Round Robin Tournament Scheduling

### 12 person RR for darts. 4 Boards 3 people per board each round.

Mattwoody · 3 · 1657

#### Mattwoody

• Newbie
• Posts: 0
on: October 03, 2022, 09:36:37 AM
Hi Everyone,
What i am looking for is a 12 person round robin
it is for a dart roster. we will be playing a double round robin. there is 4 dart boards
what i am looking to do is, have 3 groups of 4 each week. A vs B, C scores. C vs B, A scores, A vs C, B scores
I have worked it out for 9 player previously but for the life of me i am having trouble working it out for 12 people

#### Ian Wakeling

• Forum Moderator
• God Member
• Posts: 1141
Reply #1 on: October 04, 2022, 12:21:00 PM
If you have been looking for a 6 round schedule where every pair of players oppose at least once, then I am sorry to say that this is impossible - it is a mathematically proven fact.  It is possible to come close, a 6 round schedule exists (not shown) where only one pair of players does not meet - perhaps you found this already?

For the general problem with 3 players per board, some numbers of players like 9 and 15 work perfectly while others like 12 and 18 do not. I have put the smallest schedule for 12 players below where all pairs oppose at least once. Here the 1st round is short, only requiring one board.

(1  2  3) ( -  -  -) (-  -  -) (-  -  -)
(2  5 10) ( 7  4 11) (6  3  8) (1  9 12)
(3  6 11) ( 8  5 12) (4  1  9) (2  7 10)
(1  4 12) ( 9  6 10) (5  2  7) (3  8 11)
(6 12  7) (11  1 10) (8  2  9) (5  3  4)
(4 10  8) (12  2 11) (9  3  7) (6  1  5)
(5 11  9) (10  3 12) (7  1  8) (4  2  6)

Clearly, players 1 to 3 have one more match than the others, and as a consequence have 3 repeated opponents each, while players 4 to 12 only have one repeated opponent each.  When you use the schedules you may choose not to play these repeated matches and give the players a bye.

#### Ian Wakeling

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• Posts: 1141
Reply #2 on: October 04, 2022, 12:31:15 PM
Oh, I am being stupid, I didn't see that you had said double round-robin in your post.  This makes things much easier.  For example :

Round   Board   A   B   C
1   1   7   6   3
1   2   4   1   8
1   3   11   10   12
1   4   2   5   9
2   1   4   12   3
2   2   10   8   2
2   3   9   11   6
2   4   1   5   7
3   1   3   5   6
3   2   12   2   1
3   3   10   9   4
3   4   8   11   7
4   1   8   4   5
4   2   2   6   7
4   3   9   3   12
4   4   1   10   11
5   1   7   10   5
5   2   6   12   1
5   3   8   2   9
5   4   11   4   3
6   1   11   8   6
6   2   10   1   3
6   3   5   12   2
6   4   9   7   4
7   1   3   8   5
7   2   12   10   7
7   3   6   4   2
7   4   1   9   11
8   1   5   6   10
8   2   8   9   12
8   3   7   4   1
8   4   3   2   11
9   1   4   2   10
9   2   6   1   8
9   3   7   3   9
9   4   5   11   12
10   1   3   8   10
10   2   9   1   5
10   3   6   12   4
10   4   2   7   11
11   1   2   3   1
11   2   12   7   8
11   3   11   5   4
11   4   10   6   9