Tie-breaking in Swiss-system tournaments

Tie-break systems are used in chess Swiss system tournaments to break ties between players who have the same total number of points after the last round. This is needed when prizes are indivisible, such as an official "champion", trophies, or qualification for another tournament. Otherwise players often share the tied spots, with cash prizes being divided equally among the tied players. If the players are still tied after one tie-break system is used, another system is used, and so on, until the tie is broken. Most of the methods are numerical methods based on the games that have already been played or other objective factors, while some methods require additional games to be played, etc. Strength of schedule is the idea behind the methods based on the games already played: that the player that played the harder competition to achieve the same number of points should be ranked higher.

Harry Golombek points out deficiencies in most of the tie-break systems and recommends a playoff if there is time. If not, he recommends Sonneborn-Berger and then the player who has the most wins. For Swiss tournaments, he recommends the Buchholz system and the Cumulative system (Golombek 1977:322).

For Swiss chess tournaments for individuals (not teams), FIDE recommends - in an Annex to the FIDE Tournament Regulations regarding tiebreaks:

The Median system is also known as the Harkness System, after its inventor Kenneth Harkness. For each player, this system sums the number of points earned by the player's opponents, but discarding the highest and lowest. If there are nine or more rounds, the top two and bottom two scores are discarded. Unplayed games by the opponents count ½ point. Unplayed games by the player count zero points. This is also known as the Median-Buchholz System (Just & Burg 2003:199–200).

The Modified Median system is similar to the Median system, except:

This system is the same as the Median system, except that no scores are discarded (Just & Burg 2003:200). Ephraim Solkoff did not invent this system. He introduced it to the United States in 1950, but it was used in England prior to that (Harkness 1967:138).

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