Round robin for 3 or 4 players with a twist

[wmcduff]

Hi there!

I'm going to be running a tournament for a dice/board game called Roll Through the Ages (feel free to sign up at yucata.de if you like that sort of thing   ).  Response has been...quite a bit higher than anticipated, so I'm scrambling a little to figure out what large format tournaments would work well.

The plan is to have a group stage then a knockout stage of either three or four player games (think the World Cup for a simpler example two side of this).  I figured out that 405 would be a good number for this, as I could do groups of 15, take the top seven of each group with the #1 of each group getting a bye (knockout going 189->81->27->9->3->1).  However, it looks like we'll exceed that number of players.

Is there a listing somewhere of three and four player blocks where everyone plays everyone else once?  I can see 512 would be a good number using groups of sixteen (take the top five of each group, group winners getting a bye, then knockout 160->64->16->4->1).

Also, any ideas for combinations that might work well around 450?  I can manage with giving byes to the best second place scorers or something, but it seems inelegant...

Thanks for your help!

[Ian Wakeling]

Can you give an indication of how many games (per player) it is possible to play at the group stage of the tournament as this will put constraints on the problem.  Also would you allow the group stage to have both three and four player games.  Without this mixed match size it limits group size to certain nice numbers such as 15,16,21,27,28 where the odd sizes would be all three player games, and the even sizes would be all 4 player games.

So there is one very nice possibility, 16 groups of 28 players (448 players in total).  But that would involve 9 games in the group stage with all 27 possible opponents exactly once.

Ian.

[wmcduff]

I'd prefer everyone playing each other exactly once in the group stage.  Nine would be an absolute maximum number of games in the group stage.  I'm beginning to think 512 is going to work; current enrollment is at 443, and enrollment is tapering off steadily...

[Ian Wakeling]

I was thinking of playing each other exactly once.  To illustrate what I was suggesting you could have a group size of 12 players and play 5 games each as follows:

(3 9 6 12) (11 10 5 7) (4 2 1 8)
(6 1 11) (3 2 5) (7 4 9) (12 8 10)
(11 8 9) (4 12 5) (3 1 10) (6 7 2)
(11 4 3) (5 8 6) (1 7 12) (2 10 9)
(2 12 11) (9 5 1) (8 7 3) (10 6 4)

so that's 1 four player game and 4 three player games per person.  I can supply the 28 player version with 9 rounds of 4 player games if you like.    But your suggestion of 512, presumably 32 groups of 16 sounds good.  The schedule for each group would be a social square.

Hope that helps,

Ian.

[wmcduff]

Thanks for your help!  Though 448 seems like it'll be too small.  We'll see where we stand for the weekend for people signed up...  Though a hybrid 3/4 group stage is quite interesting!

[Ian Wakeling]

Other possibles might be 18 groups of 28=504, but this may present a few problems in the knockout stage.  Alternatively there is 32 groups of 15=480.  There is a schedule of 7 rounds of three player matches that will work for 15 players, see here.