The Evaluation of Tournament Results as a Maximization Problem in Probability Theory

Chess tournaments are of late always arranged so that each player meets every other player k times, where k is fixed (usually k = 2, with alternate colors) . The ranking of the players is then determined by the number of games won, where an undecided (“drawn” ) game is counted as half a win for each of the partners. This method of calculation treats all games equally, regardless of the order of play, and consequently reduces chance effects to a minimum. Apparently the procedure has worked very well in practice if only a ranking is of interest, but it fails completely for broken-off tournaments (in which the number of games played is not the same for each participant).