Round Robin Tournament Scheduling

Need help with 20 players, 3v3, rotating teams

Cas · 3 · 73

Cas

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on: August 07, 2019, 03:29:10 AM
Hello!

Thank you very much for providing this resource, it seems to have been incredibly helpful for many people, but now I got stuck on a problem I coudn't find a solution for on the forums yet.

I am hosting a tournament with at least 20 or 21 players, possibly 22, they will be playing in teams of 3 and I want to rotate those teams so everyone plays with and against everyone a certain amount of times. I would like the amount of pairings with/against each player to be as balanced as possible, being mostly the same for every player. I have no limitation for the number of rounds, but am looking for the least amount that still gives a balanced tournament.

So far I found solutions for this problem up to 19 players, but not any higher than that. Sorry if these do exist but I missed them!

Thank you in advance, looking forward to your reply.

Cas
« Last Edit: August 07, 2019, 04:00:45 AM by Cas »


Ian Wakeling

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Reply #1 on: August 08, 2019, 04:09:15 AM
Here are some examples for 20 and 21 players.  Fewer rounds are possible, say 10 rounds for 20 players and 14 rounds for 21 players, but I can't get the same level of balance.

20 players - 2 byes per round
  ( 8  9 14 v  4 13 16) (10  6  3 v  7 17 15) ( 2 18 11 v 20 19  5)  ( 1 12)
  ( 9 10 15 v  5 14 17) (11  7  4 v  8 18 16) ( 3 19 12 v  1 20  6)  ( 2 13)
  (10 11 16 v  6 15 18) (12  8  5 v  9 19 17) ( 4 20 13 v  2  1  7)  ( 3 14)
  (11 12 17 v  7 16 19) (13  9  6 v 10 20 18) ( 5  1 14 v  3  2  8)  ( 4 15)
  (12 13 18 v  8 17 20) (14 10  7 v 11  1 19) ( 6  2 15 v  4  3  9)  ( 5 16)
  (13 14 19 v  9 18  1) (15 11  8 v 12  2 20) ( 7  3 16 v  5  4 10)  ( 6 17)
  (14 15 20 v 10 19  2) (16 12  9 v 13  3  1) ( 8  4 17 v  6  5 11)  ( 7 18)
  (15 16  1 v 11 20  3) (17 13 10 v 14  4  2) ( 9  5 18 v  7  6 12)  ( 8 19)
  (16 17  2 v 12  1  4) (18 14 11 v 15  5  3) (10  6 19 v  8  7 13)  ( 9 20)
  (17 18  3 v 13  2  5) (19 15 12 v 16  6  4) (11  7 20 v  9  8 14)  (10  1)
  (18 19  4 v 14  3  6) (20 16 13 v 17  7  5) (12  8  1 v 10  9 15)  (11  2)
  (19 20  5 v 15  4  7) ( 1 17 14 v 18  8  6) (13  9  2 v 11 10 16)  (12  3)
  (20  1  6 v 16  5  8) ( 2 18 15 v 19  9  7) (14 10  3 v 12 11 17)  (13  4)
  ( 1  2  7 v 17  6  9) ( 3 19 16 v 20 10  8) (15 11  4 v 13 12 18)  (14  5)
  ( 2  3  8 v 18  7 10) ( 4 20 17 v  1 11  9) (16 12  5 v 14 13 19)  (15  6)
  ( 3  4  9 v 19  8 11) ( 5  1 18 v  2 12 10) (17 13  6 v 15 14 20)  (16  7)
  ( 4  5 10 v 20  9 12) ( 6  2 19 v  3 13 11) (18 14  7 v 16 15  1)  (17  8)
  ( 5  6 11 v  1 10 13) ( 7  3 20 v  4 14 12) (19 15  8 v 17 16  2)  (18  9)
  ( 6  7 12 v  2 11 14) ( 8  4  1 v  5 15 13) (20 16  9 v 18 17  3)  (19 10)
  ( 7  8 13 v  3 12 15) ( 9  5  2 v  6 16 14) ( 1 17 10 v 19 18  4)  (20 11)


21 players - 3 byes per round
  ( 1 16 17 v 13  6  3) ( 7 20 18 v  5 14 19) (11 12 15 v  2  8 10)  ( 9  4 21)
  ( 2 17 18 v 14  7  4) ( 8 21 19 v  6 15 20) (12 13 16 v  3  9 11)  (10  5  1)
  ( 3 18 19 v 15  8  5) ( 9  1 20 v  7 16 21) (13 14 17 v  4 10 12)  (11  6  2)
  ( 4 19 20 v 16  9  6) (10  2 21 v  8 17  1) (14 15 18 v  5 11 13)  (12  7  3)
  ( 5 20 21 v 17 10  7) (11  3  1 v  9 18  2) (15 16 19 v  6 12 14)  (13  8  4)
  ( 6 21  1 v 18 11  8) (12  4  2 v 10 19  3) (16 17 20 v  7 13 15)  (14  9  5)
  ( 7  1  2 v 19 12  9) (13  5  3 v 11 20  4) (17 18 21 v  8 14 16)  (15 10  6)
  ( 8  2  3 v 20 13 10) (14  6  4 v 12 21  5) (18 19  1 v  9 15 17)  (16 11  7)
  ( 9  3  4 v 21 14 11) (15  7  5 v 13  1  6) (19 20  2 v 10 16 18)  (17 12  8)
  (10  4  5 v  1 15 12) (16  8  6 v 14  2  7) (20 21  3 v 11 17 19)  (18 13  9)
  (11  5  6 v  2 16 13) (17  9  7 v 15  3  8) (21  1  4 v 12 18 20)  (19 14 10)
  (12  6  7 v  3 17 14) (18 10  8 v 16  4  9) ( 1  2  5 v 13 19 21)  (20 15 11)
  (13  7  8 v  4 18 15) (19 11  9 v 17  5 10) ( 2  3  6 v 14 20  1)  (21 16 12)
  (14  8  9 v  5 19 16) (20 12 10 v 18  6 11) ( 3  4  7 v 15 21  2)  ( 1 17 13)
  (15  9 10 v  6 20 17) (21 13 11 v 19  7 12) ( 4  5  8 v 16  1  3)  ( 2 18 14)
  (16 10 11 v  7 21 18) ( 1 14 12 v 20  8 13) ( 5  6  9 v 17  2  4)  ( 3 19 15)
  (17 11 12 v  8  1 19) ( 2 15 13 v 21  9 14) ( 6  7 10 v 18  3  5)  ( 4 20 16)
  (18 12 13 v  9  2 20) ( 3 16 14 v  1 10 15) ( 7  8 11 v 19  4  6)  ( 5 21 17)
  (19 13 14 v 10  3 21) ( 4 17 15 v  2 11 16) ( 8  9 12 v 20  5  7)  ( 6  1 18)
  (20 14 15 v 11  4  1) ( 5 18 16 v  3 12 17) ( 9 10 13 v 21  6  8)  ( 7  2 19)
  (21 15 16 v 12  5  2) ( 6 19 17 v  4 13 18) (10 11 14 v  1  7  9)  ( 8  3 20)


Cas

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Reply #2 on: August 23, 2019, 05:57:25 AM
Hello Ian,

Sorry for the late reply, thank you very much for you help, this is just what I was looking for!