Round Robin Tournament Scheduling

Recent Posts

41
Requests / Re: Beer Olympics Schedule - 8 Events & 9 Teams
« Last post by Ian Wakeling on October 12, 2022, 04:29:19 AM »
There are no solutions that work well when the number of teams is and odd number.  If it is important to you to have all pairs of teams facing off once, then the closest you can come is to have either:
8 teams and 7 games, or
10 teams and 9 games.
42
Requests / Re: Am I asking for the impossible?
« Last post by Ian Wakeling on October 12, 2022, 04:08:30 AM »
Ray,

I have an observation on your 24 player schedule with 8 never meeting. If you take the schedule in reply #4 above and add the following 8th round:

1  9 17 -
2 10 18 -
3 11 19 -
4 12 20 -
5 13 21 -
6 14 22 -

where "-" represents an unfilled player slot, then the schedule will have only 6 pairs of players who never meet - so improving on your 8 pairs.  To complete the schedule you are free to fill the empty slots with the remaining players 7 8 15 16 23 & 24 in any way you like.

I notice that you don't make any constraints on the byes - I believe I can do better than (26,52), but allowing 2 of the players to have 2 byes allows for better mixing.  Is that acceptable?


Ian
43
Requests / Beer Olympics Schedule - 8 Events & 9 Teams
« Last post by kambam on October 11, 2022, 03:57:37 PM »
My brain hurts trying to figure this out, it even possible. 

Here's the scenario:
We are having a Beer Olympics party - 8 games/events and 9 teams

What we want to happen is for each team to compete in every event, and to face off against each other team once. The matches will be going on simultaneously. Is there any way to make this work? I assume each team will have one bye round. Open to suggestions please and THANK YOU.
44
Requests / Re: Am I asking for the impossible?
« Last post by Ian Wakeling on October 11, 2022, 04:22:39 AM »
Hi Ray,

I am thinking about what you have posted and may respond later.   You are of course welcome to post schedules if you would like and you can do this as Excel attachments if that would be more convenient for you.  The 40 player 13 round schedule you are looking for can be found here in the top half of my reply #10.  Or if you want to know how to make it I can find a reference in the mathematical literature for you.

Ian
45
Requests / Re: 6 Players 3 games
« Last post by Ian Wakeling on October 11, 2022, 03:56:55 AM »
Would this work for you?

      Game1   Game2   Game3
Round  1   3 v 6   1 v 2   4 v 5
Round  2   6 v 2   5 v 3   1 v 4
Round  3   4 v 3   2 v 5   6 v 1
Round  4   2 v 4   3 v 1   5 v 6
Round  5   1 v 5   6 v 4   2 v 3

Round  6   4 v 5   3 v 6   1 v 2
Round  7   1 v 4   6 v 2   5 v 3
Round  8   6 v 1   4 v 3   2 v 5
Round  9   5 v 6   2 v 4   3 v 1
Round 10   2 v 3   1 v 5   6 v 4

Round 11   1 v 2   4 v 5   3 v 6
Round 12   5 v 3   1 v 4   6 v 2
Round 13   2 v 5   6 v 1   4 v 3
Round 14   3 v 1   5 v 6   2 v 4
Round 15   6 v 4   2 v 3   1 v 5

It's one schedule for 5 rounds where the columns have been rotated for the later rounds.
46
Requests / Re: Am I asking for the impossible?
« Last post by raydog on October 10, 2022, 04:35:18 PM »
I am in charge of scheduling for a euchre tournament held by a group of fraternity alums each year, where I have dealt with exactly this problem. My constraints are that we have a variable number of people participating each year, and for our initial seeding round I'd like to have as much "mixing" as possible, so (if possible):
1) everyone plays at a table at least once with every other player (either as partner or opponent);
2) if multiple meetings are required, then we don't have pairs which sit together twice while another pair never meets (or one pair meets each other 3 times while another pair hasn't yet met 2 times);
3) no two players are partners twice.

We also have a time constraint, so play exactly 8 rounds (no more, no less).

I have devised schedules for 15 to 36 players using these constraints, and found many of them by using a computer program (rather poorly designed, as I am not a great programmer) running billions of combinations and trying to find the best one. I let some scenarios run for literally weeks! Truly brute force, but it did produce results.

In the end, I was not able to optimize every scenario, but I think I found some pretty reasonable solutions. I was able to avoid any players ever meeting 3 times, but I wasn't always able to have every possible pair of players meet. I calculated the "ideal" situation by comparing the number of actual parings in the tournament (#tables X # rounds) to the number of different possible pairings = n(n-1)/2, where n is the number of players. I presume this ideal is not always achievable, but it gave me a target to shoot for.

I found ideal solutions for 16, 17, 20 and 27+ players.

For the rest, I found the following:
players       never meet (ideal)   never meet (my solution)
    18                     0                                5 
    19                     0                                12
    21                     0                                7
    22                     0                                19
    23                     13                              27
    24                     0                                8
    25                     12                              26
    26                     37                              52

in the case of 15 players, I think I am still far from optimal: I have 18 pairs never meeting and 6 pairs meeting 3 times! Fortunately, we generally have more than 15 players in attendance.

I'd be happy to share these schedules if anyone is interested, but as they are quite specific and would take a long time to type our I prefer to wait for a specific request. Also, if anyone can improve upon my results (as summarized above), please do let me know.

Finally, is there an easy way to generate the solution for 40 players? I know how to generate the perfect solution for 39 rounds (every player partnering with every other player exactly once and opposing every other player exactly twice), but is there a 13 round solution which has every possible pair meeting exactly once [from which I would just take any 8 games]?

Ray                          
47
Requests / 6 Players 3 games
« Last post by KHAYZR on October 10, 2022, 08:43:31 AM »
Hello

I am trying to host a tournament for 6 players playing 3 different games but i cant figure out how to set up the bracket.

So every player has to play all other players in every game once.

The 3 games are happening at the same time.

And i want to rotate the players so that no one plays the same matchup 2 times in a row if thats possible) 

Thanks in advice ! 
48
Requests / Re: 12 person RR for darts. 4 Boards 3 people per board each round.
« Last post by Ian Wakeling 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
49
Requests / Re: 12 person RR for darts. 4 Boards 3 people per board each round.
« Last post by Ian Wakeling 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.
50
Requests / 12 person RR for darts. 4 Boards 3 people per board each round.
« Last post by Mattwoody 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