Tiebreaks in Chess
In 1983, a roulette ball dropping into a red slot of the wheel gave Vasily Smyslov of the Soviet Union his victory in his quarterfinal world championship candidates match with Robert Huebner of West Germany. This match took place in the casino at Velden, Austria. The ball landed on zero at the first spin, but at the second turn dropped into the color Smyslov had called. Thus, Huebner was out and Smyslov advanced to the semifinal round.
In Swiss tournaments, there are a variety of tiebreak methods.
In the Cumulative (Progress) tiebreak system, you sum up the running score for each round. A win is one point, a draw is ˝ point, and a loss is 0 points. So a win, loss, win, win, and draw will have a round-by-round score of 1, 1, 2, 3, 3.5. The sum of these numbers is 10.5. A player with the same score, but with a loss, draw, win, win, win has a round-by-round score of 0, 0.5, 1.5, 2.5, 3.5. The sum is 8. The system places more weight on games won in the early rounds rather than the later rounds. The rationale for this system is that a player who scored well early in the tournament has most likely faced tougher opponents in later rounds and should therefore be favored over a player who scored poorly in the start before subsequently scoring points against weaker opponents.
Another tiebreak method, the cumulative opponent’s score, sums the cumulative scores of the player’s opponents.
In the Kashdan system, the player is awarded four points for a win, two points for a draw, one point for a loss, and none for an unplayed game. As a result, if players with no unplayed games tie, the one with fewer draws finishes higher on the tie-break (i.e., a win and a loss is better than two draws)
In the Median system (also known as Harkness system), for each player, you sum the number of points earned by the player's opponents, but discard the highest and lowest. For nine or more rounds, the top two and bottom two scores are discarded. An unplayed game by the opponent is counted as ˝ point. An unplayed game by the player is counted as 0 points.
A Modified Median system discards the lowest-scoring opponent’s score for players with more than 50% score. Players with exactly 50% score are handled as in the regular Median system. Players with less than 50% score discards the highest-scoring opponent’s core.
In the Solkoff (Buchholz) system, for each player, you sum the number of points earned by the player's opponents. It is like the Median system, but no scores are discarded.
In the Sonneborn-Berger system (also known as the Neustadtl system), add the scores of every opponent the player defeated and half of the score of every opponent the player drew. No scores are added if the player lost. This system is the most popular in round-robin tournaments where everybody plays everybody.
In some tiebreak methods, if the tied players played each other, if one of them won, then he/she finished higher on the tie-break.
In some tiebreak methods, the player with the most black pieces finishes higher on the tie-breaks.
In some tiebreak methods, the average performance rating of the players’ opponents are used.
In some tiebreak methods, the average rating of the player’s opponents are used.
The United States Chess Federation prefers the Modified Median tiebreak, followed by the Solkoff system, then the Cumulative system, then the Cumulative opponent’s score system.