6-7 and 8-9. We could move round 1 exactly in the middle. And in order not to break the original Berger
tables, we just rotate it. In other words we start with the original round 6, then 7, then 8, then 9, now round 1
and then round 2, round 3, round 4, round 5.
Let’s call it a Rotate-6 Berger Table, i.e. the original Berger Table for 10 players rotated in a way that
Round-6 is the first one to be played. There could be also a Rotate-4 or a Rotate-8 (same principle) for 10
players. When the players are six, Rotate-4 is the only sensible option (see below).
In this way we get the followind advantages:
1. Everybody starts the tournament with at least one white and one black; the unmatching round is found in
the middle of the tournament; after that round everybody ends the tournament with pairs of rounds
playing once with white and once with black
2. In a double round robin we can't avoid that all players but two will repeat the color between round #N
and #N+1, but this time there is no risk to get thrice the same color as everybody ends the first roundrobin with one white and one black and starts the second one with one white and one black.
Let's give a graphical look at some tables (in the pair <#X/#X+N>, the "bullet" means white for #X and
black for #X+N; yellow highlighting stands for the same color in more rounds)
1
2
3
Original Berger Table for double round robin - 10 players
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1/6
2/7
3/8
4/9
5/10
Analysis: 10 times a player gets the same color twice in a row, once a player gets it thrice in a row. Also:
between rounds 7 and 11 or between rounds 9 and 13, the players #1/#6 get the same color four times in five
rounds. Same goes for #2/#7 between rounds 9 and 13.
Adjusted Berger Table for double round robin - 10 players
Rounds 8-9 are switched
4
5
6
7
9
8
10
11
12
13
14
15
1
2
3
16
17
18
1/6
2/7
3/8
4/9
5/10
Analysis: 12 times a player gets the same color twice in a row. Only players #1/#4 get the same color four
times in five rounds
Rotate-6 Berger Table for double round robin - 10 players
9
1
2
3
4
5
15
16
17
18
10
11
6
7
8
12
13
14
1/6
2/7
3/8
4/9
5/10
Analysis: 12 times a player gets the same color twice in a row; nobody gets the same color four times in five
rounds
50