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1858 Morphy-Anderssen: After demolishing Loewenthal[?] (+8 -3 =2), Morphy crushed Anderssen (+7 -2 =2) who was reduced to playing the infamous "Anderson opening" in the later half of the match (1. a3?). Anderssen was considered the best player in the world prior to this encounter. However, the match was not declared as any kind of World Championship match, and Morphy declined to play in the World Championship matches that followed.
1927 Alekhine-Capablanca: After winning this match in great style, Alekhine hand picked his opponents for all his future matches, and refused to play a rematch with Capablanca.
1948 World Championship Tournament: The death of Alekhine in 1946 left the World Champion title vacant. FIDE organised a tournament to determine the new champion (the body went on to organise every subsequent match until the 1990s). Mikhail Botvinnik, Vassily Smyslov, Samuel Reshevsky[?], Paul Keres[?] and Max Euwe took part, with Botvinnik triumphing.
1951 Botvinnik-Bronstein, 1987 Kasparov-Karpov: FIDE originally used rules that stated that upon a tie, the previous WCC, if he was a candidate would retain the title.
1975 Karpov-Fischer: Fischer refused to play, insisting on different match scoring rules (declaring Fischer the winner if he achieved 9 wins before Karpov reached 10 wins, draws not counting.) Fischer declined to participate in a match held under the same conditions as the previous Fischer-Spassky match, and thus foreited the title to Karpov. For the following matches from 1978 to 1984, FIDE adopted Fischer's rule of discounting draws, but simply required the winner to achieve 6 wins.
1984 Karpov-Kasparov: This match was abandonded (Karpov did not win it, but did retain the title.) Kasparov was quickly down 4-0 in the first dozen games, then down 5-0 before winning his first. Then he won two out of the last three games, and the FIDE president simply halted the match. The 1985 rematch went back to the previous rules (defending WC needs to reach 12 points before challenger reaches 12.5 points, where draws are worth half a point to both players.)
1992 Fischer-Spassky: Although recognized by very few as a legitimate World Championship, it was billed as a World Championship rematch by Fischer and his hand picked opponent, Spassky. This match took place in Yugoslavia, while under strict santions. The US governement forbid Fischer to play in this country, but Fischer ignored this. Because of this, Fischer cannot return to the US.
1993 Karpov-Timman, Kasparov-Short: Both Karpov and Timman were soundly defeated in the candidates pre-matches by Nigel Short, who went on to play Kasparov in a match, but not under the auspices of FIDE. As a result, FIDE chose the two highest finishing remaining candidates, but excluded Yusupov by virtue of having been defeated by Timman in the quarter final match that already occurred in the same cycle.
1998 Karpov-Anand: After a tied match, the FIDE WCC was decided by a couple of rapid play tie breakers both won by Karpov. The match conditions heavily favored the defending champion Karpov over Anand, who was exhausted from the qualifying rounds. Later FIDE knockouts were altered to seed the defending champion into earlier rounds.
2000 Kramnik-Kasparov: Although defeated by Shirov in a candidates match earlier under another World Chess Championship sponsoring organization, Kramnik was hand picked by Kasparov, and was most likely the strongest player besides himself. Of course Kramnik proved to be more than Kasparov's equal by defeating him.
2002: Ponomariov-Ivanchuk: The 2002 FIDE WCC pre-tournament and final match has moved to a much faster time control which by many accounts (comments by Kasparov, and Ivanchuk among others) has significantly and noticeably reduced the quality of the games.
See also: list of chess players.