The way I look at it, World Champions that all later players copied can be said to have discovered (“discovery”) more of the truth about chess than anyone else. The most dominant Champions of their time who meet this criteria, in order of discovery+dominance, seem to be:
  1. Morphy
  2. Fischer
  3. Kasparov
  4. Capablanca
The guys below are harder to rate, but would be how I would round out the top 8.
  1. Kramnik
  2. Alekhine
  3. Lasker
  4. Smyslov

Who else should be in the top ten?

There is some interesting computer analysis of players here on Wikipedia, and some interesting opinions here on Quora.

Karpov and Botvinnik benefited from what some have described as bordering on cheating, due to Soviet control of players and rules, and are not considered by me for that reason. They are likely top ten otherwise.
Other World Champions and greats of discovery include Tal and Steinitz. I would also consider the three strongest players never to be World Champion, whom I rate as Korchnoi, Keres, and Mir Sultan Khan. Besides known problems for Korchnoi (being a Soviet defector made him a Soviet target) and Keres (war in his homeland keeping him from a World Championship bid near his peak), their results likely suffered more than is known under the Soviets.

Who is Mir Sultan Khan?

He was an incredible natural player with virtually no experience against other top players, yet with a little coaching he beat Capablanca at near his peak. Here’s an interesting article about Mir Sultan Khan.
When Google was still a young search engine, they bought the DMOZ directory of “best websites” and included those sites in their search results (sometimes). At that time I was the editor of the Chess section, and that is why you’ll see Mir Sultan Khan on the “World Champions” list — purely my attempt to gain him some recognition.

Comparing Chess Computers to Humans

For some info on greatest humans and computers of all time, see:

When I found this research on ply depth vs. rating strength, I created the chart below.  This assumes an app running on a top 2015/2016 phone, or a typical desktop computer from 2013 or so:



About my Chess experience

I used to teach chess. I was never that good, but I had some good results, the best being a performance rating (how well you did in a single tournament) of USCF 2350 for a club tournament in St. Paul in the mid-1980’s. I also finished in the money in the 1982 U.S. Open and the New York Open as a lower-rated player.
I also successfully predicted when Kasparov would lose the world championship. A bit of explanation is necessary:
I was DMOZ editor of the Chess People section when Kasparov lost the title to Kramnik, and I “publicly” predicted the loss during the match by listing his name first in the DMOZ links to the Championship match. In my opinion, Kramnik had “discovered” things about chess no one before him had understood as well, Kasparov couldn’t keep up with this advance, and it was obvious (to me) from reviewing the games.
The players favored to be finish 1st and 2nd in a tournament earn those spots by how well they play against the entire field, not against each other. So losing a game in a round doesn’t automatically advance your opponent; they could be losing to someone else at the same time.
But in a match, every game lost is a win for your opponent. So match strategy, generically, is to try to win with White and Draw with black. I felt that Kasparov was the greatest living practitioner of winning with White, and Kramnik was the greatest at drawing with Black. So games with Kasparov as White and Kramnik as Black seemed to me to be practically a clash of  ideologies. And Kasparov didn’t do well at all in those situations, it seemed to me, besides being behind on points after the second game.
So, Kramnik better understood the “margin of a draw” than anyone before him. For example, at one point, both players commented after a drawn game with Kasparov saying there seemed to be chances for a win, and Kramnik saying there were zero chances.