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After Carlsen was excluded from the 2021 FIDE Rapid championship playoffs by the Sonneborn-Berger tiebreak, chess24 reported:

He (Carlsen) criticized the rules, saying it would give his opponents an unfair advantage as long as he is the highest rated player

But Sonneborn-Berger does not take rating into account, so how does it give an unfair advantage to lower rated players?

Update: @Alexander Gardens points out the quoted complaint is about Dubai 2016, not the Rapid World Championship 2021. I suspect that clarification in the linked article was added after I asked the question - maybe someone with better Google-fu than me could confirm if that is the case.

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It doesn't; the part you quoted looks like an erroneous statement in the article. I don't see a quote by Carlsen where he explicitly says this; Carlsen does say it's unfair but not just to him:

Carlsen speaking to NRK with a rant lasting several minutes about why he thinks the tiebreak rules in this event are unfair. "I just don't think this is fair. It has to be changed." and "It's just too amateurish in a world championship." #RapidBlitz #nrksjakk

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    He actually said "is a completely idiotic rule, either everyone with the same score should play rematch, or no-one." He goes on to say "it's extremely bitter [...] For me, any tiebreak system is ok as long as it obviously doesn't hurt the sense of justice. If you first wave rematches, everyone on the same score must have rematches."
    – John K.
    Commented Dec 29, 2021 at 20:40
  • Source: Clin idiotic rule (automatically translated article).
    – John K.
    Commented Dec 29, 2021 at 20:45
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I think you have misread the article. That quote is about the tie-break system used in 2016, not this year. In 2016 the average opponent strength was used, which put Carlsen at a disadvantage. If I understand correctly, his criticism of it being unfair to higher-rated players was made in 2016, and then the rules were changed in 2017.

Carlsen later pointed out that he also lost out due to worse tiebreaks in the 2016 World Rapid Chess Championship in Dubai, where he finished third behind Vasyl Ivanchuk and Alexander Grischuk, due to a worse rating average of his opponents.

He criticized the rules, saying it would give his opponents an unfair advantage as long as he is the highest rated player. The rules were changed for the 2017 event in Riyadh.

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    Not impossible, but I don't recall those clarifications being there when I asked the question, it may have been added later.
    – firtydank
    Commented Dec 30, 2021 at 6:06
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As you can read on the Wikipedia page, the Sonneborn-Berger score of a player is the sum of the points of the opponents. This score per opponent is multiplied by 1 in case the player won, by 0.5 if the player had a draw and by 0 if the player lost. This way losing (or drawing) against an opponent with much points is 'worse' than losing (or drawing) against an opponent with low points. But you only know this at the end of the tournament :-)

Ratings have nothing to do with this. So I do not really understand what Carlsen means. Perhaps a lower rated player has more chances to win against a higher rated player in a big tournament because the higher rated player needs every win he can score and takes a little risk. I do not know. All systems to appoint a winner are not fair. This also counts for the way that Carlsen has beaten Caruana in the previous World Championship or him winning Tata-steel in 2018. There should also be a draw on tournament level :-)

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    I think your explanation is backwards. If losing results in a tiebreak-score of 0 regardless of the opponent, then losing against an opponent with a high score is exactly the same as losing against an opponent with a low score.
    – BlueRaja - Danny Pflughoeft
    Commented Dec 29, 2021 at 20:42
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    @BlueRaja-DannyPflughoeft I suspect Marco is talking about the "opportunity cost". Your ideal goal would be to win every match to maximise your score. Losing against a higher-rated opponent would leave you further away from that ideal than would losing against a lower-rated opponent.
    – TripeHound
    Commented Dec 30, 2021 at 8:53

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