Systems and combinations
Yankee bet: four selections in 11 bets
A Yankee is a system of 4 selections with 11 bets: 6 doubles, 4 trebles and 1 fourfold, the same as 2/4, 3/4 and 4/4 systems together. With a stake of 10 per bet the slip costs 110. With two winners only one double pays, so a Yankee is only in profit with three or four winners. Its return sits between that of single bets and the fourfold: with a 5% margin per selection it is 87.81% of the stake.
Contents
Key terms
- Yankee
- A system of 4 selections that plays every double, treble and the fourfold: 11 bets in total.
- Double, treble, fourfold
- A combination of 2, 3 or 4 selections. It pays only if every selection in it wins.
- Unit stake
- The stake on each of the 11 bets. The total stake is 11 times larger.
- Return rate
- The average return as a percentage of the stake, over a long run of identical slips.
What is a Yankee made of?
C(4, 2) + C(4, 3) + C(4, 4) = 6 + 4 + 1 = 11In K/N notation a Yankee is a 2/4, 3/4 and 4/4 system on the same slip. How a single K/N system is calculated is shown in the system bets guide.
Returns for every outcome
Odds of 1.80 / 2.00 / 1.70 / 2.20 and a stake of 10 per bet, 110 in total.
| Outcome | Bets that win | Return | Net |
|---|---|---|---|
| All four | 11 | 638.76 | +528.76 |
| All but 1.70 | 4 | 198.80 | +88.80 |
| All but 1.80 | 4 | 190.20 | +80.20 |
| All but 2.00 | 4 | 174.92 | +64.92 |
| All but 2.20 | 4 | 161.80 | +51.80 |
| Only 2.00 and 2.20 | 1 | 44.00 | −66.00 |
| Only 1.80 and 1.70 | 1 | 30.60 | −79.40 |
| One or none | 0 | 0.00 | −110.00 |
With three winners three doubles and one treble pay. With two winners one double with a stake of 10 pays, so its odds would have to be above 11 to return the whole stake. That is impossible when both odds are 3.31 or lower, because 3.31 × 3.31 = 10.96.
The system bet calculator for the 2/4 part works out the 6 doubles with a stake of 60. For the rest of the Yankee, change K to 3 with a stake of 40 and to 4 with a stake of 10, then add up the returns.
How often is a Yankee in profit?
If every selection carries a 5% margin, its probability is 0.95 / odds: 52.78%, 47.50%, 55.88% and 43.18%.
| Winners | Probability |
|---|---|
| 4 | 6.05% |
| 3 | 24.83% |
| 2 | 37.74% |
| 1 | 25.16% |
| 0 | 6.21% |
The slip is only in profit with three or four winners, in 30.88% of cases. The average return is 96.59 for the 110 staked.
Return rate: Yankee, singles and fourfold
A combination of K selections with a 95% return per selection returns 0.95^K. The return rate of a Yankee is therefore the average of its 11 bets.
| Bet | Return rate | Average result |
|---|---|---|
| Singles | 95.00% | −5.00% |
| Doubles (2/4) | 90.25% | −9.75% |
| Trebles (3/4) | 85.74% | −14.26% |
| Fourfold (4/4) | 81.45% | −18.55% |
| Yankee (all 11) | 87.81% | −12.19% |
A Yankee loses less than the fourfold and more than single bets. The system does not change the margin, it only spreads the stake. The same conclusion for K/N systems is shown in the accumulator vs system guide.
Lucky 15, Heinz and other named systems
| System | Selections | Bets | Made of |
|---|---|---|---|
| Trixie | 3 | 4 | 3 doubles and 1 treble |
| Patent | 3 | 7 | Trixie and 3 singles |
| Yankee | 4 | 11 | 6 doubles, 4 trebles and 1 fourfold |
| Lucky 15 | 4 | 15 | Yankee and 4 singles |
| Canadian (Super Yankee) | 5 | 26 | every combination of 2 to 5 selections |
| Heinz | 6 | 57 | every combination of 2 to 6 selections |
| Super Heinz | 7 | 120 | every combination of 2 to 7 selections |
| Goliath | 8 | 247 | every combination of 2 to 8 selections |
A Lucky 15 with the same selections and a stake of 10 per bet costs 150. With all four winners it returns 715.76, and with one winner it only returns the single, from 17.00 to 22.00. Systems of three selections are covered in the Trixie and Patent guide.
Limitations
- The examples use made-up odds and a 5% margin per selection. The real margin differs between bookmakers and markets.
- The probabilities assume independent selections. Selections from the same match or related outcomes change every number.
- Bookmakers settle postponed or cancelled matches in named systems in different ways. Check the rules before placing the bet.
- More bets do not mean a higher chance of profit. The stake is only split into more, smaller slips.