However, the most popular double round-robin is the format with six players. In this case, the original Berger table is wrecked as always:
Original Berger Table- 6 players
1 2 3 4 5 6 7 8 9 10 1 / 4 2 / 5 3 / 6
but the adjusted Berger table looks better than a Rotate-4 Berger table because there are only two players that get the same colour four times in five rounds as opposed to four.
A new solution: the Adjusted system
Adjusted Berger Table- 6 players
1 2 3 5 4 6 7 8 9 10 1 / 4 2 / 5 3 / 6
Rotate-4 Berger Table- 6 players
4 5 1 2 3 9 10 6 7 8 1 / 4 2 / 5 3 / 6
The Adjusted Berger Table still breaks the principle of symmetry between the front cycle and the back cycle. If we decide that this route is worthy, there is a close-to-perfect solution where all players, for ALL pairs of rounds, play exactly once with white and once with black: a Rotate-2 Berger Table in the front cycle and a normal( reverted) Berger table in the back cycle. Here is the graphical look for six players:
2 3 4 5 1 6 7 8 9 10 1 / 4 2 / 5 3 / 6
Nobody plays four times in five rounds with the same color and in no moment of the round-robin will a player get a color difference of + 2 or-2.
The disadvantage is obvious: right in the middle of the tournament, two back-to-back games are played with the same opponent.
The considerations of this Appendix have been implemented in Vega. At the closure of the registration of a Round Robin tournament Vega asks the user to choose how to sort the rounds of the Berger table( the default is the standard case):
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