2018 Berlin Candidates Chess Tournament

Chances for a rapids playoff

Only 3 of the remaining possible outcomes will result in a rapids playoff.

In all 3 outcomes, Mamedyarov will play Grischuk.

For this to happen, they must draw each other in the next round, both win in the final round, and Kramnik must beat Ding Liren in the next round. Even if those four games all go as indicated, the probability of the playoff is still only 7 out of the 81 combinations for the other four games.

The tiebreaks for this tournament are as follows: First, your score for the tournament. If there is a tie at the top, the first tiebreaker is direct competition between the tied players: e.g., if there are two players and one beat the other in the tournament, that one wins the tiebreak. If that's still tied, you go to the most overall wins (i.e. the fewest draws) in the tournament. If that's still tied you go to the Sonneborn-Berger method, in which you add the scores of the people you beat, and half the scores of the people you drew with (and in a round-robin tournament are thus rewarded for doing well against stronger players, although that then implies you did more poorly against weaker players). Finally, if that's tied, you will play a sequence of rapid games to determine the winner.

A historical note: back in the 1960s, they actually calculated tiebreaks like Sonneborn-Berger by hand, for tournaments with hundreds of players. It was an unbelievably tedious task, and errors were almost certain to creep in to the larger tournament results crosstables (delivered days after the tournament finished). I wrote what was probably the first computer program (in FORTRAN II) to calculate the tiebreaks and output the crosstable for chess tournaments, and I received free entry to a number of large tournaments by running my program for them.

Following is the list of combinations resulting in a playoff, with the 8-letter string indicating the results of the following respective games: (D=Draw W=White wins B=Black wins)

Mamedyarov Grischuk
DingLiren Kramnik
So Karjakin
Caruana Aronian
Grischuk Caruana
Aronian So
Karjakin DingLiren
Kramnik Mamedyarov

                Score      Direct  Wins  S-B
DBDDWWBB
 1 Mamedyarov  8.0 /14    1.0 / 2    3  54.50
 2   Grischuk  8.0 /14    1.0 / 2    3  54.50
 3  DingLiren  7.5 /14    2.5 / 4    2  53.00
 4   Karjakin  7.5 /14    2.0 / 4    4  50.50
 5    Caruana  7.5 /14    1.5 / 4    3  49.50
 6    Kramnik  6.5 /14    0.0 / 0    4  43.25
 7    Aronian  5.5 /14    1.0 / 2    2  40.25
 8         So  5.5 /14    1.0 / 2    1  39.00

DBDWWDDB
 1 Mamedyarov  8.0 /14    3.5 / 6    3  55.00
 2   Grischuk  8.0 /14    3.5 / 6    3  55.00
 3   Karjakin  8.0 /14    3.0 / 6    4  54.25
 4    Caruana  8.0 /14    2.0 / 6    4  50.75
 5  DingLiren  7.0 /14    0.0 / 0    1  49.75
 6    Kramnik  6.5 /14    0.0 / 0    4  41.50
 7         So  6.0 /14    0.0 / 0    1  40.25
 8    Aronian  4.5 /14    0.0 / 0    1  34.00

DBDBWDBB
 1 Mamedyarov  8.0 /14    1.0 / 2    3  54.50
 2   Grischuk  8.0 /14    1.0 / 2    3  54.50
 3  DingLiren  7.5 /14    1.5 / 2    2  53.00
 4   Karjakin  7.5 /14    0.5 / 2    4  50.50
 5    Caruana  7.0 /14    0.0 / 0    3  47.50
 6    Kramnik  6.5 /14    0.0 / 0    4  43.50
 7         So  6.0 /14    0.0 / 0    1  41.50
 8    Aronian  5.5 /14    0.0 / 0    2  41.00

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