Round Robin Tournament Scheduling

12 round, 3 on 3 Round Robin with random teams

johnz1 · 19 · 8672

johnz1

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Reply #15 on: January 29, 2015, 11:42:51 AM
That looks really great.  Thanks so much, Ian!


johnz1

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Reply #16 on: March 26, 2017, 03:40:42 PM
(Sorry to resurrect this thread)

Ian, any chance you have an optimal schedule for 16 players?  With somewhere between 12 and 16 games played each.

Thanks a lot for your help over the years


Ian Wakeling

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Reply #17 on: March 27, 2017, 03:47:32 AM
John,

Thanks for the interesting question.  Certainly I can make a 16 round schedule where there are 12 games played each.   For example:

  ( 1  3 11 v 10 14 13) ( 7  9 16 v  5  4 15)   ( 2 12  6  8)
  ( 2  4 12 v 11 15 14) ( 8 10  1 v  6  5 16)   ( 3 13  7  9)
  ( 3  5 13 v 12 16 15) ( 9 11  2 v  7  6  1)   ( 4 14  8 10)
  ( 4  6 14 v 13  1 16) (10 12  3 v  8  7  2)   ( 5 15  9 11)
  ( 5  7 15 v 14  2  1) (11 13  4 v  9  8  3)   ( 6 16 10 12)
  ( 6  8 16 v 15  3  2) (12 14  5 v 10  9  4)   ( 7  1 11 13)
  ( 7  9  1 v 16  4  3) (13 15  6 v 11 10  5)   ( 8  2 12 14)
  ( 8 10  2 v  1  5  4) (14 16  7 v 12 11  6)   ( 9  3 13 15)
  ( 9 11  3 v  2  6  5) (15  1  8 v 13 12  7)   (10  4 14 16)
  (10 12  4 v  3  7  6) (16  2  9 v 14 13  8)   (11  5 15  1)
  (11 13  5 v  4  8  7) ( 1  3 10 v 15 14  9)   (12  6 16  2)
  (12 14  6 v  5  9  8) ( 2  4 11 v 16 15 10)   (13  7  1  3)
  (13 15  7 v  6 10  9) ( 3  5 12 v  1 16 11)   (14  8  2  4)
  (14 16  8 v  7 11 10) ( 4  6 13 v  2  1 12)   (15  9  3  5)
  (15  1  9 v  8 12 11) ( 5  7 14 v  3  2 13)   (16 10  4  6)
  (16  2 10 v  9 13 12) ( 6  8 15 v  4  3 14)   ( 1 11  5  7)


Above all pairs of players are together in the same group of 6 exactly 4 times, pairs that partner only once oppose 3 times, while pairs that partner twice, oppose twice.  So this should be optimal for 16 rounds.

It is theoretically possible to have a perfect 20 round schedule where there are 15 games played each - all partners twice and all opponents three times.   Unfortunately I have not been able to find this yet, but if I do, I will post it here.


johnz1

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Reply #18 on: March 29, 2017, 02:01:26 PM
That is great, thank you so much Ian.  A 20 round schedule would be even better.  That'd be great if you could dig that up.

Thanks again!