Tiebreak Rules for Swiss Tournaments

The following tiebreak rules are standard for Swiss tournaments.  All Swiss tournaments run by Madison City Chess League will use these tiebreak methods, in this order, unless otherwise posted in tournament information pages.  Tiebreak rules for Round Robin tournaments are at the bottom of this page.  For more information on all of these tiebreak methods, see U.S. Chess Federation's Official Rules of Chess, 6th Edition, pages 207-214.

SS Tiebreak #1: Modified Median

A player's Modified Median score is found by adding the scores of the player's opponents, but not including the least important of those opponents.  For players tied with more than half the maximum score (3 points or higher in a 5 round tournament), the lowest-ranked opponent is removed from the Modified Median score.  For players tied with less than half the maximum score (2 or less in a 5 round tournament), the highest-ranked opponent is removed from the Modified Median score.  For players tied with exactly half the maximum score (2.5 in a 5 round tournament), the highest and lowest-ranked opponents are removed from the Modified Median score. If the tournament has nine or more rounds, then the top and/or bottom two opponents are removed from the Modified Median score.  For the purposes of determining the Modified Median, any opponent who had an unplayed game (bye, forfeit win, etc) shall have that round counted as 1/2 point towards the tied player's Modified Median, even if it was a full point bye.

Example 1: Tom and Jerry are tied with 4 points in a 5 round tournament.  Tom's opponents' scores are 1, 2, 3, 3.5, 4.  Jerry's opponents' scores are 2, 2.5, 3, 3, 4. Tom's Modified Median score is 2+3+3.5+4=12.5 (the opponent with a score of 1 is dropped).  Jerry's Modified Median score is 2.5+3+3+4=12.5 (the opponent with a score of 2 is dropped).  In this example, the Modified Median does NOT break the tie, and therefore we must go to the second tiebreak method.

Example 2: Jane and Fonda are tied with perfect scores: 7 points in a 7 round tournament.  Jane's opponents have scores of 2, 2, 3.5, 4, 5, 5, 6, but the 6-point opponent had a full-point bye in the first round.  Fonda's opponents have scores of 1, 2.5, 4, 4, 5, 5.5, 6.  Jane's Modified Median score is 2+3.5+4+5+5+5.5=25 (one of the 2-point opponents is dropped, and the 6-point opponent is counted as 5.5 because of the bye).  Fonda's Modified Median score is 2.5+4+4+5+5.5+6=27 (the 1-point opponent is dropped).  Fonda wins on tiebreaks because her Modified Median is higher than Jane's.

SS Tiebreak #2: Cumulative

The easiest to calculate, a player's Cumulative score is found by adding his/her scores from each round, from the start to the finish of the tournament.  After adding the round-scores of a player, one point is subtracted if that player had a full-point bye or unplayed win.

Example 1: In a 3 round tournament, John won his first game, drew his second, and won his third game.  John's score at round one was 1, round two was 1.5, and round three was 2.5.  His Cumulative score is 1+1.5+2.5=5.  James drew his first game and won his second and third.  James's score at round one was 0.5, round two was 1.5, round three was 2.5.  His Cumuluative score is 0.5+1.5+2.5=4.5.  In this example, John wins on tiebreaks.

Example 2: In a 5 round tournament, Sally gets a bye, wins, loses, wins, wins.  Her round scores are 1(bye), 2, 2, 3, 4.  Molly plays all five rounds: win, win, loss, win, win.  Her round scores are 1, 2, 2, 3, 4.  Although Sally and Molly have the same round scores, Sally had the bye in the first round, so their Cumulative scores will be different.  Sally's Cumulative score is (1+2+2+3+4)-1=11.  Molly's Cumulative score is 1+2+2+3+4=12.  Molly wins on tiebreaks.

SS Tiebreak #3: Solkoff

A player's Solkoff score is calculated the same way as the Modified Median, except no scores are dropped.

Example 1: Tom and Jerry (same players from the Modified Median example) are tied with 4 points in a 5 round tournament.  Tom's opponents' scores are 1, 2, 3, 3.5, 4.  Jerry's opponents' scores are 2, 2.5, 3, 3, 4. Tom's Solkoff score is 2+2.5+3+3+4=14.5.  Jerry's Solkoff score is 1+2+3+3.5+4=13.5.  Tom wins a tiebreak based on the Solkoff method.

Example 2: May and April tie in a three-round tournament with 2.5 points each.  They played each other in the final round and got a draw.  May's opponents have scores of 1, 2, and 2.5.  April's opponents also have scores of 1, 2, and 2.5, but her first opponent had a full-point bye.  May's Solkoff score is 1+2+2.5=5.5.  April's Solkoff score is 0.5+2+2.5=5 (the opponent with the bye counts as 1/2 point instead of full point).  May wins the Solkoff tiebreak.

SS Tiebreak #4: Opposition Cumulative

The Opposition Cumulative score, which is the final tiebreak for Swiss tournaments, adds the Cumulative scores (determined by the same method described above) of each tied player's opponents.

Example: In a five-round tournament, Max and Dwight tie with 3.5 points.  Max's opponents have Cumulative scores of 5, 5, 10, 13, and 10.  These are added together to make Max's Opposition Cumulative score: 5+5+10+13+10=43.  Dwight's opponents have Cumulative scores of 5, 8, 5, 13, and 11.  These are summed to make Dwight's Opposition Cumulative score: 5+8+5+13+11=42.  Even if these players tied on all of the previous tiebreaks, Max wins on the Opposition Cumulative tiebreak.

Tiebreak Rules for Round Robin Tournaments

The following tiebreak rules are standard for Round Robin tournaments.  All Round Robin tournaments run by Madison City Chess League will use these tiebreak methods, in this order, unless otherwise posted in tournament information pages.  Tiebreak rules for Swiss tournaments are at the top of this page.  For more information on all of these tiebreak methods, see U.S. Chess Federation's Official Rules of Chess, 6th Edition, pages 207-214.

RR Tiebreak #1: Sonneborn-Berger

A player's Sonneborn-Berger score is determined by adding the final scores of opponents that the player beat, adding half the final score of opponents that the player drew, and adding nothing for games lost or for games not played (byes, forfeit wins, etc).

Example 1: In a four-player Round Robin event, Amos lost to Billy, beat Charles, and beat Devin (2 points total). Billy beat Amos, drew Charles, and drew Devin (2 points total). Charles drew Billy, lost to Amos, and beat Devin (1.5 points total).  Devin drew Billy, lost to Amos, and lost to Charles (0.5 points total).  Amos and Billy are tied with 2 points.  Amos's Sonneborn-Berger score is 0+1.5+0.5=2.  Billy's Sonneborn-Berger score is 2+(1.5/2)+(0.5/2)=2+0.75+0.25=3.  Billy wins on tiebreaks.

Example 2: In a four-player Round Robin event, there is a clear winner but a tie for second place.  Ian drew Jill and Kelly, and lost to Larry (1 point total).  Jill drew Ian, beat Larry, and lost to Kelly (1.5 points total).  Kelly drew Ian, beat Jill, and lost to Larry (1.5 points total).  Larry lost to Jill, beat Kelly, and beat Ian (2 points total).  For the second place tiebreak, Jill's Sonneborn-Berger score is (1/2)+2+0=2.5.  Kelly's Sonneborn-Berger score is (1/2)+1.5+0=2.  Jill is awarded second place on tiebreaks.

RR Tiebreak #2: Head-to-Head

The head-to-head tiebreak is determined by the outcome of the game played between the two tied players.

Example 1: In a four-player Round Robin event, Evan lost to Faith and Hillary, but beat Gus (1 point total).  Faith drew against Hillary and won against Gus and Evan (2.5 points total).  Gus lost all three games (0 points total).  Hillary drew against Faith and won against Gus and Evan (2.5 points total).  Hillary and Faith are tied with 2.5 points.  Their Sonneborn-Berger scores are identical at (2.5/2)+1+0=2.25.  The game that Hillary and Faith played against each other was a draw, therefore their tie remains unbroken.

Example 2: In a six-player Round Robin event, Marissa and Roy tie for first place, and their Sonneborn-Berger scores are identical.  However, when they played each other, Marissa beat Roy.  Marissa wins the Head-To-Head tiebreak.