Systems and combinations
Trixie and Patent: two systems on three selections
A Trixie on 3 selections plays 3 doubles and 1 treble, 4 bets in total. A Patent adds 3 singles, so it has 7 bets. With odds of 1.80 / 2.10 / 1.60 and a stake of 10 per bet, a Trixie is only in profit when all three win, while a Patent can also profit with two winners if the 2.10 selection is one of them. With a 5% margin per selection a Trixie returns 89.12% of the stake and a Patent 91.64%.
Contents
Key terms
- Trixie
- A system of 3 selections with 4 bets: three doubles and one treble.
- Patent
- A system of 3 selections with 7 bets: three singles, three doubles and one treble.
- Single
- A bet on one selection. It pays when that selection wins.
- Double and treble
- A combination of 2 or 3 selections. It pays only if every selection in it wins.
What they contain: Trixie, Patent and the 2/3 system
| System | Singles | Doubles | Treble | Total |
|---|---|---|---|---|
| 2/3 system | 0 | 3 | 0 | 3 |
| Trixie | 0 | 3 | 1 | 4 |
| Patent | 3 | 3 | 1 | 7 |
In K/N notation a Trixie is a 2/3 and 3/3 system together, and a Patent is 1/3, 2/3 and 3/3. The 2/3 system on its own is explained in the 2/3 system guide.
Returns for every outcome
Odds of 1.80 / 2.10 / 1.60, as in the 2/3 system guide, and a stake of 10 per bet: a Trixie costs 40, a Patent 70 and a 2/3 system 30.
| Outcome | Trixie (40) | Patent (70) | 2/3 system (30) |
|---|---|---|---|
| All three | 160.68 | 215.68 | 100.20 |
| All but 1.60 | 37.80 | 76.80 | 37.80 |
| All but 1.80 | 33.60 | 70.60 | 33.60 |
| All but 2.10 | 28.80 | 62.80 | 28.80 |
| Only 2.10 | 0.00 | 21.00 | 0.00 |
| Only 1.80 | 0.00 | 18.00 | 0.00 |
| Only 1.60 | 0.00 | 16.00 | 0.00 |
| None | 0.00 | 0.00 | 0.00 |
With two winners a Trixie pays one double with a stake of 10, so its odds would have to be above 4 to return the whole stake. That is why a Trixie is only in profit when all three selections win.
With two winners a Patent also has two winning singles: +6.80 when 1.80 and 2.10 win, +0.60 when 2.10 and 1.60 win, and −7.20 when 1.80 and 1.60 win. With one winner it only returns the single.
The system bet calculator with these selections works out the 2/3 part. Change K to 3 with a stake of 10 for the treble, and for a Patent also to 1 with a stake of 30, then add up the returns.
How often are they in profit?
If every selection carries a 5% margin, its probability is 0.95 / odds: 52.78% for 1.80, 45.24% for 2.10 and 59.38% for 1.60.
| Measure | Trixie | Patent |
|---|---|---|
| Stake | 40.00 | 70.00 |
| Average return | 35.65 | 64.15 |
| Return rate | 89.12% | 91.64% |
| Chance of profit | 14.18% | 36.56% |
A Patent returns more than a Trixie because it includes singles, and they carry only one margin. A 2/3 system returns 0.95² = 90.25%, in between. None of the three turns the margin into a profit: a Trixie and a Patent only spread the stake across more bets.
Trixie or accumulator?
The same three selections as an accumulator with a stake of 40 have odds of 1.80 × 2.10 × 1.60 = 6.048 and return 241.92, but only if all three win. A Trixie with the same stake returns 160.68 for all three and gives part of the stake back with two winners. With a 5% margin per selection an accumulator returns 0.95³ = 85.74%, so a Trixie loses less on average. The same comparison for more selections is in the accumulator vs system guide, and the four-selection system in the Yankee bet guide.
Limitations
- The examples use made-up odds and a 5% margin per selection. The real margin depends on the bookmaker and the market.
- The probabilities assume independent selections. Selections from the same match change every number.
- Bookmakers settle postponed or cancelled matches by their own rules, most often at odds of 1.00. Check the rules before placing the bet.
- More bets do not mean a better chance of profit per unit staked. The stake is only split into more, smaller slips.