C.07 Tie-break regulations

1.       Choice of Tie-Break System

1.1     The choice of the tie-break system to be used in a tournament shall be decided in advance and shall be announced prior to the start of the tournament. If all tie-breaks fail, the tie shall be broken by drawing of lots.

1.2     A play-off is the best system, but it is not always appropriate. For  example, there may not be adequate time.

1.3     The list of all other commonly used tie-break systems is given in alphabetical order. The players shall be ranked in descending order of the respective system.

2.       Play-Off

2.1     Adequate time must be set aside for a conclusion to be reached.

2.2     The pairing system and rate of play must be determined in advance of the start of the event.

2.3     All eventualities must be covered in the regulations.

2.4     It is recommended that play-offs only be arranged for disposition of the first place, a championship or qualifying places.

2.5     Where subsidiary places are also being decided during the play- off, each position shall be determined in accordance with the play-off. For example, three players tie: number 1 wins the play-off, number 2 comes second and number 3 third. Number 2 shall receive the second prize.

2.6     Where two players are tied after the first place has been decided, they shall split any prize money to which they are entitled. For example: four players tie, and a knockout is arranged. Players 3 and 4 knocked out in the semi-final shall share the 3rd and 4th prizes equally.

2.7     Where time is limited before a closing ceremony, games between players potentially involved in such ties in the last round may be scheduled to commence earlier than other games in the tournament.

2.8     If there is a play-off it shall commence after a break of at least 30 minutes after the conclusion of the last main game involving players in the play-off. Where there are further stages, there shall be a break of at least 10 minutes between each stage.

2.9     Each game shall be supervised by an arbiter. If there is a dispute, the matter shall be referred to the Chief Arbiter. His decision shall be final.

2.10   Initial colours shall be determined by lot in all cases below.

2.11   The following is an example where time for play-off is somewhat limited.

2.11.1    If two players have to play a tie-break match, they play a two- game mini-match at the rate of all the moves in 3 minutes with 2 seconds added on for each move from move 1. If this match is tied, a new drawing of lots for colours shall take place. The winner shall be the first winner of a game. After each odd-numbered game the colours shall be reversed.

2.11.2    If three players have to take part in a play-off, they play a one-game round robin at the rate P-3’+2”. If all three players again tie, then the next tie-break shall be used (see  the list of tie-breaks), and the lowest-placed player eliminated. The procedure is then as in 2.11.1.

2.11.3    If four players have to take part in a play-off they play a knockout. The pairings shall be determined by lot. There shall be two-game elimination matches at the rate as in 2.11.1.

2.11.4    If five or more players have to take part in a play-off, they are ranked by the next tie-break (the list of tie-breaks) and all but the top four are eliminated.

2.12   The right is reserved to make necessary changes.

2.13   Where only two players are involved in the play-off, they may play at a slower rate of play, if time permits, by agreement with the CA and CO.

3.       Average Rating of Opponents AROC

3.1     The Average Rating of Opponents (ARO) is the sum of the ratings of the opponents of a player, divided by the number of games played.

3.2     The Average Rating of Opponents Cut (AROC) is the Average Rating of Opponents, excluding one or more of the ratings of the opponents, starting from the lowest-rated opponent. All forfeits and byes are to be cut from the calculation of AROC.

3.3     Average Rating of Opponents Cut 1 (AROC 1)

The Average Rating of Opponents Cut 1 (AROC 1) is the Average Rating of Opponents, excluding the lowest-rated opponent.

3.3.1      All forfeits and byes are to be cut from the calculation of AROC 1. If a player has one or more forfeits or byes, then no additional results are to be cut from the calculation of AROC 1.

4.       Buchholz System

4.1     The Buchholz System is the sum of the scores of each of the opponents of a player.

4.2     The Median Buchholz is the Buchholz reduced by the highest and the lowest scores of the opponents.

4.3     The Median Buchholz 2 is the Buchholz score reduced by the  two highest and the two lowest scores of the opponents.

4.4     The Buchholz Cut 1 is the Buchholz score reduced by the lowest score of the opponents.

4.5     The Buchholz Cut 2 is the Buchholz score reduced by the two lowest scores of the opponents.

5.       Direct Encounter

5.1     If all the tied players have met each other, the sum of points from these encounters is used. The player with the highest score is ranked number 1 and so on.

6.       Koya System for Round-Robin Tournaments

6.1     This is the number of points achieved against all opponents who have achieved 50% or more (including wins by forfeit).

6.2     The Koya System Extended

The Koya system may be extended, step by step, to include score groups with less than 50% (including wins by forfeit), or reduced, step by step, to exclude players who scored 50% (including wins by forfeit) and then higher scores.

7.       Number of Games won with the Black Pieces

8.       Number of Games played with the Black Pieces

8.1     The greater number of games played with the black pieces (unplayed games shall be counted as played with the white pieces).

9.       Sonneborn-Berger System (calculation)

9.1     Sonneborn-Berger for Round Robin Individual Tournaments is the sum of the scores of the opponents a player has defeated (including wins by forfeit) and half the scores of the players with whom he has drawn.

9.2     Sonneborn-Berger for Double Round Robin Individual Tournaments is the sum of the products of the scores in two games (including wins by forfeit) against the opponent multiplied by the number of points achieved by this opponent.

9.3     Sonneborn-Berger for Team Tournaments is the sum of the products of the scores made by each opposing team and the score made against that team. Example: In Chess Olympiads the sum of Sonneborn-Berger points is calculated as follows: match points of each opponent, excluding the opponent who scored the lowest number of match points, multiplied by the number of game points achieved against this opponent.

10.     Cumulative system

10.1   Sum of Progressive Scores

After each round a player has a certain tournament score. These scores are added to determine the total Sum of Progressive Score.

10.2   Sum of Progressive Scores Cuts

The Sum of Progressive Score reduced by the tournament score of one or more rounds, starting with the first round.

11.     Tie-Break in Team Competitions

11.1   Match points in team competitions that are decided by game points.

For example: 2 points for a won match where a team has scored more points than the opposing team, 1 point for a drawn match and 0 points for a lost match.

11.2   Game points in team competitions that are decided by match points. The tie is broken by determining the total number of game points scored.

12.     Tie-Break Systems using both the Player’s and the Opponents’ Results

12.1   Sonneborn-Berger,

12.2   The Koya System for Round-Robin Tournaments,

12.3   The Koya System Extended,

12.4   Number of games won (including wins by forfeit),

12.5   Number of games won with the Black Pieces,

12.6   Direct encounter.

13.     Tie-Break Systems using a Team's Own Results

13.1   Match points in team competitions.

13.2   Game points in team competitions that are decided by match points. The tie is broken by determining the total number of game points scored.

13.3   Direct encounter.

14.     Tie-Break Systems using the Opponent’s Results

14.1   Note that these scores are determined in each case after the application of the rule concerning unplayed games.

14.2   Buchholz System

14.2.1    Median Buchholz.

14.2.2    Median Buchholz 2.

14.2.3    Buchholz Cut 1.

14.2.4    Buchholz Cut 2.

14.2.5    Sum of Buchholz: the sum of the Buchholz scores of the opponents.

14.3   Sonneborn-Berger System

14.3.1    Sonneborn-Berger for Individual Tournaments

14.3.2    Sonneborn-Berger for Team Tournaments A: the sum of the products of the match points made by each opposing team and the match points made against that team, or

14.3.3    Sonneborn-Berger for Team Tournaments B: the sum of the products of the match points made by each opposing team and the game points made against that team, or

14.3.4    Sonneborn-Berger for Team Tournaments C: the sum of the products of the game points made by each opposing team and the match points made against that team, or

14.3.5    Sonneborn-Berger for Team Tournaments D: the sum of the products of the game points made by each opposing team and the game points made against that team.

14.3.6    Sonneborn-Berger for Team Tournaments Cut 1 A: the sum of the products of the match points made by each opposing team and the match points made against that team, excluding the opposing team who scored the lowest number of match points, or

14.3.7    Sonneborn-Berger for Team Tournaments Cut 1 B: the sum of the products of the match points made by each opposing team and the game points made against that team, excluding the opposing team who scored the lowest number of match points, or

14.3.8    Sonneborn-Berger for Team Tournaments Cut 1 C: the sum of the products of the game points made by each opposing team and the match points made against that team, excluding the opposing team who scored the lowest number of game points, or

14.3.9    Sonneborn-Berger for Team Tournaments Cut 1 D: the sum of the products of the game points made by each opposing team and the game points made against that team, excluding the opposing team who scored the lowest number of game points.

15.     Tie-Break Systems using Ratings in Individual 5 (where all the players are rated)

15.1   When a player has elected not to play more than two games in a tournament, his ARO or AROC shall be considered to be lower than that of any player who has completed more of the schedule.

15.1.1    ARO - See 3.1.

15.1.2    AROC - See 3.2.

15.2   For tie-break purposes a player who has no opponent will be considered as having played against a virtual opponent who has the same number of points at the beginning of the round and who draws in all the following rounds. For the round itself the result by forfeit will be considered as a normal result.

This gives the formula:

Svon = SPR + (1 – SfPR) + 0.5 * (n – R)

where for player P who did not play in round R:

n  = number of completed rounds

Svon    = score of virtual opponent after round n

SPR     = score of P before round R

SfPR    = forfeit score of P in round R

Example 1:

in Round 3 of a nine-round tournament Player P did not show up.

Player P’s score after 2 rounds is 1.5. The score of his virtual opponent is:

Svon = 1.5 + (1 – 0) + 0.5 * (3 – 3) = 2.5 after round 3

Svon = 1.5 + (1 – 0) + 0.5 * (9 – 3) = 5.5 at the end of the tournament

Example 2:

in Round 6 of a nine-round tournament playerP’sopponentdoesnotshowup.

Player P’s score after 5 rounds is 3.5. The score of his virtual opponent is:

Svon = 3.5 + (1 – 1) + 0.5 * (6 – 6) = 3.5 after round 6

Svon = 3.5 + (1 – 1) + 0.5 * (9 – 6) = 5.0 at the end of the tournament

15.3   For tie-break purposes all unplayed games in which players are indirectly involved (results by forfeit of opponents) are considered to have been drawn.