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So, a discussion didn't work out, so I'm proceeding according to my own judgment, in accordance with the name and idea of this tournament...
The final version of the rules regarding the order of the draw, the choice of player color, and the choice of map size:
"Player pairings will be determined for each round by drawing lots. The draw for the 1st round is completely random. After the 1st round, for all subsequent rounds, the draw is conducted among players with the same result and number of games played.
For a victory, 2 points are added to the player's score; for a loss, 2 points are deducted; for a draw, 1 point is added.
If one of the players does not have a pair among the players with the same result, then he is included in the draw among the players with a smaller difference between wins and losses. If the number of players is odd, the last remaining player who is not in the draw advances to the next round with a technical victory."
The draw determines not only the player pairing for each round, but also the player color and map size for each pair of players