No mention is given that Kasparov played what is known in the whole professional chess world as --  "The game of the Millenia" vs Topalov.  Which leaves Fischer's game vs Byrne in the dust.

#1: Carlsen - He never ceases to suprise me by grinding out wins out of equal positions.

#2: Kasparov - A brilliant attacker, an amazing calculator, I was just going over one of his games today, thinking each move "Wow! how did he manage to see all this???"

#3: Karpov - his intuition is so precise, great prophylaxis as well.

#4 Fischer - Not far behind Karpov, but his career was too short to say that he was better.

if not Fischer, then Carlson

One, out of other, things Carlson is missing in his history to be even considered among the greatest is achievements.

Kasparov trumps the list of achievements in his chess career.

Kasparov made the tiniest logical or natural move seem like there were major blunders in many many of his games when you see how he conjured major punishment on his opponents.

No one has had better opening preparation than the Legend himself.

The list of players he has trounced is a list of who's who in chess history.

His tournament victories, his years as champion....   Carlsen is not in his league at all. 

Also, Kasparov took Carlsen under his wing for quite some time and taught him and showed him a lot, even letting Carlsen, to some extent, into his very very secret vault of opening ideas and preparations.

John Wayne.     ...?

No. Borislav Ivanov, sadly.........

NOBODY can handle the Borislav when he gets goin'

The Duke can handle anybody, anywhere....?  I think he defeated Boris Ivanoclit....or whoever...at the Alamo.   

Is he related to Ivana Humpalot from Austin Powers? She was the Russian chessplayer he was playing in the movie. I think she was licking the pieces or something. It made it hard for him to focus, giving her an advantage.