Chess Tie Breaks. Buchholz system is the sum of opponents' scores. The idea is that the same score is more valuable if achieved against players with a better performances in a given tournament. It seems like an ideal tie-breaking method and has been used since the Swiss system was invented. Median-Buchholz (M-Buch.) is the same as Bucholz but discarding the highest and the lowest opposition's scores. Its idea is to eliminate distortions in Buchholz values, caused by taking into account games against run-away winners and bottom placed players. Sonnen-Berger is calculated by adding the score of each of your opponents multiplied by the score you achieved against that opponent. ie – adding the score multiplied by 1 for each opponent you beat, and the score multiplied by ½ for each opponent you drew with. Any opponent you lost to is ignored. Koya system is the number of points achieved against all participants who have scored at least 50% of the maximum possible tournament score.