Does anyone know a system how to schedule a tournament in order to find the top k players? In each game two players play and one comes out as a winner. I assume that each player has a definite strength and always the stronger player wins. Each day each player can play one game and all players can play simultaneously. I'd like to find a system where in the end tells me the top ranked players with their order. A simple knock out tournament gives the top player. A double elimination tournament can tell places 1-4, but already some care in the pairing has to be taken to ensure the knowledge of 4th place?! Is there a general scheduling system? I'd like to make it mathematically correct, rather than some common systems which give incorrect 4th places.