Round Robin Tournament Scheduling
Schedules - You must register to Post and Download => Requests => Topic started by: Cas on August 07, 2019, 03:29:10 AM
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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
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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)
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Hello Ian,
Sorry for the late reply, thank you very much for you help, this is just what I was looking for!