roughly one time in three, as we show in our piece on betting odds.
Void legs and bonuses
- A void leg (a match called off, or postponed beyond the time limit in the rules) counts at odds of 1.00 in every combination it is in, and the rest of each combination plays on. In a 3/4 the combinations with that selection become doubles. Time limits for postponed matches are in our guide to bet settlement rules, and how rarely a postponed match is played within them in our piece on postponed and abandoned matches.
- Bonuses: system bets often do not count towards a bonus's wagering requirement, so check the promotion's terms before you play a system with bonus funds or a free bet.
Small stake, big win: why accas tempt
Many bettors choose accas for a simple reason: £10 on six selections at 2.00 is odds of 64 and £640 to win. Small stake, big win. To see what that costs, we simulated 50,000 bettors for each kind of bet, each staking £10 every week for 10 years, £520 a year, on the same selections and odds as above. A six-leg acca at 2.00 landed once in 92 slips, one of six favourites once in 17, one of four selections at 2.00 once in 20, and singles at 2.00 almost every other time. The table shows how often each bet landed and the average result after 10 years, that is from £5,200 of stakes:
In black and white:
- After a year an acca looks good. At 2.00 a winning six-leg acca pays £640, more than a whole year of stakes, which is why someone you know has always just landed one. But more than half of the same bettors did not land a single one all year and lost all £520.
- After 10 years only the margin counts. The average bettor handed over £1,635 of £5,200, 31% of everything staked. On singles the loss was £314, 6%.
- You pay five times as much for the dream of a big win. Single bets lose in the long run too, but a six-leg acca loses about five times as fast.
A small stake does not change the arithmetic, only how slowly you lose. That is why your betting budget is an amount you accept as the cost of entertainment, not an investment. How to set it and stick to it is covered in our 10 bankroll rules.
When a system makes sense
- You like slips with several selections but don't want one miss to wipe out the stake: a 2 from n returns as much as doubles on average and rarely ends at zero.
- You are after a big win: then a system changes little, because big amounts come only from combinations with many selections, and those carry the highest combined margin.
- You simply want to give the bookmaker as little as possible: bet singles. No system returns more on average than the same selections played separately.
If instead of several matches you want to spread the stake over several results of one match, that is not a system but dutching, which the dutching calculator works out for you (more in what dutching is).
FAQ
Several accumulators built from the same selections. The bookmaker builds every combination of the size you choose, for example a 2 from 3 is three doubles, and pays every combination in which all the selections won.
Three selections A, B and C make three doubles: A+B, A+C and B+C. To win anything you need two winners, and with three winners all three doubles come in.
A 3 from 4 has 4 combinations of three selections, and a 3 from 8 as many as 56. The number of combinations is n! / (k! × (n − k)!), where n is the number of selections and k the size of one combination.
No more than the selections they are made of. In our simulation the average return of £100 depended on the size of the combination: singles returned £94, doubles £89 and trebles £84. A system is cheaper than an acca on the same selections, but dearer than singles.
Yes, when the stake is per combination: a 3/4 at £10 costs £40 but pays something far more often than an acca. On four favourites a 3/4 paid something 52% of the time and an acca 15%. The wins are smaller, though, and at odds below about 1.59 one winning treble does not return the stake of a 3/4.
Not in the long run. In our simulation bettors staking £10 a week on a six-leg acca at 2.00 landed one slip in 92, and the average bettor handed over £1,635 of £5,200 in 10 years. The same money on single bets cost £314.
A slip with one selection. One selection wins or loses, so the margin works only once. In our simulation singles returned £94 of every £100 on average, the most of any kind of bet.
The void selection counts at odds of 1.00 in every combination it is in, and the rest of the slip plays on. In a 3/4 the combinations with the void match become doubles.
Full-cover bets sold by British bookmakers. A Trixie is the three doubles and the treble from 3 selections (4 bets), a Yankee every double, treble and the four-fold from 4 selections (11 bets), and a Lucky 15 a Yankee plus the four singles (15 bets). The stake is per bet, so a £1 Lucky 15 costs £15.