12 team round robin tournament

[mweeks]

Hi,
I'm looking at a fair & even draw for 12 teams, broken into 3 separate days with 4 games per day (will need to play one team an extra time- preferably 1v2,3v4,5v6, etc a second time)

I am trying to add up the numbers of the teams you play each day (4 games) to be as even as possible- somewhere between 22 & 30.

For example DAY 1- team 1 plays 2, 5, 7, 12 which equals 26
                    team 12 plays 11, 6, 1, 4 which equals 22
                    team 3 plays 4, 9, 8, 11 which equals 32 (too many)

Hoping you can assist!

[Ian Wakeling]

I can't see a way to get what you want other than brute force.  Starting with any standard 12 team round robin, there are 11550 ways of assigning the 11 rounds to two groups of 4 and one group of 3,  to complete the schedule, add the preferred 12th round to the last group.  Some of these schedules will be better than others when you apply your complex criterion - something that could be investigated with a computer program to enumerate all 11 thousand possibilites.

But I am not sure that the same sum for everyone will ever be possible.  For example, if I am player 1, then the expected sum of my 4 opponents is 28 (all larger), however if I am player 12 then the expected sum is only 24 (all smaller).

[mweeks]

Thanks Ian- been trying brute force for the last few days!! Now understand it can't be perfectly even but hoping to get close- numbers adding up between 22-38.
To make it harder, teams 11 & 12 are considerably weaker, therefore a team CANNOT be drawn to play them in the same group of 4!!
I'll keep trying- thanks for your time.

[mweeks]

There's a challenge for anyone out there- a 12 team draw, play 11 teams plus a second team twice......... 4 games per set (3 sets), as EVEN as possible (i.e team 1 can't play 2,3,4,5 in one set), no team can play 11 & 12 in the same set...... when you add up the team's numbers in a set, they should hopefully be between 22-30............ hoping there is ANYONE that can help!!

[Danny_McArdle]

Hi,
I'm looking at a fair & even draw for 12 teams, broken into 3 separate days with 4 games per day (will need to play one team an extra time- preferably 1v2,3v4,5v6, etc a second time)

I am trying to add up the numbers of the teams you play each day (4 games) to be as even as possible- somewhere between 22 & 30.

For example DAY 1- team 1 plays 2, 5, 7, 12 which equals 26
                    team 12 plays 11, 6, 1, 4 which equals 22
                    team 3 plays 4, 9, 8, 11 which equals 32 (too many)

Hoping you can assist!