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Comparison of top chess players throughout history

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Several methods have been suggested for comparing the greatest chess players in history. There is agreement on a statistical system to rate the strengths of current players, called the Elo system, but disagreement about methods used to compare players from different generations who never competed against each other

Statistical methods

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Elo system

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Main articles: Elo rating system and List of chess players by peak FIDE rating

The most well known statistical method was devised by Arpad Elo in 1960 and elaborated on in his 1978 book The Rating of Chessplayers, Past and Present.[1] He gave ratings to players corresponding to their performance over the best five-year span of their career. According to this system the highest ratings achieved were:

Though published in 1978, Elo's list did not include five-year averages for later players Bobby Fischer and Anatoly Karpov. It did list January 1978 ratings of 2780 for Fischer and 2725 for Karpov.[2]

In 1970, FIDE adopted Elo's system for rating current players, so one way to compare players of different eras is to compare their Elo ratings. The best-ever Elo ratings are tabulated below. As of September 2023, there are 133 chess players in history who broke 2700, and 15 of them exceeded 2800.

Table of top 20 rated players of all-time, with date their best ratings were first achieved
Rank Rating Player Date Age
011 2882 Magnus Carlsen 2014-05May 2014 23 years, 5 months
022 2851 Garry Kasparov 1999-07July 1999 36 years, 2 months
033 2844 Fabiano Caruana 2014-10October 2014 22 years, 2 months
044 2830 Levon Aronian 2014-03March 2014 31 years, 4 months
055 2822 Wesley So 2017-02February 2017 23 years, 3 months
066 2820 Shakhriyar Mamedyarov 2018-09September 2018 33 years, 4 months
077 2819 Maxime Vachier-Lagrave 2016-08 August 2016 25 years, 9 months
088 (tie) 2817 Viswanathan Anand 2011-03March 2011 41 years, 2 months
088 (tie) 2817 Vladimir Kramnik 2016-10October 2016 41 years, 3 months
1010 (tie) 2816 Veselin Topalov 2015–07July 2015 40 years, 3 months
1010 (tie) 2816 Hikaru Nakamura 2015-10October 2015 27 years, 9 months
1010 (tie) 2816 Ding Liren 2018-11November 2018 26 years
1313 2810 Alexander Grischuk 2014-12December 2014 31 years, 1 month
1414 2804 Alireza Firouzja 2021-11December 2021 18 years, 5 months
1515 2801 Arjun Erigaisi 2024-11December 2024 21 years, 2 months
1616 2798 Anish Giri 2015-10October 2015 21 years, 3 months
1717 2795 Ian Nepomniachtchi 2023-03March 2023 32 years, 7 months
1818 2794 Gukesh Dommaraju 2024-10October 2024 18 years, 4 months
1919 2793 Teimour Radjabov 2012-11November 2012 25 years, 7 months
2020 2788 Alexander Morozevich 2008-07July 2008 30 years, 11 months

Average rating over time

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The average Elo rating of top players has risen over time. For instance, the average of the top 10 active players rose from 2751 in July 2000 to 2794 in July 2014, a 43-point increase in 14 years. The average rating of the top 100 players, meanwhile, increased from 2644 to 2703, a 59-point increase.[3] Many people believe that this rise is mostly due to an anomaly known as ratings inflation, making it impractical to compare players of different eras.[4]

Elo said it was futile to attempt to use ratings to compare players from different eras and that they could only measure the strength of a player as compared to their contemporaries. He also stated that the process of rating players was in any case rather approximate — he compared it to "the measurement of the position of a cork bobbing up and down on the surface of agitated water with a yard stick tied to a rope and which is swaying in the wind".[5][6]

Chessmetrics

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Further information: Chessmetrics

Many statisticians besides Elo have devised similar methods to retrospectively rate players. Jeff Sonas' rating system is called "Chessmetrics". This system takes account of many games played after the publication of Elo's book, and claims to take account of the rating inflation that the Elo system has allegedly suffered.[according to whom?]

One caveat is that a Chessmetrics rating takes into account the frequency of play. According to Sonas, "As soon as you go a month without playing, your Chessmetrics rating will start to drop."[7]

Sonas, like Elo, claims that it is impossible to compare the strength of players from different eras, saying:

Of course, a rating always indicates the level of dominance of a particular player against contemporary peers; it says nothing about whether the player is stronger/weaker in their actual technical chess skill than a player far removed from them in time. So while we cannot say that Bobby Fischer in the early 1970s or José Capablanca in the early 1920s were the "strongest" players of all time, we can say with a certain amount of confidence that they were the two most dominant players of all time. That is the extent of what these ratings can tell us.[8]

Nevertheless, Sonas' website does compare players from different eras. Including data until December 2004, the ratings were:

Rank 1-year peak[9] 5-year peak[10] 10-year peak[11] 15-year peak[12] 20-year peak[13]
1 Bobby Fischer, 2881 Garry Kasparov, 2875 Garry Kasparov, 2863 Garry Kasparov, 2862 Garry Kasparov, 2856
2 Garry Kasparov, 2879 Emanuel Lasker, 2854 Emanuel Lasker, 2847 Anatoly Karpov, 2820 Anatoly Karpov, 2818
3 Mikhail Botvinnik, 2871 José Capablanca, 2843 Anatoly Karpov, 2821 Emanuel Lasker, 2816 Emanuel Lasker, 2809
4 José Capablanca, 2866 Mikhail Botvinnik, 2843 José Capablanca, 2813 José Capablanca, 2798 Alexander Alekhine, 2781
5 Emanuel Lasker, 2863 Bobby Fischer, 2841 Bobby Fischer, 2810 Alexander Alekhine, 2794 Viktor Korchnoi, 2766
6 Alexander Alekhine, 2851 Anatoly Karpov, 2829 Mikhail Botvinnik, 2810 Mikhail Botvinnik, 2789 Vasily Smyslov, 2759

In 2005,[14] Sonas used Chessmetrics to evaluate historical annual performance ratings and came to the conclusion that Kasparov was dominant for the most years, followed by Karpov and Lasker. He also published the following list of the highest ratings ever attained according to calculations done at the start of each month:[15]

Rank Rating Player
1 2895 Bobby Fischer
2 2886 Garry Kasparov
3 2885 Mikhail Botvinnik
4 2878 Emanuel Lasker
5 2877 José Capablanca
6 2860 Alexander Alekhine
7 2848 Anatoly Karpov
8 2833 Viswanathan Anand
9 2826 Vladimir Kramnik
10 2826 Wilhelm Steinitz

Warriors of the Mind

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In contrast to Elo and Sonas's systems, Raymond Keene and Nathan Divinsky's book Warriors of the Mind[16] attempts to establish a rating system claiming to compare directly the strength of players active in different eras, and so determine the strongest player of all time (through December 2004). Considering games played between sixty-four of the strongest players in history, they came up with the following top ten:[17]

  1. Garry Kasparov, 3096
  2. Anatoly Karpov, 2876
  3. Bobby Fischer, 2690
  4. Mikhail Botvinnik, 2616
  5. José Raúl Capablanca, 2552
  6. Emanuel Lasker, 2550
  7. Viktor Korchnoi, 2535
  8. Boris Spassky, 2480
  9. Vasily Smyslov, 2413
  10. Tigran Petrosian, 2363

These "Divinsky numbers" are not on the same scale as Elo ratings (the last person on the list, Johannes Zukertort, has a Divinsky number of 873, which would be a beginner-level Elo rating). Keene and Divinsky's system has met with limited acceptance,[18] and Warriors of the Mind has been accused of arbitrarily selecting players and bias towards modern players.[19]

Moves played compared with computer choices

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The idea of this approach is to compare the moves played by humans to top engine moves, with the rationale that players more likely to choose these moves are also stronger.

Early efforts

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A computer-based process of analyzing chess abilities across history came from Matej Guid and Ivan Bratko at the University of Ljubljana, Slovenia, in 2006.[20] A similar project was conducted for World Champions in 2007–08 using Rybka 2.3.2a (then-strongest chess program) and a modified version of Guid and Bratko's program "Crafty".[21] CAPS (Computer Aggregated Precision Score) is a system created by Chess.com that compares players from different eras by finding the percentage of moves that matches that of a chess engine.[22]

Markovian model (2017)

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In 2017, Jean-Marc Alliot of the Toulouse Computer Science Research Institute (IRIT) presented a new method,[23] based on a Markovian interpretation of a chess game. Starting with those of Wilhelm Steinitz, all 26,000 games played since then by chess world champions have been processed by a supercomputer using the Stockfish chess engine (rated above 3310 Elo).

These predictions have proven not only to be extremely close to the actual results when players have played concrete games against one another, but to also fare better than those based on Elo scores. The results demonstrate that the level of chess players has been steadily increasing. Magnus Carlsen (in 2013) tops the list, while Vladimir Kramnik (in 1999) is second, Bobby Fischer (in 1971) is third, and Garry Kasparov (in 2001) is fourth.

Larry Kaufman (2023)

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Larry Kaufman published an article in 2023 estimating the ratings of chess players throughout history by comparing their games with the choices of top engines, using Chess.com accuracy scores. He considered only world championship matches and tournaments (official or unofficial, and including women's championships), Candidates and Interzonal events, and non-title matches between the world champion and top contenders. He ignored drawn games, because he believed that previous analyses favoured players who played cautiously, with drawn games generally having fewer inaccuracies than wins.

He estimated ratings for players at their peak years, on a scale corresponding to Elo ratings in 2023. He estimated ratings for 47 players, with the following top ten:[24]

  1. Magnus Carlsen, 2858 (peak years 2013–2021)
  2. Garry Kasparov, 2821 (peak years 1993–2001)
  3. Bobby Fischer, 2802 (peak years 1970–1972)
  4. Ian Nepomniachtchi, 2786 (peak years 2020–2022)
  5. Vladimir Kramnik, 2785 (peak years 2000–2007)
  6. Viswanathan Anand, 2780 (peak years 2007–2014)
  7. Veselin Topalov, 2773 (peak years 2005–2009)
  8. Anatoly Karpov, 2746 (peak years 1974–1984)
  9. Mikhail Tal, 2711 (peak years 1958–1960)
  10. Vasily Smyslov, 2687 (peak years 1953–1957)

(Kaufman noted however that Fabiano Caruana could not be considered by his methodology because his World Championship match had all classical games drawn. He speculated that Caruana "might well be number two of all time".)[24]

Kaufman concluded that the quality of play rose steadily by about 2.5 Elo points per year from 1900 to 2023, though he conceded that the rate was greater in the 19th century and thus that Paul Morphy "might have rivaled Fischer for the top spot if we could properly correct for these factors". He corrected ratings for 2.5 points per year before for 2017 (the midpoint of Carlsen's peak), to estimate players' strength relatively according to their time:[24]

  1. Bobby Fischer, 2917
  2. Garry Kasparov, 2871
  3. José Raúl Capablanca, 2868
  4. Alexander Alekhine, 2864
  5. Emanuel Lasker, 2862
  6. Magnus Carlsen, 2858
  7. Mikhail Tal, 2856
  8. Harry Nelson Pillsbury, 2853
  9. Vasily Smyslov, 2842
  10. Reuben Fine, 2842

He made a third list correcting by 2 points per year before 2017, instead of 2.5 points per year. That list again had Fischer first (2894) and Kasparov second (2861); and had Carlsen third on 2858.[24]

Subjective lists

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Many prominent players and chess writers have offered their own rankings of players.

Bobby Fischer (1964 and 1970)

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In 1964, Bobby Fischer listed his top 10 in Chessworld magazine: Morphy, Staunton, Steinitz, Tarrasch, Chigorin, Alekhine, Capablanca, Spassky, Tal, and Reshevsky.[25][26] He considered Morphy to be "perhaps the most accurate", writing: "In a set match he would beat anyone alive today."[27]

In 1970, Fischer named Morphy, Steinitz, Capablanca, Botvinnik, Petrosian, Tal, Spassky, Reshevsky, Svetozar Gligorić and Bent Larsen the greatest chess players in history.[28]

Irving Chernev (1974)

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In 1974, popular chess author Irving Chernev published an article titled Who were the greatest? in the English magazine CHESS.[29] He followed this up with his 1976 book The Golden Dozen, in which he ranked his all-time top twelve: 1. Capablanca, 2. Alekhine, 3. Lasker, 4. Fischer, 5. Botvinnik, 6. Petrosian, 7. Tal, 8. Smyslov, 9. Spassky, 10. Bronstein, 11. Rubinstein, and 12. Nimzowitsch.[30]

Miguel Quinteros (1992)

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In a 1992 interview GM Miguel Quinteros gave the opinion:[31] "I think Fischer was and still is the greatest chess player of all time. [...] During his absence other good chess players have appeared. But no one equals Fischer's talent and perfection."

Viswanathan Anand (2000, 2008 and 2012)

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In 2000, when Karpov, Korchnoi and Kasparov were still active, Anand listed his top 10 as: Fischer, Morphy, Lasker, Capablanca, Steinitz, Tal, Korchnoi, Keres, Karpov and Kasparov.[32]

When interviewed in 2008 shortly after Fischer's death, he ranked Fischer and Kasparov as the greatest, with Kasparov a little ahead by virtue of being on top for so many years.[33]

In 2012, Anand stated that he considered Fischer the best player and also the greatest, because of the hurdles he faced.[34]

Chess Informant readers (2001)

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Svetozar Gligorić reported in his book Shall We Play Fischerandom Chess?  (Batsford, 2002):

At the beginning of 2001 a large poll for the "Ten Greatest Chess Players of the 20th Century, selected by Chess Informant readers" resulted in Fischer having the highest percentage of votes and finishing as No. 1, ahead of Kasparov, Alekhine, Capablanca, Botvinnik, Karpov, Tal, Lasker, Anand and Korchnoi.[35]

David Edmonds and John Eidinow (2004)

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BBC award-winning journalists, from their book Bobby Fischer Goes to War: How the Soviets Lost the Most Extraordinary Chess Match of All Time  (HarperCollins, 2004):

Fischer, some will maintain, was the outstanding player in chess history, though there are powerful advocates too for Lasker, Capablanca, Alekhine, and Kasparov. Many chess players will dismiss such comparisons as meaningless, akin to the futile attempt to grade the supreme musicians of all time. But the manner in which Fischer stormed his way to Reykjavik, his breathtaking dominance at the Palma de Majorca Interzonal, the trouncings of Taimanov, Larsen, and Petrosian—all this was unprecedented. There never has been an era in modern chess during which one player has so overshadowed all others.[36]

Vladimir Kramnik (2005 and 2011)

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In a 2005 interview, Vladimir Kramnik (World Champion from 2000 to 2007) did not name a greatest player, but stated: "The other world champions had something 'missing'. I can't say the same about Kasparov: he can do everything."[37]

In an interview in 2011, Vladimir Kramnik said about Anand: "I always considered him to be a colossal talent, one of the greatest in the whole history of chess", "I think that in terms of play Anand is in no way weaker than Kasparov", and "In the last 5–6 years he's made a qualitative leap that's made it possible to consider him one of the great chess players".[38]

Leonard Barden (2008)

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In his 2008 obituary of Bobby Fischer, Leonard Barden wrote that most experts ranked Kasparov as the best ever player, with probably Fischer second and Karpov third.[39]

Levon Aronian (2012, 2015, and 2022)

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In a 2012 interview, Levon Aronian stated that he considers Alexander Alekhine the best player of all time.[40]

In a 2015 interview after the 8th round of the Sinquefield Cup, Levon Aronian stated that he considers Garry Kasparov the strongest player of all time.[41]

In a 2022 interview after the 5th round of the first leg in FIDE Grand Prix 2022, when asked if he thought that in the future Garry Kasparov or Magnus Carlsen would be considered the 'GOAT' (Greatest Of All Time), Levon Aronian stated that "I kind of feel that Magnus will be the greatest for a long long time, because for me he is probably already the greatest but it is still continuing. It will take a long time to beat his achievements."[42]

Magnus Carlsen (2012, 2015, 2020 and 2021)

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In 2012, Magnus Carlsen said that Kasparov is the greatest player of all time, adding that while Fischer may have been better at his best, Kasparov remained at the top for much longer.[43]

In December 2015 he said he would like to play Fischer and Kasparov at their peak performance.[44]

In January 2020, Carlsen said, "Kasparov had 20 years uninterrupted as the world No 1. And I would say for very few of those years was there any doubt that he was the best player. He must be considered as the best in history."[45] He made a similar claim in 2021, saying "Garry Kasparov, in my opinion, the greatest player there's ever been..."[46]

Hikaru Nakamura (2021 and 2023)

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In 2021, Hikaru Nakamura published a Youtube video entitled "Hikaru's Hot Takes on the Ten Best Chess Players of All Time"[47] in which he reviewed a chess.com article on "The 10 Best Chess Players Of All Time."[48] In this video he suggested that it was unfair to exclude Paul Morphy and Viswanathan Anand from the 10 greatest players of all time. Hikaru stated that Bobby Fischer should "obviously be number 3" and that Garry Kasparov and Magnus Carlsen should be at number 1 and number 2 respectively with the caveat that Kasparov is only number 1 due to his time as number 1 in the world being greater than Carlsen's. At the end of the video, Hikaru said he "can live with" the top 5 as: Kasparov, Carlsen, Fischer, Capablanca and Karpov but he would put from 6 through 10: Anand, Kramnik, Botvinnik, Lasker, Morphy.

During Game 6 of World Chess Championships 2023, as he was commenting on the game, Hikaru mentioned Magnus Carlsen, Garry Kasparov, Vishy Anand, Bobby Fischer, Anatoly Karpov, José Raúl Capablanca and Vladimir Kramnik as the top chess players of all time in order.[citation needed]

Anatoly Karpov (2021)

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Karpov named Capablanca, Alekhine, Fischer, himself, and Kasparov as his top five in 2021.[49]

World Champions by world title reigns

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The table below organises the world champions in order of championship wins. (For the purpose of this table, a successful defence counts as a win, even if the match was drawn.) The table is made more complicated by the split between the "Classical" and FIDE world titles between 1993 and 2006.

Champion Total Undisputed FIDE Classical Years as
Undisputed
Champion		 Years as
FIDE/Classical
Champion		 Total reign
Emanuel Lasker 6 6 27 27
Garry Kasparov 6 4 2 8 7 15
Anatoly Karpov 6 3 3 10 6 16
Mikhail Botvinnik 5 5 13 13
Magnus Carlsen 5 5 9 9
Viswanathan Anand 5 4 1 6 2 8
Alexander Alekhine 4 4 17 17
Wilhelm Steinitz 4 4 8 8
Vladimir Kramnik 3 1 2 1 6 7
Tigran Petrosian 2 2 6 6
José Raúl Capablanca 1 1 6 6
Boris Spassky 1 1 3 3
Bobby Fischer 1 1 3 3
Max Euwe 1 1 2 2
Vasily Smyslov 1 1 1 1
Mikhail Tal 1 1 1 1
Ruslan Ponomariov 1 1 2 2
Alexander Khalifman 1 1 1 1
Rustam Kasimdzhanov 1 1 1 1
Veselin Topalov 1 1 1 1
Ding Liren 1 1 1 1
Gukesh Dommaraju 1 1 0 0

See also

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References

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  1. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  2. ^ Arpad Emre Elo – 100th anniversary, Chessbase, 2003
  3. ^ World Top chess players and Statistics at FIDE.com
  4. ^ "ChessBase News | Rating inflation – its causes and possible cures". Chessbase.com. 27 July 2009. Retrieved 21 October 2013.
  5. ^ Chess Life, 1962.
  6. ^ "Arpad Emre Elo – 100th anniversary". 30 August 2003.
  7. ^ The Greatest Chess Player of All Time – Part I, Jeff Sonas, at Chessbase
  8. ^ About the Chessmetrics Rating System Archived 15 May 2012 at the Wayback Machine, by Jeff Sonas
  9. ^ "Peak Average Ratings: 1 year peak range". Archived from the original on 9 March 2012.
  10. ^ "Peak Average Ratings: 5 year peak range". Archived from the original on 9 March 2012.
  11. ^ "Peak Average Ratings: 10 year peak range". Archived from the original on 9 March 2012.
  12. ^ "Peak Average Ratings: 15 year peak range". Archived from the original on 9 March 2012.
  13. ^ "Peak Average Ratings: 20 year peak range". Archived from the original on 9 March 2012.
  14. ^ Sonas, J. (2005). "The Greatest Chess Player of All Time – Part IV". Chessbase. Part IV gives links to the 3 earlier parts
  15. ^ Sonas, J. (2005). "The Greatest Chess Player of All Time – Part II". Chessbase.
  16. ^ Warriors of the Mind, Raymond Keene and Nathan Divinsky, (1989)
  17. ^ "Divinsky-Keene rankings". Archived from the original on 26 November 2009.
  18. ^ Hooper, David; Whyld, Kenneth (1992). The Oxford Companion to Chess. Oxford University Press. ISBN 0-19-280049-3.
  19. ^ Winter, Edward (1996). Chess Explorations. Cadogan. ISBN 1-85744-171-0.
  20. ^ Computers choose: who was the strongest player?, Chessbase, 2006
  21. ^ "Compare the World Champions!", by Charles Sullivan, TrueChess, 2007
  22. ^ (DanielRensch), Daniel Rensch (3 January 2017). "Who Was The Best World Chess Champion In History?". Chess.com. Retrieved 3 January 2017.
  23. ^ Who is the master?, ICGA Journal, 39–1, April 2017
  24. ^ a b c d Kaufman, Larry (4 September 2023). "Accuracy, Ratings, and GOATs". Chess.com. Retrieved 7 September 2023. Correction: There was one error, I missed Capa's match with Kostic in 1919 due to Kostic's first name being given inconsistently. Fixing this raises Capa to 2633 in the absolute list, to 2868 (third place) in the list where number 1 in 1900 = Carlsen, and to 2821 (shared sixth place) in the list of where they would be if age 30 now. Probably there are other similar data errors I haven't caught., especially among the players of long ago.
  25. ^ Bobby Fischer, "The Ten Greatest Masters in History", Chessworld, Vol. 1, No. 1 (Jan.-Feb. 1964), pp. 56–61.
  26. ^ "Fischer's Top 10". Archived from the original on 6 February 2009.
  27. ^ the Even More Complete Chess Addict, by Mike Fox and Richard James, 1993, pp. 129–30
  28. ^ CHESS magazine, November 1970, p. 70
  29. ^ CHESS magazine, April 1974, pp. 201–202
  30. ^ Twelve Great Chess Players and Their Best Games, Irving Chernev, 1995 (reprint of 1976 edition).
  31. ^ Seirawan, Yasser; Stefanovic, George (1992). "Belgrade; Interview with GM Miguel Quinteros". No Regrets • Fischer–Spassky 1992. International Chess Enterprises. p. 255. ISBN 1-879479-09-5.
  32. ^ "The Grandmaster on his ten greatest chess players". Archived from the original on 20 November 2003.
  33. ^ "He (Fischer) and Kasparov were the greatest in history, but I judge Kasparov as a little ahead. Fischer was a phenomenon from 1970 to 1972 while Kasparov was on top for many years." – Morelia-Linares Super-GM starts today Archived 6 February 2009 at the Wayback Machine, Chessbase, 15 February 2008
  34. ^ Anand takes a dig at Kasparov, Viswanathan Anand, The Hindu
  35. ^ Gligorić, Svetozar (2002). Shall We Play Fischerandom Chess?. B.T. Batsford Ltd. p. 8. ISBN 0-7134-8764-X.
  36. ^ Edmonds, David; Eidinow, John (2004). Bobby Fischer Goes to War. HarperCollins Publishers Inc. p. 310. ISBN 0-06-051024-2.
  37. ^ "The most important interviews by GM Vladimir Kramnik, World Chess Champion 2000–2007". Kramnik.com. Archived from the original on 12 May 2008. Retrieved 21 October 2013.
  38. ^ "Vladimir Kramnik on Chess, Anand, Topalov, and his future". 31 August 2011. Archived from the original on 23 June 2012. Retrieved 28 May 2012.
  39. ^ "Most experts place him (Fischer) the second or third best ever, behind Kasparov but probably ahead of Karpov." – Obituary of Bobby Fischer, Leonard Barden, The Guardian, 19 January 2008
  40. ^ "Aronian names Alekhine best player of all time". WhyChess. 22 August 2012. Archived from the original on 19 November 2012. Retrieved 21 October 2013.
  41. ^ https://www.youtube.com/watch?v=WGdywyQlo2E "Well, in my opinion Garry is the strongest player of all time"
  42. ^ https://www.youtube.com/watch?v=bqK_eEA-9GQ The Soviet School of Trash Talking
  43. ^ "Magnus Carlsen: – Jeg tar verdensrekorden – VG Nett om Sjakk". Vg.no. 1 January 1970. Retrieved 21 October 2013.
  44. ^ Chess prodigy Magnus Carlsen: 'Bobby Fischer is my dream opponent'., 2015-12-16, CNN
  45. ^ Magnus Carlsen: ‘You need to be very fortunate to be No 1 in fantasy football’, The Guardian, 10 January 2020
  46. ^ Magnus Carlsen ranks Garry Kasparov, chess24 YouTube channel, 6 May 2021
  47. ^ "Hikaru's Hot Takes on the Ten Best Chess Players of All Time - YouTube". YouTube. 24 August 2021.
  48. ^ "The 10 Best Chess Players of All Time". 30 March 2023.
  49. ^ "Karpov at 70: "My great blunder was I agreed to hold the match with Kasparov in the Soviet Union"". chess24.com. Retrieved 4 July 2022.
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