Systems and combinations
How system bets work
A K/N system is the set of every combination of K selections out of the N you picked. The stake is split across all combinations, and only combinations in which every selection won are paid. A 3/5 system has 10 combinations, so a stake of 100 puts 10 on each, and payouts start from 3 winning selections.
Contents
Key terms
- K/N system
- A bet with N selections that is split into every combination of K selections.
- Combination
- A small accumulator of K selections. It wins only if all K selections win.
- Stake per combination
- The total stake divided by the number of combinations.
- Void selection
- A postponed or cancelled match. Most bookmakers settle it at odds of 1.00.
Number of combinations
The number of combinations is the binomial coefficient: the number of ways to choose K selections out of N.
combinations = C(N, K) = N! / (K! × (N − K)!)
stake per combination = total stake / combinations| System | Combinations | Stake per combination (of 100) |
|---|---|---|
| 2/3 | 3 | 33.33 |
| 2/4 | 6 | 16.67 |
| 3/4 | 4 | 25.00 |
| 3/5 | 10 | 10.00 |
| 4/5 | 5 | 20.00 |
| 3/6 | 20 | 5.00 |
| 4/6 | 15 | 6.67 |
Example: a 3/5 system
Five selections at odds of 1.80 / 2.00 / 1.70 / 2.20 / 1.90, a 3/5 system and a stake of 100. That is 10 combinations of 10 each.
| What won | Winning combinations | Payout | Net |
|---|---|---|---|
| All 5 selections | 10 | 703.56 | +603.56 |
| All except 2.20 | 4 | 252.34 | +152.34 |
| Only 1.80, 2.00 and 1.70 | 1 | 61.20 | −38.80 |
| Two selections or fewer | 0 | 0.00 | −100.00 |
When only three selections win, the single winning combination has odds of 1.80 × 2.00 × 1.70 = 6.12 and pays 6.12 × 10 = 61.20. The bet has a payout but is still behind.
Payout by number of winners
The payout depends not only on how many selections won but also on which ones.
| Winners | Winning combinations | Payout from | Payout to |
|---|---|---|---|
| 3 | 1 | 58.14 | 83.60 |
| 4 | 4 | 252.34 | 306.44 |
| 5 | 10 | 703.56 | 703.56 |
In this example the bet is always behind with three winners and always ahead with four.
Void selection
Most bookmakers settle a postponed or cancelled match at odds of 1.00. Combinations that include it are paid as if it were not there.
The same bet, but the match at 1.70 is postponed and the other four selections win. The selection is settled at 1.00, so all 10 combinations win: the payout is 540.04 instead of 703.56.
Systems and expected value
Every combination is a small accumulator of K selections. The odds are multiplied within it, and so is the bookmaker's margin. A system does not turn bets with a negative expected value into positive ones. It only spreads the stake so that the bet can pay out even when a selection loses. How much a system returns on average compared with an accumulator of the same selections is shown in Accumulator or system bet.
The system bet calculator with this example does the same for your own selections: the payout for every number of winners and for a void selection.
Limitations
- Rules for postponed and abandoned matches differ between bookmakers, so check your bookmaker's terms.
- Bookmakers often have a minimum stake per combination and a maximum payout per bet, which can change the result.
- The example ignores tax on winnings.
- A system does not make the selections more likely to win. It only changes how much is paid for each number of winners.