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My question is and I would like to know, Chess grandmasters Bobby Fischer[AMERICA}, Boris Spassky[RUSSIA], Anatoly Karpov[RUSSIA], and Garry Kasparov[Russia]played against one another in many tournaments in Big cities. How their ratings or rankings were determined? Are the only basis their past performances? OR those who are engaged in Bettings play their roles? please take a look at the list of chess grandmasters who are famous at the international level from 1970- 1982.

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Are the only basis their past performances?

Yes

OR those who are engaged in Bettings play their roles?

None whatsoever.

According to the Olimpbase website:

Back in 1942 the USCF used its own chess rating system (Harkness) to rank domestic players, while German Chess Federation did the same in 1948 (Ingo system). In 1959 one Arpad Elo was nominated chairman of USCF rating committee and already in 1961 he published the very first list of top US players in "Chess Life". Even though prof. Elo used to publish his own, unofficial International Rating Lists it was 1970 FIDE Congress held in Siegen, Germany that adopted the Elo system for official use. The first official list was to be published on 1st July 1971 and it was approved on consecutive FIDE congress in Vancouver, Canada, in August 1971.

Elo's unofficial international ratings dating back to 1967 are available on the Olimpbase site as are FIDE ratings from 1971 to 2001. From 2001 the FIDE ratings lists are available on the FIDE website.

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