14 Player Round Robin Doubles Tournament on 3 courts

[Pboyd001]

I have 14 players and 3 courts. We're playing doubles, so 2 will have a bye. Here's what I'm looking for, please:

• 13 Rounds or however many it takes for each player to play with everyone 
• Each player plays with everyone, no repeat match-ups; unless that's necessary to get to the point where everyone plays with everyone else
• No player has more than 2 byes (knowing some players will have 1; others 2)
• Nice, but not necessary: some brackets I've used seem to have many of the same opposition match-ups (for example; when player #8 is on the court, for 5 out of 7 games, player #2 is one of his opponents). If this can be avoided, that would be great!

Thanks so much to all you math wizards out there!! This one is scrambling my brain!

[Ian Wakeling]

14 players is not a good number for doubles play as perfect balance of parnter and opponent pairs will never be possible.  In general I think you are underestimating the number of rounds and the number of byes needed for your tournament.  There are probably three choices available to you:

• 14 rounds - this will give everyone exactly 2 byes which is good.  The downside is that everyone has 12 games each, so there is one person with whom they never partner.
• 15 rounds - the best way to make this work is to have one special pair of players who never meet, either as partners or opponents.  The special pair of players would have 12 games and 3 byes, while all other players would have 13 games and 2 byes.  Note that a 15 round schedule has slots for 90 partnerships, and there are 91 possible partnerships among 14 people, so this is the closest it is possible to come to covering all partners in a whole number of rounds.
• 16 rounds - this would be necessary if you insist that each player plays with everyone.  The 16th round could be a short round with play on just one of the courts.

For me the 1st option is best (as everyone has the same number of games), and the third option is worst, but let me know what you think and I will post a schedule.

[PBInfoHelp]

Ian,

Can you be so kind to post what the schedule would be like for OPTION 1?

Thanks so kindly!

[Ian Wakeling]

Here is a schedule for option 1 above.

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

The pairs of players who never partner are (1,9) (2,10) (3,11) (4,12) (5,13) (6,14) & (7,8).