user-1: The arrival of strong chess engines as Stockfish, Houdini or Rybka allow top players to deeply prepare lines in openings or to study better endgames.
I would expect a rating increase of top players. However, Kasparov's top score from 1999 is still the second best rating score of all time and Karpov and Fischer are still in the top twenty historical rated players.

Source: Wikipedia
If those engines have a 3600 Elo, shouldn't top players have profited from it to leave Kasparov's 2851 score in 1999 far away?
And shouldn't more than 18 players surpass Fischer's 2785 in 1972?

user20776: People are not computers.  They learn and memorize as much as possible but they can not do as much as a computer can nor as fast.  The top players are doing everything they can but they can not do it all like the computer does. 

user12873: A few things:
1) Ratings overall tend to rise due to inflation of more players entering the pool, rather than the average playing strength of players increasing. If everyone becomes better by some factor due to engines, why would top players' ratings increase? They're now playing opponents who have also gotten stronger by roughly the same amount.
2) Kasparov, Karpov, and Fischer are anomalies of a sort (Kasparov especially), considering they are all world champions. And still, they only occupy 3/20 spots on the list - all other ratings were achieved in the modern era.
3) Engines are making people stronger, but not to a huge extent. People aren't able to extract all the strength out of an engine, we just see the moves it recommends.
In summary, engines make people somewhat stronger, but in any case this wouldn't be reflected in the ratings. The pool of players is a closed system: everyone getting stronger doesn't benefit one player/group of players in particular. The way the ratings rise (at all levels) is from more people joining the system.
EDIT: one way you would see some increase purely due to engines is in a hypothetical scenario where we played against another group of people who didn't have access to our engines.
EDIT 2: Point 1 may not be entirely correct (see the discussion in the comments).

user4418: 
If those engines have a 3600 Elo, shouldn't top players have profited from it to leave Kasparov's 2851 score in 1999 far away?

No. The main effect of engines and also the internet has been to democratise chess. The top players have always had access to top level evaluation and knowledge. For lower level players that kind of knowledge, analysis, position evaluation, endgame knowledge was very difficult to acquire. 
This is important because higher level players gain rating points by beating lower level players. If those lower level players are harder to beat because of increased access to the analysis and knowledge that engines and the internet provide then it actually becomes harder to reach higher levels as measured by rating.

user17330: The question is apparently based on a misunderstanding of how ELO ratings work. There is absolutely no mechanism by which the overall increase in players' strength would lead to increase in their ELO. The actual value of the ELO rating bears no meaning; nor does the comparison of ELO at distant times. The only thing that has direct relevance is the difference in simultaneous rating between players. 
If tomorrow FIDE decided to add a constant, say, 500 points, to every player's rating, essentially nothing would change - the outcomes of games would lead to the same increments in ratings, so the rating dynamics would be the same, just at +500 points level. And the computers will provide no basepoint - their ELO is relative to human players, so they will play at 3600 rather than 3100. 
The same applies if such a constant were somehow added or subtracted gradually due to natural processes - e. g., expansion of rated players' base, players becoming inactive with higher rating than they started with, etc. And this, apparently, did happen as we witnessed rating inflation until recently. 
Similarly, if all the players suddenly, or gradually, start playing stronger, without a change of their relative strength, there is no reason to expect a change in rating dynamics. 

user19877: I think they certainly have increased their ELO, but more importantly, their overall chess strength. ELO is only a rating relative to others in the pool so it may tend to go up more slowly if everyone in the pool gets better, which they have collectively.
First, you need to take an average of the top players, rather than look at just two incredibly special players, Kasparov, and Carlsen, and their peak ratings. Fischer was a total anomaly for his time, and again, you cannot base a lot on one person. Humans probably have a limit mentally much the way runners will eventually hit a speed wall that they cannot break. It is the Bell Curve in action: Easy to make progress in the middle, but harder on the end.
ChessBase, and the first strong engine, KnightStalker (aka Fritz 1.0, renamed at version 2.0) came out in 1990, and the Internet was still in its infancy. In January of 1990, there were only two players over 2700, Karpov at 2730, and Kasparov at 2800. Today, there are 37 players over 2700, and of those, three are over 2800.
I have been playing for a long time, and anyone, who knows my handle, has seen me watching relays of the top tournaments on ICC for more than 20 years, and I can say that it is not just inflation from having actually watched the level of play improve over the years. Players at the Master-level, including even normal Masters, are MUCH better now due to the tools available today than the tools available when I first became a Master.
When I first started playing, all we had was books, and a local club. Today, I can logon virtually any day, and play a GM. I was also a ranked tennis player as a teenager, and I can tell you from that experience, playing better competition makes you better, so being able to logon and play stronger players than ever has increased the overall level of play. In addition, we now have ChessBase, and a database of about 8.3M games that can be sorted efficiently and studied. We also have engines, as noted in the question, and they certainly have also added to our chess knowledge, and fundamentally changed how the top players prepare. Lastly, I mentioned books, and as an avid collector (I had 1800 at my peak), I can tell you that even the quality of the material in books is on another level since when I started.
I cannot tell you what proportion of all these advances have played toward X-number of rating points increase, but I can tell you that without a doubt, they all have lead to players at the top levels, and even down some, being much better overall.

-1: <p>The arrival of strong chess engines as Stockfish, Houdini or Rybka allow top players to deeply prepare lines in openings or to study better endgames.</p>

<p>I would expect a rating increase of top players. However, Kasparov's top score from 1999 is still the second best rating score of all time and Karpov and Fischer are still in the top twenty historical rated players.</p>

<p><a href="https://i.stack.imgur.com/uPLV3.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/uPLV3.png" alt="Enter image description here"></a></p>

<p>Source: <a href="https://en.wikipedia.org/wiki/Comparison_of_top_chess_players_throughout_history" rel="nofollow noreferrer">Wikipedia</a></p>

<p>If <a href="http://www.computerchess.org.uk/ccrl/404/" rel="nofollow noreferrer">those engines have a 3600 Elo</a>, shouldn't top players have profited from it to leave Kasparov's 2851 score in 1999 far away?</p>

<p>And shouldn't more than 18 players surpass Fischer's 2785 in 1972?</p>
 20776: <p>People are not computers.  They learn and memorize as much as possible but they can not do as much as a computer can nor as fast.  The top players are doing everything they can but they can not do it all like the computer does. </p>
 12873: <p>A few things:</p>

<p>1) Ratings overall tend to rise due to inflation of more players entering the pool, rather than the average playing strength of players increasing. If everyone becomes better by some factor due to engines, why would top players' ratings increase? They're now playing opponents who have also gotten stronger by roughly the same amount.</p>

<p>2) Kasparov, Karpov, and Fischer are anomalies of a sort (Kasparov especially), considering they are all world champions. And still, they only occupy 3/20 spots on the list - all other ratings were achieved in the modern era.</p>

<p>3) Engines are making people stronger, but not to a huge extent. People aren't able to extract all the strength out of an engine, we just see the moves it recommends.</p>

<p>In summary, engines make people somewhat stronger, but in any case this wouldn't be reflected in the ratings. The pool of players is a closed system: everyone getting stronger doesn't benefit one player/group of players in particular. The way the ratings rise (at all levels) is from more people joining the system.</p>

<p>EDIT: one way you would see some increase purely due to engines is in a hypothetical scenario where we played against another group of people who didn't have access to our engines.</p>

<p>EDIT 2: Point 1 may not be entirely correct (see the discussion in the comments).</p>
 4418: <blockquote>
  <p>If those engines have a 3600 Elo, shouldn't top players have profited from it to leave Kasparov's 2851 score in 1999 far away?</p>
</blockquote>

<p>No. The main effect of engines and also the internet has been to democratise chess. The top players have always had access to top level evaluation and knowledge. For lower level players that kind of knowledge, analysis, position evaluation, endgame knowledge was very difficult to acquire. </p>

<p>This is important because higher level players gain rating points by beating lower level players. If those lower level players are harder to beat because of increased access to the analysis and knowledge that engines and the internet provide then it actually becomes harder to reach higher levels as measured by rating.</p>
 17330: <p>The question is apparently based on a misunderstanding of how ELO ratings work. There is <strong>absolutely no mechanism</strong> by which the overall increase in players' strength would lead to increase in their ELO. The actual value of the ELO rating bears no meaning; nor does the comparison of ELO at distant times. The only thing that has direct relevance is the <em>difference in simultaneous</em> rating between players. </p>

<p>If tomorrow FIDE decided to add a constant, say, 500 points, to every player's rating, essentially nothing would change - the outcomes of games would lead to the same increments in ratings, so the rating dynamics would be the same, just at +500 points level. And the computers will provide no basepoint - their ELO is relative to human players, so they will play at 3600 rather than 3100. </p>

<p>The same applies if such a constant were somehow added or subtracted gradually due to natural processes - e. g., expansion of rated players' base, players becoming inactive with higher rating than they started with, etc. And this, apparently, did happen as we witnessed rating inflation until recently. </p>

<p>Similarly, if all the players suddenly, or gradually, start playing stronger, <em>without a change of their relative strength</em>, there is no reason to expect a change in rating dynamics. </p>
 19877: <p>I think they certainly have increased their ELO, but more importantly, their overall chess strength. ELO is only a rating relative to others in the pool so it may tend to go up more slowly if everyone in the pool gets better, which they have collectively.</p>

<p>First, you need to take an average of the top players, rather than look at just two incredibly special players, Kasparov, and Carlsen, and their peak ratings. Fischer was a total anomaly for his time, and again, you cannot base a lot on one person. Humans probably have a limit mentally much the way runners will eventually hit a speed wall that they cannot break. It is the Bell Curve in action: Easy to make progress in the middle, but harder on the end.</p>

<p>ChessBase, and the first strong engine, KnightStalker (aka Fritz 1.0, renamed at version 2.0) came out in 1990, and the Internet was still in its infancy. In January of 1990, there were only two players over 2700, Karpov at 2730, and Kasparov at 2800. Today, there are 37 players over 2700, and of those, three are over 2800.</p>

<p>I have been playing for a long time, and anyone, who knows my handle, has seen me watching relays of the top tournaments on ICC for more than 20 years, and I can say that it is not just inflation from having actually watched the level of play improve over the years. Players at the Master-level, including even normal Masters, are MUCH better now due to the tools available today than the tools available when I first became a Master.</p>

<p>When I first started playing, all we had was books, and a local club. Today, I can logon virtually any day, and play a GM. I was also a ranked tennis player as a teenager, and I can tell you from that experience, playing better competition makes you better, so being able to logon and play stronger players than ever has increased the overall level of play. In addition, we now have ChessBase, and a database of about 8.3M games that can be sorted efficiently and studied. We also have engines, as noted in the question, and they certainly have also added to our chess knowledge, and fundamentally changed how the top players prepare. Lastly, I mentioned books, and as an avid collector (I had 1800 at my peak), I can tell you that even the quality of the material in books is on another level since when I started.</p>

<p>I cannot tell you what proportion of all these advances have played toward X-number of rating points increase, but I can tell you that without a doubt, they all have lead to players at the top levels, and even down some, being much better overall.</p>
