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I support Mozych's idea, but with teams of 4, it would be even more interesting.
Stages:
Registration
Selection of 4 captains from among the strongest
Team formation from the remaining players (a player can refuse one captain's offer, but must accept the second offer). This condition will help balance the teams.
Then, seeding of players within the team.
First, 1-1, 2-2, 3-3, 4-4 play.
Then 1-2, 2-1, 3-4, 4-3 play.
In total, there will be 6 games. And the 2 strongest teams play the final round.