How important is context?
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What is important for me is to remember what I planned to do. Sometimes I forget traps set by my opponent that I already saw through.
When I'm playing a drawn out correspondance game I usually have to review the past couple of moves before making another one. It refreshes my sense of what I've been trying to do, and what I think my opponent has been trying. Without that retrospect, the board often looks like just so many shapes.
Is this true for you as well? Clearly someone who excells at chess puzzles is good at picking up without the historical context of a particular game. Is it not possible, if your brain is trained properly, to see each round in complete isolation and still make the best possible move each time?