From: Asle Olufsen <oluf <at> IFI <dot> UIO <dot> NO>
Date: 2 oct 1997
Subject: Re: Round robins

> Is there a simple process for setting up a round robin for an even (say 20)
> number of players so everyone plays everyone else once.
>
> Obviously it's possible; by trial and error I can set up a matrix for a
> smaller number of players (8) but the trial part seems to grow quite
> rapidly as the number increases.

The following formula seems to work.

n is the numer of player and must be an even number. Enumerate the
player from 1 to n, and the rounds from 1 to n-1.

Player i plays in round j against:

if i=n : 1 + mod((n/2)*(j+1) -1, n-1)
if mod(j-2*i+1,n-1)=0 : n
else : mod(j-i,n-1)+1

If the "colors" also are predifined then
player i moves first in round j if
mod(j/2*(n-1)+i-(n+1)/2, n) < n/2


> Incidentally, this is part of a larger problem I'm working on of having a
> round robin tournament of doubles teams (you're right, they're not Shogi
> players) in which each player plays with each other player against each
> other player twice. If any one has any insight into this larger problem I
> would also be interested in hearing from you.

Use the same scheme twice (but reverse the colors).

Oluf