Rotating Mixed Partner Round Robin - 12 people

[Cindi]

Hi. I have 3 pickleball courts and 12 players, 6 male and 6 female, so I can have 3 games play at a time. I'd like a schedule where each female plays with each male once and against new opponents each time before repeating partners. Looking for 2 rounds of play (12 games) where in the second round each M/F pairing plays against a different team than in the first round. Thanks in advance for your help!

[Ian Wakeling]

I am not sure how many rounds you are asking for.  You would need 6 rounds for all M/F pairs to partner each other once, but then you say 2 rounds, which would be 6 games in my estimation.

[Cindi]

Sorry for the confusion! I'm looking for 12 rounds total. In the first 6 rounds each female player would match up with each male player once, and play against unique M/F pairs each time. In rounds 7-12, each M/F pair would play against a different M/F pair than they did the first time. Does that make more sense?

[Ian Wakeling]

Thanks, that's much clearer now. I have just made the schedule below, which I think might work, although I have very little control over the "differnt M/F pair than they did 1st time" aspect.  Have a look at let me know if you think it useable.


[(M4 F4):(M5 F3)] [(M6 F6):(M1 F2)] [(M2 F5):(M3 F1)]
[(M4 F1):(M2 F4)] [(M1 F5):(M6 F3)] [(M3 F2):(M5 F6)]
[(M1 F1):(M4 F2)] [(M2 F3):(M6 F4)] [(M3 F6):(M5 F5)]
[(M6 F2):(M4 F6)] [(M3 F5):(M1 F3)] [(M2 F1):(M5 F4)]
[(M5 F1):(M6 F5)] [(M4 F3):(M2 F2)] [(M1 F6):(M3 F4)]
[(M1 F4):(M6 F1)] [(M4 F5):(M2 F6)] [(M3 F3):(M5 F2)]

[(M5 F5):(M4 F1)] [(M2 F3):(M1 F6)] [(M6 F2):(M3 F4)]
[(M4 F4):(M3 F6)] [(M2 F5):(M1 F2)] [(M6 F3):(M5 F1)]
[(M3 F1):(M1 F3)] [(M5 F6):(M2 F4)] [(M4 F2):(M6 F5)]
[(M6 F4):(M3 F5)] [(M2 F2):(M5 F3)] [(M4 F6):(M1 F1)]
[(M1 F4):(M5 F2)] [(M6 F1):(M2 F6)] [(M3 F3):(M4 F5)]
[(M3 F2):(M2 F1)] [(M6 F6):(M4 F3)] [(M5 F4):(M1 F5)]

[Cindi]

That looks great, Ian. Thank you so much! :-)

[Cindi]

Hi. I've run through the schedule and realize I forgot to add one more criteria: in the first 6 rounds, each female should play against each of the other females once (and one twice in round 6), and the same for rounds 7-12, with the repeated female opponent being different than the one in the first 6 rounds, also being played in round 12. So at the end of all rounds, each female will have played against all other females twice, and two of the females 3 times. Lastly, is it possible to pair each female with the males in the same order for rounds 1-6 and 7-12? So that F1 pairs with M1 in rounds 1 and 7, with M2 in rounds 2 and 8, etc.
Thanks again for all your help! Happy New Year! 

[Ian Wakeling]

Hi Cindi,

As a whole, the schedule I showed will have some of the opposition pair balance that you asked for but it will not be perfect.  For example it is OK for F1, as she plays against F2,F3 & F6 twice and against F4 & F5 three times - except that the three games against F4 all occur in the first 6 rounds.

You are asking for a perfect 6 round schedule, but I don't believe that it exists.  It is possible to specify the 18 games necessary, but I have found no way of 'resolving' them into 6 rounds of 3.   Note that it is possible to make 9 rounds of two games, but I guess you do not want to use only two courts and have byes.

[Cindi]

We usually only get through 8-10 rounds of play before we run out of time - would that help not having to resolve perfectly into 2 x 6 rounds? 
 
So if we create a total of 10 rounds, here are my priorities:
 
Each F partners with each M in first 6 rounds, then repeats 4 partners (preference for repeating partners from rounds 1-4 instead of 5-6) for 10 rounds total
 
F1 plays against M1-M6 and F2-F6 and repeats one F in first 6 rounds but doesn’t play against same F in consecutive rounds. Also preference for not playing against same M as partnered with in previous round.
 
In your example below, I would prefer that F1 plays against F2-F6 in the first 6 rounds before playing against them again. Each F will hopefully be able to play against each F twice in the 10 rounds if possible. If that's impossible with the 3 court configuration then I would loosen the requirement of playing against each F in the first 6 rounds, but trying to distribute them as evenly as possible to avoid playing against the same F in consecutive rounds, or only playing with 3 Fs in the first half, while still playing with each F twice.

Let me know if this is possible. If not I will loosen my requirements a bit more.

[Ian Wakeling]

I am not sure I can help much more here - the only way forward I see is writing software to optimize an 8-10 round schedule.  Your requirements above are too ambitious, as you still want the first 6 rounds to have best possible balance.  I did some searching and found that I have previously posted the  18 games in the 9 round format here.  You will see that the 18 games have the repeated same sex opposition pairs that you mention above, but I have found no way of playing the games simultaneously over three courts.

[Cindi]

Hi Ian. Thank you for all your help thus far. I’m still trying to find a way to make this work. I have one M/F pair (spouses) who would prefer not to partner together but would be OK playing against each other once or twice to make the rotation work. Would that make it any easier or just add to the complexity of the problem? I can give up the preference for variety in consecutive rounds as long as we can get as close as possible to the following: 
 
10 rounds 6F/6M, 3 courts
F: oppose each F twice
F: partner with each M once or twice 
(**one F/M pair (spouses) do not partner and can play against each other once or twice if absolutely necessary)
F: oppose each M once or twice. (or not at all in the case of the spouse pair)
M: play against each M twice
 
I looked at your 18 games in the 9 round format and it would be great except that I’d like all the players to be able to play the full 3 hours without byes. I tried to match up partners from the bye group to create another court but ran into problems with players partnering more than twice as I’m sure you are aware ;-)