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

Just imagine Fischer training with today's computers!

Its not even possible to say that one person has more moves that agree with the computer so they are better.

Is it easier to play computer moves against worse players then better ones.

I think he'd have a very close match with Carlsen in that case.  Maybe he'd even win though Carlsen's style and skillset isn't an easy one to deal with. 

In terms of greatness no one is.

Training methods and materials have advanced a great deal since Fischer's day. 

...thanks in large part to Fischer ;).  Fischer's example of preparation and the emergence of chess engines are the 2 factors that made the larger set of "super GMs" possible.  One was going to happen regardless of players' input.

I would say that chess did not cause Fischer's mental illness.  He was probably born with Asperger's Syndrome, likely developed a personality disorder of some sort, and eventually because bipolar.

If Fischer lived in the 19th century, he'd maybe have been an outlaw chewing tobacco and spitting on Dogs heads. Chess players are a tough crowd. Even Mikhail Tal was hopeless at everyday tasks like making a hot water bottle.

Anyone with past contact with asperger sufferers will see the link. Asperger, with a bunch of help from Fischer, made Fischer what he was.

Playing against the smaller set of top players is actually how Carlsen maintains and slowly increases his rating.  He and most top players now cherry-pick their opposition to avoid any changes of dropping significant ratings points to a 2600-2700 player.

Nakamura said himself that he avoids the US championship to preserve his rating.  As for Nakamura being better than Fischer, Nakamura himself says "no" emphatically to that one, so... ;)

Even tactics trainer teaches the same lesson.  People with 2000+ TT ratings always complain when that everlasting bug presents them with <2000 problems and they inevitably miss a few and drop like a rock.  It's easier to maintain and increase TT ratings by only accepting problems that are higher rated than your current position.

The gap vs. peers is the best measure.  Carlsen would have to be rated 2950 to enjoy the same gap Fischer had.

You don't get a higher rating simply by playing top opponents, the rating system is "fair" except when you play much weaker opponents, then you can "cheat" it. If Carlsen wanted to cherry pick fields to gain rating he would only play much weaker opponents. Against all players more than 400 Elo below him he would still get 0.8 for winning, so playing only 2100s-2300s would be the way to gain Elo points. When Vallejo wanted to reach 2700 some years ago he played a few events against quite weak opposition and won more or less all his games and passed 2700.

"The gap vs. peers is the best measure.  Carlsen would have to be rated 2950 to enjoy the same gap Fischer had"

But is gap vs peers on one list or for years what matters most? Fischer had 30-70 points, and then on one list, published the month before he retired, he had 125 points. Is consistently being 70-80 points ahead of a player like Karpov (2nd or 3rd greatest ever to many) for many years worse than being 30-70 points ahead of Spassky and then once being 125 points ahead. It depends on how one measures. If gap to #2 is the best measure Topalov would be greater than Anand and Kramnik. 

That's an interesting supposition, but since I have the actual behavior of almost all the top players on my side of the equation, I'll stick with mine.

As for being "fair"...ratings are easy to manipulate.  Take two players of exactly equal strength, say 1500, and start chess.com accouts for them both, then have the first one play 1300s to start off with, and have the other one play 1700s.  When you see how incredibly long it will take the former to reach the same rating as the latter achieves almost right away, maybe you'll see how the system is only fair in aggregate, not in individual cases.

"I have the actual behavior of almost all the top players on my side of the equation"

I think they want to play top events because that is where the challenge lies. They hardly avoid playing some open against 2500s instead of Norway chess because they want to protect their rating, I think it simply is because the best players want to play the toughest events and prove themselves there.

It can never be proven but I believe Robert James Fischer (in a match) not just a game would beat anyone in history if he was motivated with enough money and fame. He played to win and could pull rabbits from his hat right before your eyes. I knew him during his Pasadena days at the Central Library at 285 East Walnut. He didn't talk much, wore sunglasses, a slouch hat, read chess books and Issac Kashdan's column in the LA Times. He played to win not to draw. A lot of today's knowledge was the body of work he accomplished! I'd put him roughly very close to Kasparov. Carlsen ain't there yet but still could become the best ever. He's not adding much theory or pazazz to the game... as he grinds them out waiting it seems for his opponent to make a mistake. I'm 70 now I've seen a lot and still follow the GM's and their games.

"For me right now I think being the world number one is a bigger deal than being the world champion because I think it shows better who plays the best chess. That sounds self-serving but I think it’s also right."  - Magnus Carlsen

Maintaining his rating is more important to Carlsen than winning the WC.  It's the same for most players at the top.  Once you claw your way up there over many years of concentrated effort, it is entirely natural that the rating number becomes something protected at all costs.

These players do not play for the challenge, or love of the game alone.  Let's face it, past a certain point, preparation is not challenging nor fun, it is drudge work.  What drives these players past 2500-2700 is the need to be the best, and their rating is the primary measuring stick.  Chess is just their chosen venue.

I think these results weigh in Fischer's favor versus Karpov.

He was =5-6th in an Interzonal at the age of 15.  He never had the support that the Soviet chess machine gave their top-flight grandmasters.

At age 18, Fischer won the 1962 Stockholm Interzonal (17.5-4.5), 1.5 points ahead of Petrosian and Geller.  Petrosian would become the world champion that cycle.

Fischer won the 1970 Palma de Mallorca Interzonal (18.5-4.5; 0.804 winning %age) by 3.5 points over Geller, Hubner, and Larsen.

By way of comparison, Karpov (age 22) tied for first with Korchnoi (age 42, in the 1973 Leningrad Interzonal (13.5-3.5; 0.794), 1 point ahead of 45-year old Robert Byrne.

Whereas in 1971, Fischer went 6-0 over Taimanov, 6-0 over Larsen, and 6.5-2.5 over former WC Petrosian, Karpov went 5.5-2.5 over Polugaevsky, 7-4 over former WC Spassky; 12.5-11.5 over Korchnoi.

It would be hard to argue that the level of competition in the 1970 and 1973 Interzonals, or in the Candidate's matches, was greatly dissimilar.  Indeed, in 1973, there were two Interzonals (the other in Petropolis), so one might argue that Fischer faced more, stronger, players in 1970, than Karpov in 1973.  Just the same, Fischer's 1970-1972 results against the top players of that cycle, certainly seem better tha Karpov's just three years later.

Presuasively argued, @JaimeD.  Thanks.

Lots better than the many, many, hairsplitting assertions based on rating points, and ad nauseum stats.

Yes, GM's are (in general) stronger today than in the past.  But So What ?  

JGambit, you'll have to explain why you believe the past players were weaker than now. I don't know if we have any objective data to make any claims available on that, do you know of any? I believe a computer analysis of players games is a great indicator of who played the best chess.

Indeed. It doesn't diminish anything.

It's the search for the holy grail of chess.