Round robin to play all players except your teammates

[wsucards]

We run a cribbage tournament consisting of 4-person teams, but each player competes for themselves in addition to competing for the team. The idea is that each player plays all the players from the other teams, but teammates do not play against each other. When we have an even number of teams, it's easy to set up a rotation to make this happen (we have a rotation of the teams, then within that, we rotate through all the individual matchups). However, if we have an odd number of teams, we want to find a rotation that will eliminate the need for having byes, while still not matching up teammates. Any suggestions?

I've used this site for other, similar things and have been very happy with it. Thanks for putting this together!

Jeff

[Ian Wakeling]

Jeff,

Let's say there are 3 4-person teams [ABCD], [EFGH] and [IJKL]. Then you could play the following 8 rounds:

(C E) (D G) (B K) (A L) (H J) (F I)
(D H) (A K) (G I) (E J) (B F) (C L)
(A I) (F J) (G L) (C H) (D K) (B E)
(G J) (H I) (D F) (C K) (B L) (A E)
(F K) (C G) (B H) (A J) (E I) (D L)
(E L) (B J) (A H) (D I) (C F) (G K)
(A F) (H L) (E K) (B G) (C I) (D J)
(B I) (D E) (C J) (F L) (A G) (H K)

which I think covers all pairs of players between teams. Does that work, or did you have a different number (or size) of teams in mind?

Ian

[wsucards]

Ian,

Thank you for the work on this. That is basically what I'm looking for, but I was hoping to find a more generic solution that I can apply to a range of potential teams (probably 5 to 13 teams, at most). When I originally posted this, I was thinking of something like what I found for another project I did, where the starting positions of each player were posted, and for subsequent games, each player moves to the next higher position (i.e. - player 1 moves on to where player 2 just played, player 2 moves to where player 3 just played, etc). From that starting point, I was able to generate all the subsequent matchups using a formula in Excel.

Would you have a template like this that I could build off of? If not, it's no big deal. It's not worth spending a lot of time/effort on.

Jeff

[Ian Wakeling]

Jeff,

The schedule above came from a computer search algorithm, and unfortunately when I try something as large as 13 teams of 4 it blows up.  So I am also intersted to know if there are mathematical constructions of these tournaments.  My instinct is that it would be more complicated than the cyclic method you implemented in Excel, but I could be wrong.

Ian

[wsucards]

Ian,

I appreciate the attempt to find an answer. If I find anything more, I'll try to post it here.

Jeff