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 ."
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