Martin Thoresen wrote:It's not so much my opinion but some complaints that appeared in the TCEC chat during Stage 2. The current pairing system for single round robins doesn't work if there is an even number of participants, then one engine will get either all black or all white. So Stage 2 had to be changed to an uneven number of participants (from 18 to 19). Even so, some engines got 4-5 whites in a row, then 7-8 blacks then rest whites and vice versa.

Ah OK, I see. It is the color assignment that is broken.

Well, for whom it is of any interest, there exists a simple pairing algorithm that works for any number of players (and can even be applied in real OTB tourneys without the aid of any computer):

Put all (N) Chess boards on a long table, alternating their orientation. For an odd number of players (2N-1) put only one chair with board N (which isn't really used in that case; that player has the BYE). Now after every round, all players move one chair to their right, wrapping around the end of the table when they reach it.

This will make everyone play against everyone else, because swinging around the table at board N switches them from the odd to the even group. They will also alternate color on every round (because this is how you layed out the boards), even when they swing around the table at board 1. As with an odd number of players there is an even number of rounds, they will all get exactly as many whites and blacks.

Now for an even number of players you use exactly the same system, except you put a second chair at board N. And player nr 2N will ALWAYS remain at board N, moving to the opposite side of the table on every round (so that he strictly alternates color), and the 'one-chair to the right' rule skips the chair he is on, and is applied after he swaps places with his latest opponent. This means all other players now get a white or black (depending on the round) between the game they play on one side of board N-1 and the other (in which they obviously have opposite colors). So they will get two times the same color in a row. But this is the ONLY case where they get two times the same color; in all other rounds they will strictly alternate color.

No turning of boards is necessary. No player has to move more than two chairs to the right ever. (And only two chairs when he moves directly between board N-1 and board N at the opposite side of the table, which each player does only once, except player 2N, who never does it.) In an OTB computer tourney this means you have to move equipment only once every two rounds!

In an engine tourney, where the games of a round are not played simultaneously, you can always play them in the order board 1 -> board N. This will always cause maximum separation between the games of any player; there will never be two games in a row by the same player, (except with <= 6 players); there will always be N-2 other games between games of the same player.