20 players. Group A and B

[blascogo]

Hello,

First of all, I would like to thank you for the work you do, which is a great help in organising competitions.

I have been looking for solutions for a tournament of 20 players in which we have two groups of players, group A and group B.  As far as I can see, it is a complex situation, but I am not sure if I have read all the messages about this. The idea is to play in pairs of two and mix the players as much as possible. We would play 4 games each day, leaving 4 players free to act as referees.
What would be the best fixture to ensure that the tournament is fair?

Best regards 

[Ian Wakeling]

I think you are asking for a 10 player doubles schedule which can be used separately on the two groups.  But there is no good schedule for 10 players - see the last reply in this thread for more.

[blascogo]

Hi! Thanks for your reply.
I am actually asking for a 20 players planification in doubles format. Every day, 16 players will play in couples. Every couple is formed by a player from Group A and a player from Group B. In this format, we will play 4 matches (16 players) and 4 players are left out, acting as umpires in the matches.
I hope it is clear now.
Thanks again.

[Ian Wakeling]

This is the same format as mixed doubles.  Ideally there should be a multiple of 5 rounds so that everyone can have the same number of matches, and also referee the same number of times.  The following could work for 5 rounds:

(m01 f04 v m05 f01) (m07 f02 v m06 f03) (m04 f08 v m03 f06) (m08 f07 v m02 f05)
(m05 f09 v m04 f10) (m06 f01 v m10 f03) (m09 f04 v m02 f06) (m03 f05 v m01 f02)
(m02 f03 v m01 f09) (m08 f10 v m03 f01) (m10 f08 v m07 f04) (m09 f07 v m04 f02)
(m07 f05 v m09 f01) (m08 f09 v m06 f06) (m05 f02 v m02 f08) (m01 f07 v m10 f10)
(m07 f09 v m03 f07) (m09 f10 v m06 f08) (m10 f06 v m05 f05) (m08 f03 v m04 f04)

It's not quite perfect, as the pair (f3 m6) meet twice).

[blascogo]

Thanks for that. 

I would like that every "m" play against every other "m" (the same applies to every "f"). I am expecting a tournament that will last, at least, 9 rounds. Is this possible. The structure that you proposed here: A-Flight/B-Flight teams that change every week is quite alike to what I am looing for but I am not willing to play 5 matches per week. Can you make a distribution  with this in mind, please?

Thanks!

[Ian Wakeling]

For "m" to play against every other "m" you need to have more than 9 rounds.  If it's possible to have an optimal schedule, then after 10 rounds each "m" will have had 8 out of the other 9 "m"s as opponents, then in the 11th round the 2 players with byes, will still be on 8 opponents, so the theoretical minimum number of rounds is 12.  However, if you are also considering "m" against "f" then there are 10 possible opponents and the minimum number of rounds is 13.  My software is not able to achieve anything useful in 13 rounds, so the best I can offer is the schedule below in 15 rounds.  Hope that might be of some use.

(m01 f03 v m04 f02) (m02 f05 v m06 f01) (m07 f07 v m03 f04) (m08 f06 v m05 f08)
(m04 f06 v m02 f04) (m10 f03 v m05 f09) (m06 f05 v m03 f02) (m09 f10 v m01 f01)
(m09 f04 v m03 f03) (m02 f07 v m01 f09) (m04 f10 v m10 f08) (m08 f01 v m07 f02)
(m10 f02 v m05 f01) (m09 f09 v m07 f10) (m02 f06 v m08 f07) (m01 f08 v m06 f05)
(m06 f10 v m04 f07) (m07 f09 v m05 f03) (m10 f05 v m08 f04) (m03 f06 v m09 f08)
(m02 f02 v m09 f06) (m04 f05 v m07 f08) (m06 f04 v m05 f09) (m03 f07 v m08 f03)
(m01 f05 v m02 f03) (m06 f07 v m10 f01) (m03 f10 v m07 f06) (m05 f02 v m04 f04)
(m03 f05 v m05 f10) (m08 f02 v m02 f08) (m04 f03 v m09 f01) (m01 f04 v m10 f09)
(m03 f08 v m10 f01) (m06 f09 v m09 f06) (m02 f07 v m07 f03) (m01 f10 v m08 f02)
(m08 f09 v m09 f05) (m10 f10 v m01 f06) (m07 f04 v m06 f01) (m05 f07 v m04 f08)
(m08 f09 v m04 f01) (m09 f10 v m05 f04) (m06 f08 v m01 f07) (m10 f06 v m07 f05)
(m09 f02 v m10 f07) (m02 f09 v m03 f08) (m07 f01 v m01 f06) (m06 f03 v m08 f10)
(m01 f02 v m03 f04) (m10 f08 v m09 f03) (m04 f09 v m08 f05) (m02 f01 v m05 f10)
(m10 f04 v m02 f10) (m03 f01 v m04 f07) (m06 f02 v m07 f03) (m05 f06 v m01 f05)
(m08 f08 v m07 f04) (m06 f06 v m04 f03) (m09 f07 v m05 f05) (m03 f09 v m02 f02)

[blascogo]

Thank you so much for the fixture.