Systems and combinations
System bet 2/3: the simplest system bet
A 2/3 system turns 3 selections into 3 doubles, so each gets a third of the stake. If all three selections win, all three doubles pay; if one loses, one double pays. With one loser the ticket is only in profit if the odds of the remaining double are above 3.
Contents
Key terms
- 2/3 system
- A three-selection ticket split into every combination of two selections, which means three doubles.
- Double
- A small ticket of two selections. It pays only if both win.
- Accumulator
- An ordinary ticket on which every selection has to win. With three selections it is a treble.
Three doubles
Odds of 1.80 / 2.10 / 1.60 and a stake of 60, so each double gets 20.
| Double | Odds | Payout |
|---|---|---|
| 1.80 · 2.10 | 3.78 | 75.60 |
| 1.80 · 1.60 | 2.88 | 57.60 |
| 2.10 · 1.60 | 3.36 | 67.20 |
| Total | 200.40 |
Payout for every outcome
The same ticket: odds of 1.80 / 2.10 / 1.60 and a stake of 60.
| What won | Winning doubles | Payout | Net |
|---|---|---|---|
| All three | 3 | 200.40 | +140.40 |
| All but 1.60 | 1 | 75.60 | +15.60 |
| All but 1.80 | 1 | 67.20 | +7.20 |
| All but 2.10 | 1 | 57.60 | −2.40 |
| One or none | 0 | 0.00 | −60.00 |
With one loser, one double with a third of the stake pays. It returns the whole stake only if its odds are above 3: odds of 2.88 are not, so the ticket without the 2.10 selection is at a loss even though it pays out.
System or treble from the same three
The same three selections as a treble with a stake of 60: the odds are 1.80 × 2.10 × 1.60 = 6.048 and the payout is 362.88 (net +302.88), but only if all three win. Any loser means −60.00.
A 2/3 system gives up part of the top payout (200.40 instead of 362.88) so that the ticket still returns money when one selection loses. The wider picture, with the expected return, is in Accumulator or system bet.
Probability
Every selection wins with the same probability p, independently of the others. A 2/3 system pays when at least two selections win, a treble only when all three do.
| p | 2/3 system: 2 or more | Treble: all 3 |
|---|---|---|
| 0.40 | 35.20% | 6.40% |
| 0.50 | 50.00% | 12.50% |
| 0.60 | 64.80% | 21.60% |
The probability for the system is 3 × p² × (1 − p) + p³, and for the treble p³.
A 2/3 system with the treble added (four bets in total) is called a Trixie.
The system bet calculator with this example works out the payout for every outcome, including a void selection.
Limitations
- The probabilities in the table assume the same probability for all three selections and independent matches.
- A system does not make any selection more likely to win. It only changes how the stake is spread.
- Bookmakers may set a minimum stake per combination, so the stake is not always split into exact thirds.
- The example ignores tax on winnings.