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gwern comments on Generalizing From One Example - Less Wrong
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Right. In fact, chess is the perfect example here.
Many chess grandmasters are famous for being able to recall perfectly games and board positions from years or decades ago, but there are also (somewhat) famous studies to the effect that their recall drops to normal when given random board positions. If their recall is due to a 'mental image', the mental image is certainly not a 64x64 pixelized grid but something quite different.
(Well, the recall drops back to moderate improvement over normal, with diminishing returns for level of expertise rather than being downright astounding.)
The reason's obvious for anyone who played chess. You see that knight is threatening this pawn, which is protected by this bishop, etc. You (well, me at least) literally see such relations when playing the chess, i.e. you train to see it at higher level just as we all train to see a 3d cube as a 3d cube rather than as shaded faces of said cubes. Someone who can't do that, chances are, won't be a good chess player.
I suck at chess. I have trouble keeping all those relationships in mind. So my strategy is always to do a bunch of capture exchanges so the board is simpler and my disadvantage is somewhat reduced. :-)
I love that strategy too! Charge!
Exactly, and chess is such a good model for studying the general phenomenon of this kind of expertise. A concentrated focus on building an enormous database of significant patterns and the development of the ability to use long term memory with almost the same malleability that we commonly use working memory but confined to that domain limited problem.
I would also say that someone who can't do that is not yet a good chess player. This is a core human skill. With some work everyone (who does not have some cognitive disability) will develop the skills you are talking about. They may still be terrible at at the strategic side of the game but the pattern matching is nigh inevitable.