How do top players use computers to improve their play? This question is inspired by yesterday's matches between Hikaru Nakamura + Rybka vs Stockfish. Nakamura was allowed to use an older version of Rybka to help him, and Stockfish was allowed to play with its full strength but not use an opening book or an endgame tablebase.

Question 1: How might players such as Nakamura use Rybka to improve their play against a computer opponent?

I can come up with a few naive guesses: check their own moves for blunders; check the computer's suggestions to see if there are some convoluted move sequences which lead to a huge advantage; and letting the computer play the endgame for them. This does not need to be the full story though. Maybe there are useful features that chess engines have that I am not aware of. I'm also wondering to what degree a human player would rely on his own intuition: would he always play his own moves assuming the computer never suggested a blunder or an amazing winning move which is difficult to see?



My second very similar question is inspired by a few comments by Nakamura in a reddit thread, namely


  Fischer would almost certainly lose to [people such as myself, Carlsen, and Kasparov], but this is due to the fact that the game has so fundamentally changed. If Fischer had a few years to use computers, I think he would probably be on the same level.


and


  I think mainly what can be learned from computers is a deeper understanding that almost all positions are ok with accurate play. In the past, many people assumed certain positions were automatically bad, but computers have shown that the rules and thought processes aren't always accurate!


Question 2: How have computers changed the way top players play today (when unassisted by computers)?

What is meant by the first quote? The second quote indicates that one might not want to give up too early, but does not suggest any change in playstyle.
How might players such as Nakamura use Rybka to improve their play against a computer opponent?


  ... check their own moves for blunders; check the computer's suggestions
  to see if there are some convoluted move sequences which lead to a
  huge advantage ...


I believe you said it yourself here. A computer would be used in order to check if the move that the GM thinks would be a good move is indeed the best move to exploit the existing position. I doubt that it would play the end game fully, I am positive that the GM thinks through every move of the game instead of trusting blindly the computer, but most likely definitely the opening would be played by the machine, at least till about move 5-7, until the position changes known book course.Additionally, the computer would most likely have some kind of a database of the previous games played between other players, so if the position played was already played by someone else a while back, it could be used to not make the same mistake or, vice-versa, to build a long term plan.

How have computers changed the way top players play today (when unassisted by computers)?

OK, I do understand that this might get a bit long, but bear with me. Ill bold the important points. Computers have made the modern top players much more tactically aware and ready than the chess players before them. This is what the quote about Fischer is talking about: Fischer did not have the opportunity to analyse his games and study lines to such a far extent as is done by the modern top players using computer technology. About the second quote: with the knowledge that there is a possible accurate move in virtually any position, top players would dedicate more time to thinking and finding that one single accurate move, than just assuming that the position was lost and thats it. This makes the game much more interesting and thrilling, because you know that the accurate move exists, its just the matter of finding it. 

About how computers help top players prepare: so basically, theres 4 reasons why computers are used today for chess:


Playing against software program
Keeping track of games (Databases)
Using software to analyse your games
Using software to do chess problems


Out of those 4 points, the one that interest us are the bolded two. 

Keeping track of games (Databases) is used usually to analyse the openings, and then comparing them to how they were played by other top-players in order to evaluate one's own position and/or learn something from others. You could've never thought that that move would bring any use, but if Kasparov's been whipping it out right and left for the past 5 years with great success, you might as well try giving it a go. 

Using software to analyse your games is the primary use of computer engine by top-players. After every official game they play, the will analyse their games and see where they did wrong and where they could do better. The programs are usually proficient in tactics and opening theory, so for someone like Magnus Carlsen, whose opening is not as strong compared to other GM's like Kasparov and etc, a computer engine would be the best an fastest way to improve. And of course, if they find that what they did in game is not the strongest move in the position, next time they would be aware of it and follow the move that was suggested by the engine. Usually this would happen once again in the opening, because middle games repeat quite rarely if played against different opponents.