Greatest chess player of all time
Encyclopedia
This article examines a number of methodologies that have been suggested for the task of comparing top chess players throughout history, particularly the question of comparing the greatest players of different eras. Statistical methods offer objectivity but, whilst there is agreement on systems to rate the strengths of current players, there is disagreement and controversy on whether such techniques can be applied to players from different generations who never competed against each other.

Elo System

Perhaps the best-known statistical model is that devised by Arpad Elo
Árpád Élo
Arpad Emrick Elo is the creator of the Elo rating system for two-player games such as chess. Born in Egyházaskesző, Austro-Hungarian Empire, he moved to the United States with his parents as a child in 1913.Elo was a professor of physics at Marquette University in Milwaukee, Wisconsin. He was...

. In his 1978 book The Rating of Chessplayers, Past and Present, 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:
  • 2725 – José Raúl Capablanca
    José Raúl Capablanca
    José Raúl Capablanca y Graupera was a Cuban chess player who was world chess champion from 1921 to 1927. One of the greatest players of all time, he was renowned for his exceptional endgame skill and speed of play...

  • 2720 – Mikhail Botvinnik
    Mikhail Botvinnik
    Mikhail Moiseyevich Botvinnik, Ph.D. was a Soviet and Russian International Grandmaster and three-time World Chess Champion. Working as an electrical engineer and computer scientist at the same time, he was one of the very few famous chess players who achieved distinction in another career while...

    , Emanuel Lasker
    Emanuel Lasker
    Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...

  • 2700 – Mikhail Tal
    Mikhail Tal
    Mikhail Tal was a Soviet–Latvian chess player, a Grandmaster, and the eighth World Chess Champion.Widely regarded as a creative genius, and the best attacking player of all time, he played a daring, combinatorial style. His play was known above all for improvisation and unpredictability....

  • 2690 – Alexander Alekhine
    Alexander Alekhine
    Alexander Alexandrovich Alekhine was the fourth World Chess Champion. He is often considered one of the greatest chess players ever.By the age of twenty-two, he was already among the strongest chess players in the world. During the 1920s, he won most of the tournaments in which he played...

    , Paul Morphy
    Paul Morphy
    Paul Charles Morphy was an American chess player. He is considered to have been the greatest chess master of his era and an unofficial World Chess Champion. He was a chess prodigy...

    , Vasily Smyslov
    Vasily Smyslov
    Vasily Vasilyevich Smyslov was a Soviet and Russian chess grandmaster, and was World Chess Champion from 1957 to 1958. He was a Candidate for the World Chess Championship on eight occasions . Smyslov was twice equal first at the Soviet Championship , and his total of 17 Chess Olympiad medals won...

    .


(Though published in 1978, Elo's list did not include five-year averages for Bobby Fischer
Bobby Fischer
Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...

 and Anatoly Karpov
Anatoly Karpov
Anatoly Yevgenyevich Karpov is a Russian chess grandmaster and former World Champion. He was the official world champion from 1975 to 1985 when he was defeated by Garry Kasparov. He played three matches against Kasparov for the title from 1986 to 1990, before becoming FIDE World Champion once...

. It did list January 1978 ratings of 2780 for Fischer and 2725 for Karpov.)

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 July 2011, there were 79 chess grandmasters in history who broke the 2700 limit and six of them were even capable of overcoming the 2800 line. Most astonishing were performances by players like R.J. Fischer, A. Karpov and G. Kasparov, who achieved their peak ratings in early era (1972, 1994, 1999).
Table of top 20 rated players ever, with date their best ratings were first achieved
Rank Rating Player Year-month Country
1 2851 Garry Kasparov
Garry Kasparov
Garry Kimovich Kasparov is a Russian chess grandmaster, a former World Chess Champion, writer, political activist, and one of the greatest chess players of all time....

1999-07
2 2826 Magnus Carlsen
Magnus Carlsen
Sven Magnus Øen Carlsen is a Norwegian chess Grandmaster and chess prodigy who is currently the number-one ranked player in the world. In January 2010 he became the seventh player ranked number one in the world on the official FIDE rating list...

2010-07
3 2817 Viswanathan Anand
Viswanathan Anand
V. Anand or Anand Viswanathan, usually referred as Viswanathan Anand, is an Indian chess Grandmaster, the current World Chess Champion, and currently second highest rated player in the world....

2011-03
4 2813 Veselin Topalov
Veselin Topalov
Veselin Aleksandrov Topalov is a Bulgarian chess grandmaster. He currently has the sixth highest rating in the world, and was the challenger facing world champion Viswanathan Anand in the World Chess Championship 2010, losing the match 6½–5½....

2006-07
5 2811 Vladimir Kramnik
Vladimir Kramnik
Vladimir Borisovich Kramnik is a Russian chess grandmaster. He was the Classical World Chess Champion from 2000 to 2006, and the undisputed World Chess Champion from 2006 to 2007...

2002-01
6 2808 Levon Aronian
Levon Aronian
Levon Grigor Aronian is an Armenian chess Grandmaster and the reigning World Blitz Chess Champion. On the September 2011 FIDE list, he has an Elo rating of 2807, making him number three in the world and Armenia's number one...

2011-03
7 2788 Alexander Morozevich
Alexander Morozevich
Alexander Morozevich is a Russian chess Grandmaster. In the November 2011 FIDE list, he had an Elo rating of 2762, making him the 9th-highest rated player in the world, although he has previously ranked as high as second, in the July 2008 list....

2008-07
8 2788 Sergey Karjakin
Sergey Karjakin
Sergey Alexandrovich Karjakin is a Russian chess grandmaster. He was a chess prodigy and holds the record for both the youngest International Master, eleven years and eleven months, and grandmaster in history, at the age of twelve years and seven months...

2011-07
9 2787 Vassily Ivanchuk 2007-10
10 2785 Bobby Fischer
Bobby Fischer
Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...

1972-04
11 2781 Teimour Radjabov
Teimour Radjabov
Radjabov's knight sacrifice, 21. ... Ngxe5, was praised by several strong players for its bravery, including English grandmaster Nigel Short. Said Short of the move, "Radjabov plays very imaginatively... he just won't give up, he is extremely tenacious and will always find a way to muddy the...

2011-11
12 2780 Anatoly Karpov
Anatoly Karpov
Anatoly Yevgenyevich Karpov is a Russian chess grandmaster and former World Champion. He was the official world champion from 1975 to 1985 when he was defeated by Garry Kasparov. He played three matches against Kasparov for the title from 1986 to 1990, before becoming FIDE World Champion once...

1994-07
13 2774 Hikaru Nakamura
Hikaru Nakamura
Hikaru Nakamura is an American chess Grandmaster . He has been ranked among the top six players in the world by FIDE....

2011-03
14 2773 Alexander Grischuk
Alexander Grischuk
Alexander Igorevich Grischuk is a Russian chess grandmaster and Russian Champion in 2009.-Chess career:In the FIDE World Chess Championship 2000, Grischuk he made it to the semifinals, losing to Alexei Shirov....

2011-01
15 2772 Shakhriyar Mamedyarov
Shakhriyar Mamedyarov
Shakhriyar Hamid oglu Mammadyarov , also known for his Shah nickname, is a chess Grandmaster. On the September 2010 FIDE rating list he was ranked number nine in the world with an Elo rating of 2756....

2011-01
16 2765 Peter Svidler
Peter Svidler
Peter Veniaminovich Svidler is a Russian chess grandmaster.He is six-time Russian champion ....

2006-01
17 2764 Ruslan Ponomariov
Ruslan Ponomariov
Ruslan Olegovich Ponomariov is a Ukrainian chess player and former FIDE World Champion.-Early career:Ponomariov was born in Horlivka in Ukraine. In 1994 he placed third in the World Under-12 Championship at the age of ten. In 1996 he won the European Under-18 Championship at the age of just...

2011-07
18 2763 Peter Leko
Péter Lékó
On the way to winning the prestigious Corus chess tournament in 2005, Lékó defeated Grandmaster Viswanathan Anand with the black pieces. The moves were:...

2005-04
19 2761 Boris Gelfand
Boris Gelfand
Boris Abramovich Gelfand is a Belarus-born Israeli chess Grandmaster. He won the 2011 Candidates Tournament and will challenge Viswanathan Anand for the World Chess Championship 2012.-Biography:...

2010-01
20 2761 Pavel Eljanov
Pavel Eljanov
Pavel Eljanov is a Ukrainian chess grandmaster.In 1999, he was a member of the Ukrainian national youth team, which won the U-16 Chess Olympiad in Artek, Ukraine.Eljanov won the Corus B 2007 in Wijk aan Zee, Holland with a score of 9/13...

2010-09


The average Elo rating of top players has risen over time. For instance, the average of the top 100 active players rose from 2644 in July 2000 to 2697 in March 2011, a 53-point increase. Many people believe that this rise is mostly due to a system artifact known as ratings inflation, making it impractical to compare players of different eras.

Arpad Elo was of the opinion that it was futile to attempt to use ratings to compare players from different eras; in his view, they could only possibly measure the strength of a player as compared to his or her 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".

Chessmetrics

Many statistician
Statistician
A statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...

s since Elo have devised similar methods to retrospectively rate players. Jeff Sonas, for example, calls his system Chessmetrics
Chessmetrics
Chessmetrics is a system for rating chess players devised by Jeff Sonas. It is intended as an improvement over the Elo rating system.-Implementation:...

. 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 apparently suffered.

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". While it may be in the best interest of the fans for chess-players to remain active, it is not clear why a person's rating, which reflects his/her skill at chess, should drop if the player is inactive for a period of time.

Sonas, like Elo, acknowledges that it is useless to try to compare the strength of players from different eras. In his explanation of the Chessmetrics system, he says:
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 Jose 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.


Nevertheless Sonas' Web site does compare players from different eras, and shows that in such cases the Chessmetrics system is rather sensitive to the length of the periods being compared. Including data until December 2004, the rankings were:
Position 1 year 5 years 10 years 15 years 20 years
1 Bobby Fischer
Bobby Fischer
Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...

Garry Kasparov Garry Kasparov Garry Kasparov Garry Kasparov
2 Garry Kasparov
Garry Kasparov
Garry Kimovich Kasparov is a Russian chess grandmaster, a former World Chess Champion, writer, political activist, and one of the greatest chess players of all time....

 
Emanuel Lasker Emanuel Lasker Anatoly Karpov Anatoly Karpov
3 Mikhail Botvinnik
Mikhail Botvinnik
Mikhail Moiseyevich Botvinnik, Ph.D. was a Soviet and Russian International Grandmaster and three-time World Chess Champion. Working as an electrical engineer and computer scientist at the same time, he was one of the very few famous chess players who achieved distinction in another career while...

 
José Capablanca Anatoly Karpov Emanuel Lasker Emanuel Lasker
4 José Capablanca  Mikhail Botvinnik José Capablanca José Capablanca Alexander Alekhine
5 Emanuel Lasker
Emanuel Lasker
Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...

 
Bobby Fischer Bobby Fischer Alexander Alekhine Viktor Korchnoi
Viktor Korchnoi
Viktor Lvovich Korchnoi ; pronounced in the original Russian as "karch NOY"; Ви́ктор Льво́вич Корчно́й, born March 23, 1931 is a professional chess player, author and currently the oldest active grandmaster on the tournament circuit...

6 Alexander Alekhine
Alexander Alekhine
Alexander Alexandrovich Alekhine was the fourth World Chess Champion. He is often considered one of the greatest chess players ever.By the age of twenty-two, he was already among the strongest chess players in the world. During the 1920s, he won most of the tournaments in which he played...

 
Anatoly Karpov
Anatoly Karpov
Anatoly Yevgenyevich Karpov is a Russian chess grandmaster and former World Champion. He was the official world champion from 1975 to 1985 when he was defeated by Garry Kasparov. He played three matches against Kasparov for the title from 1986 to 1990, before becoming FIDE World Champion once...

 
Mikhail Botvinnik Mikhail Botvinnik Vasily Smyslov
Vasily Smyslov
Vasily Vasilyevich Smyslov was a Soviet and Russian chess grandmaster, and was World Chess Champion from 1957 to 1958. He was a Candidate for the World Chess Championship on eight occasions . Smyslov was twice equal first at the Soviet Championship , and his total of 17 Chess Olympiad medals won...


In a 2005 ChessBase
ChessBase
ChessBase GmbH is a German company that markets chess software, maintains a chess news site, and operates a server for online chess. Set up in 1998, it maintains and sells massive databases, containing most historic games, that permit analysis that had not been possible prior to computing...

 article, Sonas uses Chessmetrics to evaluate historical annual performance ratings and comes to the conclusion that Kasparov was dominant for the most years, followed closely by Karpov and Lasker.

Warriors of the Mind

In contrast to Elo and Sonas's systems, Raymond Keene
Raymond Keene
Raymond Dennis Keene OBE is an English chess Grandmaster, a FIDE International Arbiter, a chess organiser, and a journalist and author.p196 He won the British Chess Championship in 1971, and was the first player from England to earn a Grandmaster norm, in 1974. In 1976 he became the second...

 and Nathan Divinsky
Nathan Divinsky
Nathan Joseph Divinsky is a Canadian mathematician, chess master, and chess writer, who is also known for being the former husband of the 19th Prime Minister of Canada, Kim Campbell. Divinsky and Campbell were married from 1972 to 1983....

's book Warriors of the Mind 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. Considering games played between sixty-four of the strongest players in history, they come up with the following top ten:

These "Divinsky numbers" are not on the same scale as Elo ratings (the last person on the list, Johannes Zukertort
Johannes Zukertort
Johannes Hermann Zukertort was a leading chess master of German-Polish-Jewish origin. He was one of the leading world players for most of the 1870s and 1880s, and lost to Wilhelm Steinitz in the World Chess Championship 1886, which is generally seen as the first World Chess Championship match, he...

, has a Divinsky number of 873, which would be a beginner-level Elo rating). Keene and Divinsky's system has met with limited acceptance, and Warriors of the Mind has also been criticised for its arbitrary selection process and bias towards modern players.

Actual moves played compared with computer choices

A computer-based method of analyzing chess abilities across history came from Matej Guid and Ivan Bratko
Ivan Bratko
Dr. Ivan Bratko is a Slovene computer scientist.Bratko received his Ph.D. in 1978 from the University of Ljubljana. He is a D. Sc. Professor of Computer and Information Science at the Faculty of Computer and Information Science at the University of Ljubljana...

 from the Department of Computer and Information Science of University of Ljubljana
University of Ljubljana
The University of Ljubljana is the oldest and largest university in Slovenia. With 64,000 enrolled graduate and postgraduate students, it is among the largest universities in Europe.-Beginnings:...

, Slovenia
Slovenia
Slovenia , officially the Republic of Slovenia , is a country in Central and Southeastern Europe touching the Alps and bordering the Mediterranean. Slovenia borders Italy to the west, Croatia to the south and east, Hungary to the northeast, and Austria to the north, and also has a small portion of...

, in 2006. The basis for their evaluation was the difference between the position values resulting from the moves played by the human chess player and the moves chosen as best by a chess program, Crafty
Crafty
Crafty is a chess program written by UAB professor Dr. Robert Hyatt. It is directly derived from Cray Blitz, winner of the 1983 and 1986 World Computer Chess Championships....

. They also compared the average number of errors in the player's game. Opening moves were excluded, in an attempt to negate the progress in chess opening
Chess opening
A chess opening is the group of initial moves of a chess game. Recognized sequences of opening moves are referred to as openings as initiated by White or defenses, as created in reply by Black. There are many dozens of different openings, and hundreds of named variants. The Oxford Companion to...

 theory. According to their analysis, the leader was José Raúl Capablanca
José Raúl Capablanca
José Raúl Capablanca y Graupera was a Cuban chess player who was world chess champion from 1921 to 1927. One of the greatest players of all time, he was renowned for his exceptional endgame skill and speed of play...

, followed closely by Vladimir Kramnik
Vladimir Kramnik
Vladimir Borisovich Kramnik is a Russian chess grandmaster. He was the Classical World Chess Champion from 2000 to 2006, and the undisputed World Chess Champion from 2006 to 2007...

.

The "Classical" World Chess Championship matches were analyzed, and the results for the fourteen Classical World Champions were presented.

Players with fewest average errors:
The method received a number of criticisms, including: the study used a modified version of Crafty rather than the standard version; even the standard version of Crafty was not strong enough to evaluate the world champions' play; one of the modifications restricted the search depth to 12 half-moves, which is often insufficient. As of 2006 Crafty's Elo rating was 2657, below many historical top human players and several other computer programs.

A similar project was also conducted in 2007 using Rybka
Rybka
Rybka is a computer chess engine designed by International Master Vasik Rajlich. , Rybka is one of the top-rated engines on chess engine rating lists and has won many computer chess tournaments...

 2.3.2a and a modified version of Crafty
Crafty
Crafty is a chess program written by UAB professor Dr. Robert Hyatt. It is directly derived from Cray Blitz, winner of the 1983 and 1986 World Computer Chess Championships....

 20.14.

Analysis by Rybka 3 and comparisons with modern ratings http://web.zone.ee/chessanalysis/summary450.pdf

Subjective lists

A number of prominent players and writers have attempted to rank the greatest players. Generally these lists attempt to combine the two methods above—performance, and analysis of games.

Bobby Fischer (1964)

In 1964 Bobby Fischer
Bobby Fischer
Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...

 listed his top 10 in Chessworld magazine: Morphy
Paul Morphy
Paul Charles Morphy was an American chess player. He is considered to have been the greatest chess master of his era and an unofficial World Chess Champion. He was a chess prodigy...

, Staunton
Howard Staunton
Howard Staunton was an English chess master who is generally regarded as having been the world's strongest player from 1843 to 1851, largely as a result of his 1843 victory over Saint-Amant. He promoted a chess set of clearly distinguishable pieces of standardised shape—the Staunton pattern—that...

, Steinitz
Wilhelm Steinitz
Wilhelm Steinitz was an Austrian and then American chess player and the first undisputed world chess champion from 1886 to 1894. From the 1870s onwards, commentators have debated whether Steinitz was effectively the champion earlier...

, Tarrasch
Siegbert Tarrasch
Siegbert Tarrasch was one of the strongest chess players and most influential chess teachers of the late 19th century and early 20th century....

, Chigorin
Mikhail Chigorin
Mikhail Ivanovich Chigorin also was a leading Russian chess player...

, Alekhine
Alexander Alekhine
Alexander Alexandrovich Alekhine was the fourth World Chess Champion. He is often considered one of the greatest chess players ever.By the age of twenty-two, he was already among the strongest chess players in the world. During the 1920s, he won most of the tournaments in which he played...

, Capablanca
José Raúl Capablanca
José Raúl Capablanca y Graupera was a Cuban chess player who was world chess champion from 1921 to 1927. One of the greatest players of all time, he was renowned for his exceptional endgame skill and speed of play...

, Spassky
Boris Spassky
Boris Vasilievich Spassky is a Soviet-French chess grandmaster. He was the tenth World Chess Champion, holding the title from late 1969 to 1972...

, Tal
Mikhail Tal
Mikhail Tal was a Soviet–Latvian chess player, a Grandmaster, and the eighth World Chess Champion.Widely regarded as a creative genius, and the best attacking player of all time, he played a daring, combinatorial style. His play was known above all for improvisation and unpredictability....

, Reshevsky
Samuel Reshevsky
Samuel "Sammy" Herman Reshevsky was a famous chess prodigy and later a leading American chess Grandmaster...

.

Irving Chernev (1976)

In 1976 chess author Irving Chernev
Irving Chernev
Irving Chernev was a prolific Russian-American chess author. He was born in Priluki in the Russian Empire and emigrated to the United States in 1920. Chernev was a national master strength player, and was obsessed with chess...

 published the book The Golden Dozen, in which he ranked his all-time top twelve: 1. Capablanca
José Raúl Capablanca
José Raúl Capablanca y Graupera was a Cuban chess player who was world chess champion from 1921 to 1927. One of the greatest players of all time, he was renowned for his exceptional endgame skill and speed of play...

, 2. Alekhine
Alexander Alekhine
Alexander Alexandrovich Alekhine was the fourth World Chess Champion. He is often considered one of the greatest chess players ever.By the age of twenty-two, he was already among the strongest chess players in the world. During the 1920s, he won most of the tournaments in which he played...

, 3. Em. Lasker
Emanuel Lasker
Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...

, 4. Fischer
Bobby Fischer
Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...

, 5. Botvinnik
Mikhail Botvinnik
Mikhail Moiseyevich Botvinnik, Ph.D. was a Soviet and Russian International Grandmaster and three-time World Chess Champion. Working as an electrical engineer and computer scientist at the same time, he was one of the very few famous chess players who achieved distinction in another career while...

, 6. Petrosian
Tigran Petrosian
Tigran Vartanovich Petrosian was a Soviet-Armenian grandmaster, and World Chess Champion from 1963 to 1969. He was nicknamed "Iron Tigran" due to his playing style because of his almost impenetrable defence, which emphasised safety above all else...

, 7. Tal
Mikhail Tal
Mikhail Tal was a Soviet–Latvian chess player, a Grandmaster, and the eighth World Chess Champion.Widely regarded as a creative genius, and the best attacking player of all time, he played a daring, combinatorial style. His play was known above all for improvisation and unpredictability....

, 8. Smyslov
Vasily Smyslov
Vasily Vasilyevich Smyslov was a Soviet and Russian chess grandmaster, and was World Chess Champion from 1957 to 1958. He was a Candidate for the World Chess Championship on eight occasions . Smyslov was twice equal first at the Soviet Championship , and his total of 17 Chess Olympiad medals won...

, 9. Spassky
Boris Spassky
Boris Vasilievich Spassky is a Soviet-French chess grandmaster. He was the tenth World Chess Champion, holding the title from late 1969 to 1972...

, 10. Bronstein
David Bronstein
David Ionovich Bronstein was a Soviet chess grandmaster, who narrowly missed becoming World Chess Champion in 1951. Bronstein was described by his peers as a creative genius and master of tactics...

, 11. Rubinstein
Akiba Rubinstein
Akiba Kiwelowicz Rubinstein was a famous Polish chess Grandmaster at the beginning of the 20th century. He was scheduled to play a match with Emanuel Lasker for the world championship in 1914, but it was cancelled because of the outbreak of World War I...

, and 12. Nimzowitsch.

Viswanathan Anand (2008)

When interviewed shortly after Fischer's death, then current world champion Viswanathan Anand
Viswanathan Anand
V. Anand or Anand Viswanathan, usually referred as Viswanathan Anand, is an Indian chess Grandmaster, the current World Chess Champion, and currently second highest rated player in the world....

 ranked Kasparov first and Fischer second.

Earlier in 2000, when Karpov, Korchnoi and Kasparov were still active, Anand listed his top 10 as: Fischer
Bobby Fischer
Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...

, Morphy
Paul Morphy
Paul Charles Morphy was an American chess player. He is considered to have been the greatest chess master of his era and an unofficial World Chess Champion. He was a chess prodigy...

, Em. Lasker
Emanuel Lasker
Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...

, Capablanca
José Raúl Capablanca
José Raúl Capablanca y Graupera was a Cuban chess player who was world chess champion from 1921 to 1927. One of the greatest players of all time, he was renowned for his exceptional endgame skill and speed of play...

, Steinitz
Wilhelm Steinitz
Wilhelm Steinitz was an Austrian and then American chess player and the first undisputed world chess champion from 1886 to 1894. From the 1870s onwards, commentators have debated whether Steinitz was effectively the champion earlier...

, Tal
Mikhail Tal
Mikhail Tal was a Soviet–Latvian chess player, a Grandmaster, and the eighth World Chess Champion.Widely regarded as a creative genius, and the best attacking player of all time, he played a daring, combinatorial style. His play was known above all for improvisation and unpredictability....

, Korchnoi
Viktor Korchnoi
Viktor Lvovich Korchnoi ; pronounced in the original Russian as "karch NOY"; Ви́ктор Льво́вич Корчно́й, born March 23, 1931 is a professional chess player, author and currently the oldest active grandmaster on the tournament circuit...

, Keres
Paul Keres
Paul Keres , was an Estonian chess grandmaster, and a renowned chess writer. He was among the world's top players from the mid-1930s to the mid-1960s....

, Karpov
Anatoly Karpov
Anatoly Yevgenyevich Karpov is a Russian chess grandmaster and former World Champion. He was the official world champion from 1975 to 1985 when he was defeated by Garry Kasparov. He played three matches against Kasparov for the title from 1986 to 1990, before becoming FIDE World Champion once...

 and Kasparov
Garry Kasparov
Garry Kimovich Kasparov is a Russian chess grandmaster, a former World Chess Champion, writer, political activist, and one of the greatest chess players of all time....

.

Leonard Barden (2008)

In his 2008 obituary of Bobby Fischer, Leonard Barden
Leonard Barden
Leonard William Barden is an English chess master, columnist, author, and promoter. The son of a dustman, he was educated at Whitgift School, South Croydon, and Balliol College, Oxford, where he read Modern History. He learned to play chess at age 13 while in a school shelter during a German air...

 wrote that most experts ranked Kasparov as the greatest ever, with either Fischer or Karpov second.

Vladimir Kramnik (2011)

In an interview with Vladislav Tkachiev
Vladislav Tkachiev
-Biography:In 1982, he moved to Kazakhstan with his parents and learnt to play chess a year later. A winner of the Kazakhstani Youth Championship in 1985, he went on to represent Kazakhstan at the 1992 Chess Olympiad in Manila and was twice the national champion....

 for the website WhyChess, former World Champion Vladimir Kramnik
Vladimir Kramnik
Vladimir Borisovich Kramnik is a Russian chess grandmaster. He was the Classical World Chess Champion from 2000 to 2006, and the undisputed World Chess Champion from 2006 to 2007...

 stated that he considered Viswanathan Anand
Viswanathan Anand
V. Anand or Anand Viswanathan, usually referred as Viswanathan Anand, is an Indian chess Grandmaster, the current World Chess Champion, and currently second highest rated player in the world....

 as a colossal talent and one of the greatest in the whole history of chess.

World Champions by world title reigns

The number of world championship wins, or world championship reigns, can be considered as a guide to player greatness. 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
Emanuel Lasker
Emanuel Lasker
Emanuel Lasker was a German chess player, mathematician, and philosopher who was World Chess Champion for 27 years...

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Garry Kasparov
Garry Kasparov
Garry Kimovich Kasparov is a Russian chess grandmaster, a former World Chess Champion, writer, political activist, and one of the greatest chess players of all time....

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Anatoly Karpov
Anatoly Karpov
Anatoly Yevgenyevich Karpov is a Russian chess grandmaster and former World Champion. He was the official world champion from 1975 to 1985 when he was defeated by Garry Kasparov. He played three matches against Kasparov for the title from 1986 to 1990, before becoming FIDE World Champion once...

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Mikhail Botvinnik
Mikhail Botvinnik
Mikhail Moiseyevich Botvinnik, Ph.D. was a Soviet and Russian International Grandmaster and three-time World Chess Champion. Working as an electrical engineer and computer scientist at the same time, he was one of the very few famous chess players who achieved distinction in another career while...

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Alexander Alekhine
Alexander Alekhine
Alexander Alexandrovich Alekhine was the fourth World Chess Champion. He is often considered one of the greatest chess players ever.By the age of twenty-two, he was already among the strongest chess players in the world. During the 1920s, he won most of the tournaments in which he played...

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Wilhelm Steinitz
Wilhelm Steinitz
Wilhelm Steinitz was an Austrian and then American chess player and the first undisputed world chess champion from 1886 to 1894. From the 1870s onwards, commentators have debated whether Steinitz was effectively the champion earlier...

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Viswanathan Anand
Viswanathan Anand
V. Anand or Anand Viswanathan, usually referred as Viswanathan Anand, is an Indian chess Grandmaster, the current World Chess Champion, and currently second highest rated player in the world....

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Vladimir Kramnik
Vladimir Kramnik
Vladimir Borisovich Kramnik is a Russian chess grandmaster. He was the Classical World Chess Champion from 2000 to 2006, and the undisputed World Chess Champion from 2006 to 2007...

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Tigran Petrosian
Tigran Petrosian
Tigran Vartanovich Petrosian was a Soviet-Armenian grandmaster, and World Chess Champion from 1963 to 1969. He was nicknamed "Iron Tigran" due to his playing style because of his almost impenetrable defence, which emphasised safety above all else...

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José Raúl Capablanca
José Raúl Capablanca
José Raúl Capablanca y Graupera was a Cuban chess player who was world chess champion from 1921 to 1927. One of the greatest players of all time, he was renowned for his exceptional endgame skill and speed of play...

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Boris Spassky
Boris Spassky
Boris Vasilievich Spassky is a Soviet-French chess grandmaster. He was the tenth World Chess Champion, holding the title from late 1969 to 1972...

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Bobby Fischer
Bobby Fischer
Robert James "Bobby" Fischer was an American chess Grandmaster and the 11th World Chess Champion. He is widely considered one of the greatest chess players of all time. Fischer was also a best-selling chess author...

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Max Euwe
Max Euwe
Machgielis Euwe was a Dutch chess Grandmaster, mathematician, and author. He was the fifth player to become World Chess Champion . Euwe also served as President of FIDE, the World Chess Federation, from 1970 to 1978.- Early years :Euwe was born in Watergraafsmeer, near Amsterdam...

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Vasily Smyslov
Vasily Smyslov
Vasily Vasilyevich Smyslov was a Soviet and Russian chess grandmaster, and was World Chess Champion from 1957 to 1958. He was a Candidate for the World Chess Championship on eight occasions . Smyslov was twice equal first at the Soviet Championship , and his total of 17 Chess Olympiad medals won...

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Mikhail Tal
Mikhail Tal
Mikhail Tal was a Soviet–Latvian chess player, a Grandmaster, and the eighth World Chess Champion.Widely regarded as a creative genius, and the best attacking player of all time, he played a daring, combinatorial style. His play was known above all for improvisation and unpredictability....

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Ruslan Ponomariov
Ruslan Ponomariov
Ruslan Olegovich Ponomariov is a Ukrainian chess player and former FIDE World Champion.-Early career:Ponomariov was born in Horlivka in Ukraine. In 1994 he placed third in the World Under-12 Championship at the age of ten. In 1996 he won the European Under-18 Championship at the age of just...

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Alexander Khalifman
Alexander Khalifman
Alexander Valeryevich Khalifman is a Soviet and Russian chess Grandmaster of Jewish descent; he is also a former FIDE champion.When Khalifman was 6 years old, he was taught chess by his father....

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Rustam Kasimdzhanov
Rustam Kasimdzhanov
Rustam Kasimdzhanov is an Uzbekistani chess Grandmaster, best known for winning the FIDE World Chess Championship 2004. He was born in Tashkent, in the former Uzbek Soviet Socialist Republic...

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Veselin Topalov
Veselin Topalov
Veselin Aleksandrov Topalov is a Bulgarian chess grandmaster. He currently has the sixth highest rating in the world, and was the challenger facing world champion Viswanathan Anand in the World Chess Championship 2010, losing the match 6½–5½....

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