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Did anyone watch Poker Superstars II? It's basically like that.

6 man tourney. I have 24 players. I want to have each player play against every other player at least. I don't want anyone playing against a particular player more than twice. I want each player to play 6 games.

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According to Wikipedia, Kathy Liebert and Todd Brunson played each other 4 times in the elimination matches, so they were pretty far from having a balanced schedule. Still, would your players mind that much if you gave up and used the PSI schedule?