Caps Tournament

[Highley]

This game is similar to horseshoes.  However I will describe what kind of format I need.
I have 24 players.  Each player needs to play against and with another player and play at a different spot (rotation through)  to make it fair. There are no teams in scoring, however you play as a team for the rounds and each individual gets a point if they win the round.  So, for example, I have player 1 and 2 playing 3 and 4, 5 and 6 playing 7 and 8, 9 and 10 playing 11, 12 and so on players 21, 22, 23, 24 will have a bye.  
4 people will have a bye each round because I only have 5 playing fields.  Next round will be 1 and 3 play 7 and 9, etc.

Caps is an outdoor game, similar to horseshoes but it is portable - that's it in a nutshell.  
So recap - 24 players, 5 playing fields, 4 people will always have a bye and I need each person to play with and against another individual but always moving through the fields to make it all fair.

Thanks!!

[Ian Wakeling]

Is the schedule below useful?  The cyclic pattern where one round can be generated from the previous one, means that everyone will play exactly 4 times on each field.  But is 24 rounds too many?

    Field 1         Field 2         Field 3         Field 4         Field 5          Byes
(24 16 v 23  6) ( 4 17 v 19 21) (14  5 v  9  8) (10 13 v 11  1) (12  7 v 20  2)  (15 18  3 22)
( 1 17 v 24  7) ( 5 18 v 20 22) (15  6 v 10  9) (11 14 v 12  2) (13  8 v 21  3)  (16 19  4 23)
( 2 18 v  1  8) ( 6 19 v 21 23) (16  7 v 11 10) (12 15 v 13  3) (14  9 v 22  4)  (17 20  5 24)
( 3 19 v  2  9) ( 7 20 v 22 24) (17  8 v 12 11) (13 16 v 14  4) (15 10 v 23  5)  (18 21  6  1)
( 4 20 v  3 10) ( 8 21 v 23  1) (18  9 v 13 12) (14 17 v 15  5) (16 11 v 24  6)  (19 22  7  2)
( 5 21 v  4 11) ( 9 22 v 24  2) (19 10 v 14 13) (15 18 v 16  6) (17 12 v  1  7)  (20 23  8  3)
( 6 22 v  5 12) (10 23 v  1  3) (20 11 v 15 14) (16 19 v 17  7) (18 13 v  2  8)  (21 24  9  4)
( 7 23 v  6 13) (11 24 v  2  4) (21 12 v 16 15) (17 20 v 18  8) (19 14 v  3  9)  (22  1 10  5)
( 8 24 v  7 14) (12  1 v  3  5) (22 13 v 17 16) (18 21 v 19  9) (20 15 v  4 10)  (23  2 11  6)
( 9  1 v  8 15) (13  2 v  4  6) (23 14 v 18 17) (19 22 v 20 10) (21 16 v  5 11)  (24  3 12  7)
(10  2 v  9 16) (14  3 v  5  7) (24 15 v 19 18) (20 23 v 21 11) (22 17 v  6 12)  ( 1  4 13  8)
(11  3 v 10 17) (15  4 v  6  8) ( 1 16 v 20 19) (21 24 v 22 12) (23 18 v  7 13)  ( 2  5 14  9)
(12  4 v 11 18) (16  5 v  7  9) ( 2 17 v 21 20) (22  1 v 23 13) (24 19 v  8 14)  ( 3  6 15 10)
(13  5 v 12 19) (17  6 v  8 10) ( 3 18 v 22 21) (23  2 v 24 14) ( 1 20 v  9 15)  ( 4  7 16 11)
(14  6 v 13 20) (18  7 v  9 11) ( 4 19 v 23 22) (24  3 v  1 15) ( 2 21 v 10 16)  ( 5  8 17 12)
(15  7 v 14 21) (19  8 v 10 12) ( 5 20 v 24 23) ( 1  4 v  2 16) ( 3 22 v 11 17)  ( 6  9 18 13)
(16  8 v 15 22) (20  9 v 11 13) ( 6 21 v  1 24) ( 2  5 v  3 17) ( 4 23 v 12 18)  ( 7 10 19 14)
(17  9 v 16 23) (21 10 v 12 14) ( 7 22 v  2  1) ( 3  6 v  4 18) ( 5 24 v 13 19)  ( 8 11 20 15)
(18 10 v 17 24) (22 11 v 13 15) ( 8 23 v  3  2) ( 4  7 v  5 19) ( 6  1 v 14 20)  ( 9 12 21 16)
(19 11 v 18  1) (23 12 v 14 16) ( 9 24 v  4  3) ( 5  8 v  6 20) ( 7  2 v 15 21)  (10 13 22 17)
(20 12 v 19  2) (24 13 v 15 17) (10  1 v  5  4) ( 6  9 v  7 21) ( 8  3 v 16 22)  (11 14 23 18)
(21 13 v 20  3) ( 1 14 v 16 18) (11  2 v  6  5) ( 7 10 v  8 22) ( 9  4 v 17 23)  (12 15 24 19)
(22 14 v 21  4) ( 2 15 v 17 19) (12  3 v  7  6) ( 8 11 v  9 23) (10  5 v 18 24)  (13 16  1 20)
(23 15 v 22  5) ( 3 16 v 18 20) (13  4 v  8  7) ( 9 12 v 10 24) (11  6 v 19  1)  (14 17  2 21)

Each player above will have 20 different partners and will see all other players in opposition either once or twice.

[Highley]

Thank you.  Is there any way of keeping it to 12 rounds which would then give each person 2 byes through the tournament, and being able to complete the tournament in 1 day?

[Ian Wakeling]

12 rounds is a much harder problem, but I think I have found something that will work.

    Field 1         Field 2         Field 3         Field 4         Field 5          Byes
( 3 15 v 20 16) ( 6 19 v  1  7) ( 5  4 v 10 14) (23  2 v 13 22) (17  9 v 24  8)  (18 12 21 11)
( 4 16 v 21 17) ( 1 20 v  2  8) ( 6  5 v 11 15) (24  3 v 14 23) (18 10 v 19  9)  (13  7 22 12)
( 5 17 v 22 18) ( 2 21 v  3  9) ( 1  6 v 12 16) (19  4 v 15 24) (13 11 v 20 10)  (14  8 23  7)
( 6 18 v 23 13) ( 3 22 v  4 10) ( 2  1 v  7 17) (20  5 v 16 19) (14 12 v 21 11)  (15  9 24  8)
( 1 13 v 24 14) ( 4 23 v  5 11) ( 3  2 v  8 18) (21  6 v 17 20) (15  7 v 22 12)  (16 10 19  9)
( 2 14 v 19 15) ( 5 24 v  6 12) ( 4  3 v  9 13) (22  1 v 18 21) (16  8 v 23  7)  (17 11 20 10)
( 9  4 v  7 19) (20 13 v 17 12) (11 24 v 16 22) ( 6 14 v  8 10) ( 3 21 v  5 15)  ( 1 18  2 23)
(10  5 v  8 20) (21 14 v 18  7) (12 19 v 17 23) ( 1 15 v  9 11) ( 4 22 v  6 16)  ( 2 13  3 24)
(11  6 v  9 21) (22 15 v 13  8) ( 7 20 v 18 24) ( 2 16 v 10 12) ( 5 23 v  1 17)  ( 3 14  4 19)
(12  1 v 10 22) (23 16 v 14  9) ( 8 21 v 13 19) ( 3 17 v 11  7) ( 6 24 v  2 18)  ( 4 15  5 20)
( 7  2 v 11 23) (24 17 v 15 10) ( 9 22 v 14 20) ( 4 18 v 12  8) ( 1 19 v  3 13)  ( 5 16  6 21)
( 8  3 v 12 24) (19 18 v 16 11) (10 23 v 15 21) ( 5 13 v  7  9) ( 2 20 v  4 14)  ( 6 17  1 22)

Above everyone gets 2 byes, plays twice on each field, has 10 different partners and 20 different opponents.  There are 12 pairs of players who never meet either as partners or opponents, these are:

   ( 1   4)
   ( 2   5)
   ( 3   6)
   ( 7  10)
   ( 8  11)
   ( 9  12)
   (13  16)
   (14  17)
   (15  18)
   (19  22)
   (20  23)
   (21  24)

Finally there are some players who have 2 consecutive byes in rounds 7 to 12, but I think this could be avoided if you rearrange the order of the rounds.

Can you tell us what a game of Caps involves? I have no idea myself.

[Highley]

Thank you!

[Highley]

Ok so one more request.  I am in need of the same thing but for 20, 22, 26 players.  Unfortunately the range is needed to go with the 24 players you kindly provided, but my tournament this year is not set and I want to be prepared for the unexpected.  Still 12 rounds.

Thanks so much