Who is the greatest chess player of all time ?? Bobby Fischer ??

What do you mean by it isn't easy to show the same dominance [..] if you don't have the same opportunities as your competitors? Are you suggesting Carlsen can't dominate his contemporaries to the extent Fischer did because they can use computers for preparation? Don't forget Carlsen has access to computers too! Same goes for Kasparov: a 20-21 years old Garry could do no better than 7-4 against a 52 years old Korchnoi and 8.5-4.5 against a 63(!) years old Smyslov. Kasparov's supporters usually argue that the theory advanced significantly in the 12 years Fischer had been away from the board (which should explain the close matches in the post Fischer era), forgetting that Kasparov's opponents weren't the only ones to benefit from the theory advancements. 

In fact if there's one name in this list who was at the greatest disadvantage compared to his contemporaries, that was Fischer. No he didn't do it all by himself (as often stated), but the help he received during his formative years - both in terms of financial support and coaching - was nowhere near to what top soviet players were receiving. 

As far as I understand (please correct me if I'm wrong), top chess engines have clearly surpassed humans tactically, but when it comes to positional understanding top players still have the upper hand. (if I'm not mistaken there was an article recently to that effect on chess.com). The day chess engines show clear superiority over top humans both tactically and strategically, then I'd like to have another look at caps scores. Another problem with these computer based comparisons is the selection of games subjected to analysis. Do they compare players at the same age, at their peak only (I can see disagreements over one player's peak years), do they submit all available games for analysis?

Finally, it's entirely possible that Carlsen or Kasparov or both were objectively stronger at their peak than Fischer, but there's still no absolute certainty how such a match would have turned out. Neither players faced the other (excluding the 3 blitz/rapid games between Kasparov and a 13 years old Carlsen), and the human factor has to be considered. Last but not least, the rating differences between these 2 and Fischer were 66 and 97 points respectively. We have seen surprising match results at similar rating gaps.

https://www.chess.com/article/view/should-we-trust-computers

Exactly, thanks! This is the article I was referring to.

If someone plays better, they play better.  Maybe if other players had better tools and education they would have been better.  We don't know.  We only know how strong they actually were.  On that list, Magnus is first, followed by Kramnik or Kasparov.  Maybe Fischer would be stronger with computers.  Fact is, he wasn't as strong as Magnus based on move accuracy.  Tools are just as much a part of playing strength as anything else.  Maybe Magnus is only stronger because of computers, but he is stronger.

”What do you mean by it isn't easy to show the same dominance [..] if you don't have the same opportunities as your competitors?”

Carlsen has a computer, his competitors have computers. Carlsen is great because he is better than his competitors. The pre-computer players didn’t have computers, their competitors didn’t have computers, the best players were great because they were better than their competitors.

If suggesting that Carlsen wouldn’t be great if he didn’t have a computer means that he wouldn’t be great if he alone didn’t have a computer that is one thing. He certainly would be less great compared to competitors that had advantages he didn’t have. If the suggestion is that Carlsen would be less great if all modern players were without computers, this means that they are supposed to be less engine dependant than he is, and I don’t think that is the case. I think Carlsen relies much less on engine prep than on outplaying opponents from close to equal positions thanks to simply being the better ”human” player.

”Don't forget Carlsen has access to computers too! Same goes for Kasparov: a 20-21 years old Garry could do no better than 7-4 against a 52 years old Korchnoi and 8.5-4.5 against a 63(!) years old Smyslov”

Well, that was good enough :-) Korchnoi had beaten Portisch (World #2 in 1981) 6-3 while Smyslov had beaten Hubner (World #5) and Ribli (top ten in 1983) in matches in the same Candidates. I don’t know if computers had much to do with Kasparov’s results in the early 1980s, but not much to frown about beating Korchnoi and Smyslov easily. Kasparov was still quite young and some 150 Elo from his peak.

I would have agreed with this comment a couple of months ago.  Although, I believe that AlphaZero does both better than any human or computer that ever existed.  So, that day has finally come.  Too bad chess.com can't use AlphaZero for it's CAPS scores.  

Only according to Stockfish, which is very tactics based.   I'd love to see AlphaZero's assessment of their CAPS scores.  

Don't get me wrong, it was even better than "good enough". 

But there's a difference between good enough and unbelievable. 

Also I don't think there's any evidence to suggest that Smyslov at 63 (2600) was stronger than Petrosian at 42 (2640), or that Korchnoi at 52 (2610) played better than Larsen at 36 (2660). Heck, even Taimanov had a higher rating in 1971 than any of the 3 players Kasparov faced in the candidates matches.

As for world championship matches, Kasparov never defeated anyone by a 12.5-7.5 margin, unless you consider the match with Short a true WC match (in 1993, Short was 2665 and #12 in the world).

I can go on but no need to labor the point: as far as peak strength is concerned there's a case to be made for both Kasparov and Carlsen (though I believe the jury is still out), but when it comes to dominance, nobody can touch Fischer. 

"I don't think there's any evidence to suggest that Smyslov at 63 (2600) was stronger than Petrosian at 42 (2640), or that Korchnoi at 52 (2610) played better than Larsen at 36 (2660). Heck, even Taimanov had a higher rating in 1971 than any of the 3 players Kasparov faced in the candidates matches"

So how did Fischer do in his first two candidates compared to how Kasparov did in his first? :-) 

"As for world championship matches, Kasparov never defeated anyone by a 12.5-7.5 margin, unless you consider the match with Short a true WC match"

Why wouldn't it be considered a true WC match? Short qualified by winning the FIDE Candidates where he won a match against Karpov. Then it's difficult to compare beating Karpov in matches with beating Spassky. And is for example Alekhine's beating Bogo 15.5-9.5 more impressive than his beating Capablanca 18.5-15.5 just because he scored a bigger plus against Bogo? Fischer won 12.5-8.5 against Spassky, but Kasparov's beating Short 12.5-7.5 doesn't have to be the more impressive result just because he won easier.

Define "time". Then define "all time". Do you include future in "all time"? Do you include engines in the set of chess players? Please be more specific.

I was tempted to say "let's not change the subject" but fine, let's have that

First of all, Fischer's allegations of prearrangement in Curacao (unlike other bizarre allegations he made over the years) are now considered factual even by former soviet players. 

Second, both 1959 and 1962 candidates were round robin tournaments, not knock out matches.

Third, you have to consider the level of opposition. If you think Beliavsky and Korchnoi in 1983 were stronger than Tal, Keres and Petrosian in 1959 and 1962 respectively, go ahead and state your case. But I hope we can at least agree that Smyslov was a more formidable opponent at 38 than 63.

Collusion, tournament format and opposition aside, it's probably fair to say that at 17-19 Fischer was less dominant - on those occasions at least - than Kasparov at 20-21 (after all, he started playing chess a bit later than Kasparov and had far less support). The reason I stated "on those occasions at least" is because Fischer won the 1962 and 1970 Interzonals by larger margins than Kasparov (who actually won a split interzonal without having to deal with Ribli and Smyslov). 

Why wouldn't it be considered a true WC match?

It's not a question of true/untrue, it's one of significance/relevance. Fischer scored 12.5-7.5 against the reigning world champion (#2 rating wise). Kasparov won by the same margin against a challenger who was #12. When pitted against #2, Kasparov never won by more than 2 points.

"Fischer's allegations of prearrangement in Curacao (unlike other bizarre allegations he made over the years) are now considered factual even by former soviet players"

Fischer lost lost 3 of his first 5 games, and 5 of his first 13 games. I don't think anyone seriously thinks some short draws between Keres and Petrosian was the cause of that. He just played far from well enough and finished three points from a top three spot. Petrosian didn't lose any games in 27 rounds. After 21 rounds Fischer had lost 7 games, Geller and Keres taken together lost one game in these 21 rounds. 

"both 1959 and 1962 candidates were round robin tournaments, not knock out matches"

That's true, I have no idea how that affected the outcome though. Fischer scored a minus in his four games against Korchnoi in Curacao, but finished 0.5 ahead in the tournament (not a big margin if Fischer is to be believed that Korchnoi threw lots of games in the event...).

"If you think Beliavsky and Korchnoi in 1983 were stronger than Tal, Keres and Petrosian in 1959 and 1962 respectively, go ahead and state your case"

That they certainly weren't (even if Korchnoi isn't to be underestimated, he was #3 as late as in 1984 and #5 in 1989, while Beliavsky was #3 in 1985), but then Kasparov won against them with a big margin instead of finishing far behind them.

"Why wouldn't it be considered a true WC match?

It's not a question of true/untrue, it's one of significance/relevance. Fischer scored 12.5-7.5 against the reigning world champion (#2 rating wise). Kasparov won by the same margin against a challenger who was #12. When pitted against #2, Kasparov never won by more than 2 points"

Fischer's 12.5-8.5 against Spassky is difficult to compare with for example Kasparov's match wins against Karpov. No one considers Spassky to be in the same league as Karpov. Tal scored the same 12.5-8.5 against a reigning World Champion as Fischer did, but I don't think he is anywhere close as great as Kasparov.

Fischer-Spassky, 12.5 - 8.5 yes, but, if you consider the 1st game, Bobby's 29th move Bxh2, blunder or some way to create complications, it doesn't matter give it to Borris. How about game 2 though? Forfeit. could have been 13.5-8.5 or 12.5 - 9.5, either way we'll never know. This has probably been mentioned but, how about the 6 - 0 whitewashing of Taimanov and Larson in the candidates and a win in the first game with Petrosian, then a loss, 3 draws and four straight wins? A couple of famous Grandmasters once said, "Even when your ahead of him you know you're going to lose" and "He can toss the pieces up in the air and they land on the right squares". Things change, technology changes, but we can only compare Bobby to his contemporaries.  

Difficult, but still somewhat relevant.

Look, we can't have it both ways. Either ratings aren't stable over time (in which case arguments like "Carlsen and Kasparov are stronger than Fischer because they had higher ratings" can be called into question), or they are stable over time, in which case comparisons based on ratings and performance ratings are to a certain extent possible.

Between 1985-1990 (the era of Kasparov-Karpov titanic struggles) Karpov's rating fluctuated between 2700 and 2755, some 40-95 rating points higher than Spassky's 1972 rating. Now I know Spassky has been the target of a variety of insults over the years (mainly because of catering to Fischer's demands and "handing over" the crown), but speaking strictly in terms of performance, I doubt you'd refer to somebody within 100 rating points of yourself as being in a different league. 

Finally, for those interested in that kind of stuff, here's a summary of performance ratings for the WC matches of 1972, 1985, 1986, 1987, and 1990.

And for reference also the candidate matches that lead to these:

Looking at these, it's becoming clear that the old saying "Fischer was more dominant because he faced weaker opposition" is at best a half truth. It's true when referring to the one and only WC match he played, and even then his performance rating was still higher or same with Kasparov's in any of the 4 K-K matches. But in the candidate matches the picture is clear: not only was Fischer's opposition somewhat stronger, but his performance was well beyond what would have been expected based on the rating difference.

I'd say the brilliant sacrifices and intuitive combinations by Mikhail Tal make him the best. He treated chess as an art, not a science.

Especially since Short wasn't even close to Spassky's level.  Also, Fischer forfeited one of his games vs Spassky, so technically it was 12.5-7.5.   

I think people often value achievements based on which players they like. In tennis few would say that Player X was the greatest, among other things because he scored 6-0 6-0 6-0 in the quarter final, even though he only won a Grand Slam event once. If Player Y won Wimbledon eight times, even if he did it by scoring 3-2 in sets in every match he played, I think almost everyone would consider Player Y to be greater. If Player X was comparatively better than his competitors the one time he won would be considered rather irrelevant. 

In chess I think it is Fischer that has caused many to evaluate greatness not in how many top events the players won, but in distance to #2 at one point in time. This measure makes Topalov greater than Anand and Kramnik, and Morozevich (who was #1 one day on the live rating list...) greater than the Korchnoi of the 1970s, who lost two matches with the smallest possible margin against Karpov. Fischer is of course a case that is different compared to many others, but it is rare to see other players evaluated with the same measures. 

Carlsen has probably caused many to evaluate greatness as having the highest rating, and that is even worse... Having a higher rating today than some player from the past doesn’t say much about greatness in itself. Radjabov may have reached a higher rating than Fischer and Karpov, but his achievements are not anywhere near to make him comparable to them with regards to greatness.

Who the heck is Radjabov?   Isn't that the guy that beat Kasparov once, with a knight sac?   He isn't even in the top 500 of all-time.  You have a good point with the tennis comparison though.  I don't hear anyone saying that Bjorn Borg was better than Federer, Sampras, Nadal or Kjokavic, even though Borg dominated for a short time.