Magnus is already champion? No world champion ever recovered after -2 score.
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After Magnus took a 4-2 lead over Anand, I've decided to look at the history of World Championship matches - who, if ever, managed to come back from two (or more) behind and at least equalize the score at some point?
The first official World Championship match was unique in many ways - there was no World Champion, after all, only two candidates. Johannes Zukertort led 4-1 after winning 4 games in a row, but Wilhelm Steinitz managed to equalize, and then even win convincingly with +5 score.
In all subsequent matches, there was a champion and a candidate. Let's see how the matches went after someone achieved +2 lead. Winner of the match is first in the pairs, not the incumbent champion.
Champion led +2:
1889, Steinitz - Chigorin. Steinitz led 6-4; Chigorin never managed to equalize, Steinitz won 10.5-6.5.
1891, Steinitz - Gunsberg. Steinitz led 6-4; Gunsberg never managed to equalize, Steinitz won 10.5-8.5.
1896/97, Lasker - Steinitz. Lasker led 2-0, eventually increasing the lead to 9-2 without any wins for Steinitz. Lasker went on to win 12.5-4.5, with Steinitz winning only 2 games.
1907, Lasker - Marshall. Lasker led 2-0, eventually increasing the lead to 11.5-3.5 without any wins for Marshall. Lasker won 8 games, drew 7 and lost none.
1908, Lasker - Tarrasch. Lasker led 2-0, Tarrasch won game 3, then Lasker led 3-1 and never let the lead drop below +2, eventually winning 10.5-3.5. Lasker won 8 games, drew 5 and lost 3.
1910, Lasker - Janowski. Lasker led 3-1, eventually increasing the lead to 9.5-1.5 without any wins for Janowski. Lasker won 8 games, drew 3 and lost none.
1929, Alekhine - Bogoljubov. Alekhine led 5-3, then increased the lead to 8-4. Bogoljubov never managed to get the lead below +2, Alekhine won 15.5-9.5.
1934, Alekhine - Bogoljubov. Alekhine led 3-1. Bogoljubov never managed to equalize, Alekhine won 15.5-10.5.
1954, Botvinnik - Smyslov. Botvinnik led 2-0, then increased the lead to 3.5-0.5. Smyslov managed to recover and even led 6-5 after game 11. Then Botvinnik led 9-7; the match eventually ended 12-12, Botvinnik retained his title.
1966, Petrosian - Spassky. Petrosian led 6-4, Spassky managed to equalize 9.5-9.5. Then Petrosian led 12-10 and won 12.5-11.5.
1978, Karpov - Korchnoi. Karpov led 8-6, then 10-7. Korchnoi managed to equalize 15.5-15.5, then Karpov won the last game and the match 16.5-15.5 (6 wins).
1981, Karpov - Korchnoi. Karpov led 2-0, then 3.5-0.5. Korchnoi never managed to get the lead below +2, Karpov won 11-7 (6 wins).
1984, Karpov - Kasparov. Karpov led 4-2, eventually increasing the lead to 16-11 (with no wins for Kasparov). Kasparov managed to decrease the lead to 25-23 at the game 48, after which the match was cancelled.
1986, Kasparov - Karpov. Kasparov led 8-6, then 9.5-6.5. Karpov equalized 9.5-9.5, then Kasparov led 11.5-10.5 and won the match 12.5-11.5.
1990, Kasparov - Karpov. Kasparov led 11-9, Karpov never managed to equalize, Kasparov won 12.5-11.5.
1993 (PCA), Kasparov - Short. Kasparov led 2.5-0.5, then eventually increased the lead to 10.5-4.5. Short never managed to recover, Kasparov won 12.5-7.5.
1993 (FIDE), Karpov - Timman. Karpov led 6-4, then eventually increased the lead to 10.5-5.5. Timman never managed to recover, Karpov won 12.5-8.5.
1995 (PCA), Kasparov - Anand. Kasparov led 7.5-5.5, then 8.5-5.5 and eventually won the match 10.5-7.5.
1996 (FIDE), Karpov - Kamsky. Karpov led 4-2, then 5-2 and 6.5-2.5. Kamsky never managed to get the lead below +2, Karpov won 10.5-7.5.
2006, Kramnik - Topalov. Kramnik led 2-0, then Topalov equalized 4-4 and led 5-4, Kramnik drew the classical match 6-6 and then won the tie breaks.
2008, Anand - Kramnik. Anand led 3.5-1.5, then 4.5-1.5. Kramnik never managed to get the lead below +2, Anand won 6.5-4.5.
Candidate led +2:
1892, Steinitz - Chigorin. Chigorin led 6-4; Steinitz then equalized 7-7, then Chigorin and Steinitz repeatedly won their respective games with White to tie 10-10, and then Steinitz won the tie-break to emerge as winner with score 12.5-10.5 (wins 10-8).
1894, Lasker - Steinitz. Lasker led 5-3, then won three more games in a row. Steinitz never managed to equalize, Lasker won 12-7.
1921, Capablanca - Lasker. Capablanca led 6-4, eventually increasing the lead to 9-5. After the 14th game, Lasker forfeited the match.
1927, Alekhine - Capablanca. Alekhine led 11.5-9.5. Capablanca never managed to equalize, Alekhine won 18.5-15.5 (6 wins)
1937, Alekhine - Euwe. Alekhine led 5-3, then increased the lead to 6.5-3.5. Euwe never managed to get the lead below +2, Alekhine won 15.5-9.5.
1957, Smyslov - Botvinnik. Smyslov led 5-3, then increased the lead to 7-5. Botvinnik never managed to equalize, Smyslov won 12.5-9.5.
1958, Botvinnik - Smyslov. Botvinnik led 2-0, then 3-0. Smyslov never managed to get the lead below +2, Botvinnik won 12.5-10.5.
1960, Tal - Botvinnik. Tal led 4-2, then 5-2. Botvinnik never managed to equalize, Tal won 12.5-8.5.
1961, Botvinnik - Tal. Botvinnik led 4.5-2.5. Tal never managed to equalize, Botvinnik won 13-8.
1963, Petrosian - Botvinnik. Petrosian led 10-8, then 11-8 and eventually won 12.5-9.5.
1969, Spassky - Petrosian. Spassky led 5-3, Petrosian equalized 5.5-5.5. Then Spassky led 10.5-8.5 and eventually won 12.5-10.5.
1985, Kasparov - Karpov. Kasparov led 10.5-8.5, Karpov never managed to equalize, Kasparov won 13-11.
2000 (Classical), Kramnik - Kasparov. Kramnik led 6-4, all following games were drawn, and Kramnik won 8.5-6.5.
Nobody led +2:
1910, Lasker - Schlechter. Schlechter led 3-2, and then Lasker managed to win the very last game to draw the match 5-5.
1951, Botvinnik - Bronstein. A very equally matched contest where both players had +1 leads. The match ended 12-12, Botvinnik retained the title.
1987, Kasparov - Karpov. Karpov actually took the +1 lead three times while Kasparov led only once. Kasparov managed to win the very last game to draw the match 12-12.
2004 (Classical), Kramnik - Leko. Leko led 4.5-3.5, and then Kramnik managed to win the very last game to draw the match 7-7.
2010, Anand - Topalov. An evenly matched contest when both Anand and Topalov had +1 leads. Anand won the last classical game to win the match cleanly 6.5-5.5.
2012, Anand - Gelfand. Gelfand led 4-3, Anand immediately equalized, drew the classical match and then won tie breaks.
Both players led +2:
1935, Euwe - Alekhine. Alekhine led 3-1, then increased the lead to 5-2. Euwe equalized 7-7. Alekhine then led 10.5-8.5, but Euwe again equalized 10.5-10.5. Then Euwe led 14-12, Alekhine never managed to equalize and lost 15.5-14.5.
1972, Spassky - Fischer. Spassky led 2-0. Fischer equalized 2.5-2.5, then led 5-3 and increased the lead to 6.5-3.5. Spassky never managed to get the lead below +2 and lost 12.5-8.5.
One thing is clear after studying this data. Since 1894, if a challenger achieves +2 lead at any stage of a World Championship, he wins the match. No exceptions. So, basically, we can declare Magnus Carlsen the new champion already.