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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