(From the US Chess Federation’s Official Rules of Chess, 7th Edition by Tim Just)
Unless a different method has been posted or announced before the start of the first round, players will expect the following sequence of tiebreak systems to be employed as the first four tiebreakers. Any variation to be used within the various systems should be posted also. These systems (and some additional ones) are explained in detail following the list.
1. Modified Median
4. Cumulative of Opposition
The Median system, also known as the Harkness system for inventor Kenneth Harkness, evaluates the strength of a player’s opposition by summing the final scores of his or her opponents and then discarding the highest and lowest of these scores. In the Modified Median system, players who tie with even scores (an even score is equal to exactly one half of the maximum possible score), have the highest- and lowest-scoring opponents’ scores excluded. The system is modified for players with non-even scores to disregard only the least significant opponents’ scores: the lowest-scoring opponent’s score is discarded for tied players with plus scores and the highest-scoring for tied players with minus scores. For tournaments of nine or more rounds, the top two and bottom two scores are discarded for even-score ties, the bottom two scores for plus-score ties, and the top two scores for minus-score ties. These scores are adjusted for unplayed games, which count a half point each, regardless of whether they were byes, forfeits, or simply rounds not played after an opponent withdrew. So an opponent who won the first two games, lost the third, withdrew and did not play rounds four or five would have an adjusted score of 3 points (1+1+0+0.5+0.5 = 3). These adjusted scores are used only to calculate the opponent’s tiebreaks. The player’s own score is not changed.
If the player involved in the tie has any unplayed games, they count as opponents with adjusted scores of 0.
The Solkoff system is the same as the Median system except that no opponents’ scores are discarded.
To determine cumulative tiebreak score, simply add up the cumulative (running) score for each round. For example, if a player’s results were win, loss, win, draw, loss, the wall chart would show a cumulative score round by round as 1, 1, 2, 2.5, 2.5. The cumulative tiebreak total is 9 (1+1+2+2.5+2.5 = 9). If another player scored 2.5 with a sequence 1, 2, 2.5, 2.5, 2.5, the tiebreak points scored would be 10.5 (1+2+2.5+2.5+2.5 = 10.5). The latter player’s tiebreaks are higher because he or she scored earlier and presumably had tougher opposition for the remainder of the event. One point is subtracted from the sum for each unplayed win or full-point bye (22B); likewise, one-half point is subtracted from the sum for each unplayed draw or half-point bye.
Cumulative scores of opposition
The cumulative tiebreak points of each opponent are calculated and these are added together.