131:, and a loss; his round-by-round score will be 1, 1, 2, 2½, 2½. The sum of these numbers is 9. Additionally, one point is subtracted from the sum for each unplayed win, and ½ point is subtracted for each unplayed draw. In the previous example, if the fourth-round draw was instead a ½ point bye, then ½ point would be subtracted and the final sum would be 8½.
214:
1886 Sonneborn criticized the system and suggested an improvement that would give a better-weighted score. His suggestion was to add the square of the player's points to the amount calculated as above. In 1887 and 1888 Berger studied
Gelbfuhs' system and the suggestion of Sonneborn. This improvement became known as the Sonneborn-Berger system.
45:, use various criteria 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 titles, trophies, or qualification for another tournament. Otherwise players often share the tied spots, with cash prizes being divided equally among the tied players.
213:
What we call the
Sonneborn-Berger system was not invented by Sonneborn or Berger, and it was not originally designed for tie-breaking. It was invented by Oscar Gelbfuhs about 1873 to be used as a weighted score in round-robin tournaments. It would be used instead of the raw score for final places. In
197:
Sonneborn–Berger score considers the strength of opponents each player faced, or the head to head result if the tied players have already played against each other during the tournament. If a player defeated a strong player then they get more "credit" for that win or draw. This is done by adding the
138:
A practical benefit of the cumulative system is that it is simple to track with pen and paper when running a large tournament. Of course in the age of computers and smart phones, instead of accumulating points scored against weak players, we could just calculate who had the toughest schedule as with
134:
This system places more weight on games won in the early rounds and the least weight on games won in the final 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
87:
For each player, this system sums the number of points earned by the player's opponents, excluding 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.
52:
are also used in Swiss-system tournaments, while others exploit the particular features of the Swiss system. 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
139:
the
Solkoff and median systems. An alternative explanation for the popularity of the cumulative system is that it is easier for coaches, players and the audience to follow the potential scores and prizes, as the point totals don't vary and only need to be added to from round to round.
183:, this system awards 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).
57:
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. In other games, results may supply more data used for breaking ties.
217:
When the system is used to break ties between equally scoring players, adding in the square of the player's raw score does no good, so the
Sonneborn improvement is omitted. However, the system has retained the Sonneborn-Berger name.
118:
This system is the same as the Median system, except that no scores are discarded. 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.
262:
Among tied players, the player whose first loss came last gets priority. If player A's first loss was in round 4 and player B's first loss was in round 2, player A gets priority. This was a tiebreaker used by
254:
Championship uses a formula based on strength of schedule and margin of victory within games; it also allows for byes. (Not relevant in games such as chess without a defined margin of victory.)
230:
of the player's opponents. The "performance rating" of a player is basically the rating the player would receive if they had started the tournament without a rating.
53:
have already been played or other objective factors, while some methods require additional games to be played. In chess, where results are simply win/loss or draw,
17:
310:. White gets more time on the clock, but must win (i.e. a draw counts as a win for Black). The player who wins the draw of lots may choose which color they play.
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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.
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scores of every opponent the player beats and half of the score of every opponent the player draws. The system was named after
William Sonneborn and
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The player with the most wins finishes highest on tie-breaks. This is used as the first tie-break rule for individual tournaments in ICCF.
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points out deficiencies in most of the tie-break systems and recommends a playoff if there is time. If not, he recommends
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If a player arrives after the first round is paired, the player loses priority. This tiebreaker is currently used by
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To calculate this, sum the running score for each round. For example, if a player has (in order) a win, loss, win,
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Players who scored the same number of points on tie-breaks, then the winner is the one who won in a personal game.
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player who scored poorly in the start before subsequently scoring points against weaker opponents.
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Players with less than 50% score have only their highest-scoring opponent's score discarded.
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Players with more than 50% score have only their lowest-scoring opponent's score discarded;
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and then the player who has the most wins. For Swiss tournaments, he recommends the
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The player that had the black pieces the most times finishes highest on tie-breaks.
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Buchholz Cut 1 (the
Buchholz score reduced by the lowest score of the opponents);
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Players with exactly 50% score are handled as in the regular Median system;
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Buchholz (the sum of the scores of each of the opponents of a player);
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recommends these as the first four tie-breaking methods to be used:
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The greater number of wins with Black pieces, not counting forfeits.
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The
Modified Median system is similar to the Median system, except:
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This sums the cumulative scores of the player's opponents.
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rules provide for a single fast decisive game, known as
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The tie is broken by one or more games played with fast
344:For Swiss tournaments for individuals (not teams),
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41:and other board games, and in card games such as
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206:. The system is the main tie-breaking system in
467:U.S. Chess Federation's Official Rules of Chess
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238:The average rating of the player's opponents.
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451:(second ed.), Oxford University Press,
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50:tiebreakers used in other group tournaments
700:FIDE Handbook, Appendix C, Section 11.5.3
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318:As a last resort, ties are broken by a
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72:The Median system is also known as the
27:Determining winner in chess tournaments
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465:Just, Tim; Burg, Daniel B. (2003),
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746:Tie-breaking in group tournaments
410:Golombek's Encyclopedia of Chess
159:Most games with the black pieces
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448:The Oxford Companion to Chess
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706:, 2018, came into force 2019
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234:Average rating of opposition
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382:Cumulative opponent's score
358:The greater number of wins;
341:and the Cumulative system.
151:Result between tied players
143:Cumulative opponent's score
62:Median / Buchholz / Solkoff
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326:Order of tiebreak criteria
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469:(fifth ed.), McKay,
202:, but it was invented by
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31:Swiss system tournaments
431:Official Chess Handbook
208:round robin tournaments
277:Pokémon Organized Play
265:Pokémon Organized Play
222:Opponent's performance
193:Sonneborn–Berger score
187:Sonneborn–Berger score
82:Median-Buchholz System
367:U.S. Chess Federation
76:, after its inventor
717:Just & Burg 2003
675:Just & Burg 2003
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610:Just & Burg 2003
597:Just & Burg 2003
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571:Just & Burg 2003
558:Just & Burg 2003
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519:Just & Burg 2003
506:Just & Burg 2003
493:Just & Burg 2003
283:Speed play-off games
167:Most wins (Baumbach)
55:strength of schedule
250:used in the World
248:Brightwell Quotient
242:Brightwell Quotient
427:Harkness, Kenneth
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730:Categories
399:References
393:Tiebreaker
379:Cumulative
308:Armageddon
293:Fast chess
123:Cumulative
37:common in
547::200–201)
508::199–200)
495::199–200)
412:, Crown,
314:Coin flip
271:Tardiness
80:, or the
638::136–37)
445:(1992),
429:(1967),
408:(1977),
387:See also
433:, McKay
376:Solkoff
252:Othello
175:Kashdan
114:Solkoff
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320:random
228:rating
43:bridge
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291:, or
48:Some
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704:FIDE
471:ISBN
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365:The
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304:FIDE
246:The
129:draw
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