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I saw some grandmasters looking up or sideways during calculations. Why don't they just look at the board and visualize? Wouldn't that be easier?

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    They may get confused by where the pieces actually are (which messes up with where they are calculating them to be in the future) – David May 19 at 20:48
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    I took a few lessons from a then IM, now GM. He strongly recommended NOT looking at the board for the reason given by @David – Ian Bush May 19 at 21:46
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    In Chapter 1 ("The Chess Image") of his book Psychology in Chess, Nikolai Krogius gives several examples of famous grandmasters miscalculating because they mentally left a piece or pawn on its original square during their mental calculations. – Timothy Chow May 19 at 22:38
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Expanding on the great comments of @David and @Timothy Chow, GM Nikolai Krogius talks about the role of the residual image in his book Psychology in Chess. This is an image that stays and blurs the calculations. The residual image is the transfer of judgment from a past position to a new situation. The past then acts on the present.

To combat this residual image and to improve concentration, Krogius recommends practicing blindfold chess or analyzing without using a chess board. By not looking at the board, the player must constantly check the position of the pieces, thus erasing the residual image.


Here is an example of the residual image. At the beginning of the position the Bishop in b3 controls the square g8, but not ... at the end.

[FEN "r3k3/1p5p/p2R4/4p1Q1/4P1bP/PBq5/6P1/5K2 w - - 0 1"]
[title "Ilyin-Genevsky - Nenarokov, Moscow 1922"]

1.Bf7+! Kf8 2.Qh6+?? (2.Rf6!+-) Kxf7 3.Rf6+? (3.Qxh7+ Ke8 4.Qg6+ Ke7 5.Qf6+=) Kg8! {and now Black is better!}

Check also this article on ChessBase India, which asks your question

*We often see top chess players not looking at the board while calculating. It seems that their attention is somewhere else, yet after a few minutes they make the move without having even glanced at the position. What do you think they were doing for the last few minutes? Well, they were thinking in their head. They did not need to see the chess board to calculate the variations. They could do it in their head. So how do these super GMs calculate without a chess board? How are they able to make complex decisions in their mind, which normal players cannot fathom.

They welcome GM Vidit Gujrathi on how to calculate better in blindfold.

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