Mental models in chess In “Chess as a Behavioral Model for Cognitive Skill Research,” Mechner writes the following about mental representation of the game by blindfold chess masters:


  But the bombshell, which prompts the present reexamination of
  ‘‘visualization,’’ is this: blindfold chess masters consistently
  report that what they visualize are not images of pieces or
  chessboards, but abstractions of these with minimal or no physical
  features. A typical report is, ‘‘I do not visualize real pieces but I
  know where they are.’’
  
  ...
  
  The fourteen or so blindfold champions quoted by Hearst and Knott
  describe what they do in these terms: ‘‘no mental pictures,’’
  ‘‘abstract knowledge,’’ ‘‘I know where the pieces are,’’ ‘‘only an
  abstract type of representation,’’ ‘‘only relationships,’’ ‘‘no real
  picture,’’ ‘‘the significance of a piece,’’ ‘‘knowing what combination
  or plan is in progress,’’ ‘‘lines of force,’’ ‘‘pieces are only friend
  or foe, carriers of particular actions,’’ ‘‘sort of formless visions
  of the positions,’’ and so forth. Many of the masters report that they
  have no mental image at all (p.151).


The masters also confirm that blindfold chess improves their performance in normal chess.

However:


  Some of the strongest masters find the actual sight of a chess position to be more distracting than helpful when thinking ahead during a game.


Now, normal chess encourages a physical representation, when the game vision is more like geometry than algebra. That's compelling because humans get used to visual models since childhood. But extending the analogy with mathematics, the "algebraic" form is more powerful.

So in normal chess, a player has to make a choice: developing a visual representation or adopting the blindfold chess relationship model. That's the foundation to build chess memory and calculations on.

What approach is more promising in the long run? Which one do top players use?
I used to try to imagine the whole board and it always seemed my mind would focus more narrowly. Then, one time when I was doing an exhibition in public versus just one opponent, I suddenly saw the chessboard a different way: it was floating in darkness and the board was translucent, so I could move around the board and see it (and the pieces) from different perspectives. I can't say it improved my play a lot, but it was an amazing experience. I hadn't been seeking a better way. It just appeared to me.

I haven't tried to play blindfold very much over the years, but I have studied chess quite a lot and earned the national master title. I guess our imagination is working hard in any of these ways we do chess.