System bet calculator
› Enter your selections and odds, pick a K/N system and a stake. For every number of winning selections you see the payout and the net profit. The chance is calculated from the odds only (1/odds), it is not a prediction.
Build a system from statistics on StatsAIWhat is a K/N system bet?
A K/N system is a bet slip with N selections that is split into every possible combination of K selections. Each combination is a separate small bet with the same stake. A combination pays only if all of its selections win, so a system can still pay out when some selections lose.
C(N, K) = N! / (K! · (N − K)!)
The number of combinations is the binomial coefficient. A 3/5 system has C(5, 3) = 10 combinations, a 4/7 system has 35 and a 5/10 system has 252.
Example: a 3/5 system
This is the example the calculator opens with, with fixed numbers: it does not change when you edit the calculator above. Odds 1.85 · 2.10 · 1.70 · 2.40 · 1.95, total stake 10.00. A 3/5 system has 10 combinations, so the stake per combination is 1.00.
- Exactly 3 win: 1 combination pays, payout 6.13 – 9.83, net −3.87 – −0.17.
- Exactly 4 win: 4 combinations pay, payout 27.27 – 35.39, net +17.27 – +25.39.
- All 5 win: all 10 combinations pay, payout 79.16, net +69.16.
With 3 or 4 winners the payout depends on which selections win, so it is shown as a range. With these odds the 3/5 system is only in profit when at least 4 selections win.
Payout is not the same as net profit
The payout is everything the bookmaker pays back, including your stake. Net profit is the payout minus the total stake. With systems the difference matters: a winning combination does not mean you are in profit. In the example above, with 3 winners one combination pays, but the payout is less than the total stake of 10.00.
How many combinations a system has
Rows are the number of selections (N), columns are K. The highlighted cell is the system currently chosen in the calculator.
| N \ K | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 3 | · | · | · | · | · | · | · | · | · | · | · | · |
| 4 | 6 | 4 | · | · | · | · | · | · | · | · | · | · | · |
| 5 | 10 | 10 | 5 | · | · | · | · | · | · | · | · | · | · |
| 6 | 15 | 20 | 15 | 6 | · | · | · | · | · | · | · | · | · |
| 7 | 21 | 35 | 35 | 21 | 7 | · | · | · | · | · | · | · | · |
| 8 | 28 | 56 | 70 | 56 | 28 | 8 | · | · | · | · | · | · | · |
| 9 | 36 | 84 | 126 | 126 | 84 | 36 | 9 | · | · | · | · | · | · |
| 10 | 45 | 120 | 210 | 252 | 210 | 120 | 45 | 10 | · | · | · | · | · |
| 11 | 55 | 165 | 330 | 462 | 462 | 330 | 165 | 55 | 11 | · | · | · | · |
| 12 | 66 | 220 | 495 | 792 | 924 | 792 | 495 | 220 | 66 | 12 | · | · | · |
| 13 | 78 | 286 | 715 | 1,287 | 1,716 | 1,716 | 1,287 | 715 | 286 | 78 | 13 | · | · |
| 14 | 91 | 364 | 1,001 | 2,002 | 3,003 | 3,432 | 3,003 | 2,002 | 1,001 | 364 | 91 | 14 | · |
| 15 | 105 | 455 | 1,365 | 3,003 | 5,005 | 6,435 | 6,435 | 5,005 | 3,003 | 1,365 | 455 | 105 | 15 |
Bookmaker rules differ
- Most bookmakers settle a void or postponed match at odds of 1.00.
- A bookmaker may require a minimum stake per combination or round the stake. You can enter the minimum in the “Minimum per combination” field.
- Tax, deposit fees and the maximum payout depend on the bookmaker and the country. The calculator does not include them.
- Some bookmakers offer bankers and systems with several K at once (for example 2,3/5). The calculator does not cover them yet.
FAQ
How many combinations are in a 4/7 system?
35. The number of combinations is C(7, 4) = 35, so a total stake of 350 is split into 35 combinations of 10.
Does a system pay more than an accumulator?
Not when every selection wins. The same stake is split across combinations, so the top payout of a system is lower than an accumulator with the same selections. The advantage is that a system can still pay out when some selections lose.
What does the chance in the calculator mean?
It is the probability implied by the odds alone: 1/odds for a selection, and for the system the probability that at least K selections win. Bookmakers build a margin into their odds, so the real chance is usually a little lower. It is not a prediction.
What if a match is postponed?
Most bookmakers settle a void selection at odds of 1.00, so the combinations that include it are paid without it. Enter odds of 1 and mark the selection as won. Rules differ, so check your bookmaker's terms.