Round Robin Tournament Scheduling

### 12 Players, 4 Per Match

sonicbacon123 · 8 · 9478

#### sonicbacon123

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on: October 26, 2014, 02:21:28 PM
So my friends and I want to have a tournament but the one we did last year wasn't too well received. All the match ups were decided with an RNG so it wasn't as fair. I know what a basic round robin is and I have decided to do a round robin this year for fairness sake but it gets a bit complicated, at least for me, with 4 more players than last year and since it is 4 people per match it isn't as simple as throwing the names in a tournament generator.

So what I am trying to figure out is a Round Robin Tournament with 12 players, 4 per match. I don't want it to be as simple as players 1 through 4 have a match, then the next round it is players 2 through 5. I know taking on the same people again will be inevitable but I 'd want it to go something like this...

Round 1: {1 2 3 4}   {5 6 7 8}   {9 10 11 12}
Round 2: {4 6 8 11} {1 5 9 12} {2 3 7 10}

Once I start trying to lay out combinations it just throws me off. I'm not sure if they're is a solid method to this or not. I doubt many round robins are ever done like this so I couldn't find much when searching. The closest I found was a 16 player round robin with 4 per match on this site but I couldn't figure out how to bring it down to 12.

I just want it to be as fair as possible. Any help is appreciated. And there is a chance not everyone will be able to make it so if anyone could show me how to make an 8 player, 4 per match tournament as well that would be great!
« Last Edit: October 26, 2014, 02:23:49 PM by sonicbacon123 »

#### Ian Wakeling

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Reply #1 on: October 27, 2014, 03:23:10 PM
It's not clear what you mean by 'as fair as possible', so you may need to define that.

The schedule for 16 players, 4 per match, is special and it is not possible to have something similar if there are less than 16 players.

Here are some possibilities for 12 players to consider:

4 rounds

8 rounds

#### sonicbacon123

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Reply #2 on: October 27, 2014, 09:23:48 PM
What I mean by fair as possible is that everyone takes on everyone an equal amount of times, or at least as close to that as I can get. The 8 round format you linked is looking pretty good. Unless anyone knows of something better without there being an insane amount of rounds. I am also looking for a good format for 8 players with 4 per match.
« Last Edit: October 27, 2014, 09:24:14 PM by sonicbacon123 »

#### Ian Wakeling

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Reply #3 on: October 28, 2014, 02:19:45 AM
It's not good news, as the fewer rounds there are, the more unfair the schedule will be.  With 8 players you will need 7 rounds before you can have a balanced schedule.

#### sonicbacon123

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Reply #4 on: October 28, 2014, 03:02:17 PM
That's actually great since matches don't take that long. Thank you very much!

#### Dichotomy

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Reply #5 on: January 19, 2015, 02:14:40 AM
Thought I would necro this thread rather then start an identical one, hope thats OK

I am also interested in the solution(if it exists) to this problem.

I have an identical problem to the OP, 12 teams with 4 teams per match (all players play the game at the same time, its a boardgame). Each ROUND consists of 3 match's, with each team participating in a single match of 4 unique teams. Or put another way, all 12 teams participate each round, spread across 3 matchs, and only ever participate in a single match per round.

I would like to know the MINIMUM number of rounds (I assume it will be quite large) that will result in each team participating in a match, with each other team, an EQUAL number of times.

If this number is not ridiculously high, then a schedule to go along with it would also be appreciated. I am hoping that someone has some stat software they can plug this into ?

Games are short in duration, and the schedule will be played over a year or more, so a high number is not too much of a problem.

Thankyou for your time, I do appreciate it.

BTW After reading some of the response s above, it would seem to indicate that a solution is not possible, regardless of how many rounds you play. Is this correct  or am I reading it wrong.
« Last Edit: January 19, 2015, 02:19:05 AM by Dichotomy »

#### Ian Wakeling

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Reply #6 on: January 20, 2015, 09:15:05 AM
Dichotomy,

This is perfectly possible if you have a multiple of 11 rounds.  Click on the 'schedules' button above and then bring up '12 Items' and 'Whist'.  Ignore the assignments to two pairs, and you have your schedule for 3 tables(boards).

Ian.

#### Dichotomy

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Reply #7 on: January 20, 2015, 09:53:06 AM
Thankyou for this. I am doing this now. Thanks again.

OK I have done done what you suggested.

THANKYOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

I did not know these schedules were available on the site (my fault for not paying enough attention). I have spent the best part of the past 3 nights looking up solutions for this and was beginning to think I was going to have to knock up my own program using the graph theory primer you have provided in many places across the web as a basis. I am very glad I did not have to, as although the project appeals to me I wanted really wanted to have this solution for the weekend!

Everything told me it should be possible, and I could not see any logical reason why it would not be, but after reading the above posts in the wee small hours of the morning I got myself confused and self doubt crept in Figured my certainty was just lack of expertise in disguise, which it probably was, but I am going to take the win anyway:)

So once again, thankyou very much for your time, and whoever provided the schedules thanks to them too.

Have a great day/night, you have made my week !
« Last Edit: January 20, 2015, 10:05:18 AM by Dichotomy »