Appendix C: Round Robin
The pairings obtained by the Berger’ s tables have disadvantages when the number of players is even. In the following it is shown how to improve them( 2).
Two simple definitions that will be used in this paper: |
2N |
number of players |
# X |
player with the X draw number |
As a sample start, here is the Berger table for 10 players:
1
4
7
|
1
10
|
2
9
|
3
8
|
4
7
|
5
6
|
2 |
10
6
|
7
5
|
8
4
|
9
3
|
1
2
|
3 |
2
10
|
3
1
|
4
9
|
5
8
|
6
7
|
|
10
7
|
8
6
|
9
5
|
1
4
|
2
3
|
5 |
3
10
|
4
2
|
5
1
|
6
9
|
7
8
|
6 |
10
8
|
9
7
|
1
6
|
2
5
|
3
4
|
|
4
10
|
5
3
|
6
2
|
7
1
|
8
9
|
8 |
10
9
|
1
8
|
2
7
|
3
6
|
4
5
|
9 |
5
10
|
6
4
|
7
3
|
8
2
|
9
1
|
This is usually acceptable, until two things are noticed:
1. there is one player(# 1) that always starts the tournament with two whites and another player(# N + 1 = 6 in the previous table) always starts with two blacks; this may be considered weird
2. because of how the Berger tables are generated, for 2N-2 players(# N and # 2N are the exceptions), the color that they have in the first round is the opposite of what they get in the last round. Therefore, if there is a double round robin tournament, having to revert the color from round 1 in round N + 1, in rounds N and N + 1 those 2N-2 players get twice the same color. This is not easily avoidable. But an undesired consequence of this is that # 1 and # N + 1, that have the same color in the first two rounds, get three blacks(# 1) or three whites(# N + 1).
So a recommendation was put in the rules( 3): exchange round N-1 and round N in the front cycle. Although this adjustment introduces some asymmetry between the front and the back cycle, it avoids the streak of three consecutive whites or blacks. Still the # 1 plays four times with black in a five round span( conversely # N + 1 plays four times with white).
Rotating tables
If we exclude the first round, each player plays once with white and once with black every two rounds. It is the first round that complicates matters and makes somebody start the first two rounds with the same color. Also it creates problems in double-round Round Robin, as shown above.
The idea is to move the first round in the middle of the round-robin. Or more precisely in the middle of pairs of rounds < 2K, 2K + 1 >.
For instance, let ' s look at our 10 round example: after excluding round 1, we have 4 pairs of rounds 2-3, 4-5,
2 The following Appendix relies heavily on a document authored by International Arbiter Roberto Ricca
3 FIDE handbook, C. 06- Annex 1: Berger Tables for Round-Robin Tournaments: " For a double-round tournament it is
recommended to reverse the order of the last two rounds of the first cycle. This is to avoid three consecutive games with the same colour."
49