Thank you for the addition, your memory is mostly correct. I drudged out my copy of GEB, first part of Chapter X, and we're both correct. Both groups of players

Thank you for the addition, your memory is mostly correct. I drudged out my copy of GEB, first part of Chapter X, and we're both correct. Both groups of players are given a 5-second glance at the board. If the game is a real game, the pros can assemble the board very quickly, and they do make mistakes but they're mistakes that other pros recognize as strategically invariant, while the normal people take longer (accuracy not mentioned). Given a random board, they both perform the same. The general point is the same: the pros perceive the board differently, because they see the emergent patterns. My contention is that this is the heart of intuition (or at least an important subset of intuition).