Help with whist-style tournament, 16 players, 8 rounds **no repeated opponents**

[Cindi]

Hi. I need help coming up with a rotating partner round robin schedule for 16 pickleball players (4 courts) but only 8 rounds, where you get to play against ALL of the other players. I have found numerous options online, but all of them are for the full 15 rounds and we only have time to play 8 and if I try just taking the top or bottom 8 as others have suggested we end up playing with some opponents more than once and some not at all. I'd like to be able to play with 8 unique partners, and against all 15 of the other players within the 8 rounds. I believe with this schedule there should only be one opponent who is repeated. Could you please help? Thanks in advance!

Here's what I'm currently using, which is perfect if you're player #1. Otherwise you start repeating opponents by round 6 or 7.

[Ian Wakeling]

Hi Cindi,

This problem can be solved by adapting the spouse avoiding schedule here.  Take the 1st 7 rounds, ignore the distinction between 'H' and 'W', and treat H1 to H8 & W1 to W8 as 16 different players, then you will have a schedule where all players have 7 different partners and 14 different opponents.  Ignore the 8th round in the post I linked to, instead add the following as the extra round:

(H1 H2 v W1 W2) (H3 H4 v W3 W4) (H5 H6 v W5 W6) (H7 H8 v W7 W8)

All the 8 partnerships in the round above must be new (as previously 'H' has never partnered 'H', or 'W' partnered 'W').  The round above also covers the 8 opposition pairs previously avoided (H1 v W1), (H2 v W2),...,(H8 v W8).  So the repeated opponents that you are expecting will be (H1 v W2), (H2 v W1), (H3 v W4), etc...

Hope that helps.

[Cindi]

Hi Ian! Thank you so much for this! It was melting my brain trying to find the unique pairings out of the 15 rounds I've generated using other tools. And how funny there are "spouse-avoiding mixed double round robins"...that might come in handy on another day, lol! 

[Cindi]

Hi Ian,

I implemented the new round robin schedule in our games last week (awesome!) and I realize I need to take it a step further. How would I balance the schedule for positioning on 4 courts and north/south positioning on each court so each player plays an equal amount of games on each court and on each side? 

Here is what you gave me so far:

(H1 W4 v H2 W7) (H3 W1 v H4 W5) (H5 W3 v H6 W8) (H7 W6 v H8 W2)
(H1 W7 v H3 W6) (H2 W5 v H7 W3) (H4 W2 v H5 W8) (H6 W1 v H8 W4)
(H1 W6 v H4 W8 ) (H2 W4 v H8 W5) (H3 W7 v H5 W2) (H6 W3 v H7 W1)
(H1 W3 v H5 W4) (H2 W8 v H6 W7) (H3 W5 v H8 W6) (H4 W1 v H7 W2)
(H1 W5 v H6 W2) (H2 W1 v H3 W8) (H4 W3 v H8 W7) (H5 W6 v H7 W4)
(H1 W8 v H7 W5) (H2 W3 v H4 W6) (H3 W2 v H6 W4) (H5 W7 v H8 W1)
(H1 W2 v H8 W3) (H2 W6 v H5 W1) (H3 W4 v H7 W8) (H4 W7 v H6 W5)
(H1 H2 v W1 W2) (H3 H4 v W3 W4) (H5 H6 v W5 W6) (H7 H8 v W7 W8 )

Thanks in advance for your help!

[Ian Wakeling]

I don't think that it is possible to re-arrange the games above, that is to say reorder the 4 games within each row, so that players play exactly twice on each court.  My guess is that it will be possible for similar schedules with more courts - 24 players on 6 courts might be the smallest that works.

I don't have any software that could try to optimize the balance for either the courts or the north/south ends.  The only advice I can offer is to randomize the order of the four games in each row, and also randomly assign each side of each game to north/south, that would be better than using the schedule exactly as it appears above where H1 is always on court 1 north.