(my answers)
After g3 your king has a faster route to become active in an endgame. e.g. Kg2-f3-e4
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Pieces that look at enemy pieces are more mobile by nature. You can't capture your own pieces. Bishops blocked by their own pawns are, in general, bad... but so are knights! (or any piece)
With a locked center, flank breaks are common, and so knights on c and f files will generally be in the way.
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Open files farther away from your king are more important. A king on g1 is 1 move away from guarding the e2 infiltration square. A king on g1 is many moves from guarding the b2 infiltration square. So Rb1 is preferred.
I'm not getting on the forums very often. I may check this tomorrow. I hope it gets some views / comments.
I've been thinking about this lately... and maybe the knowledge is in some books... but just general logical things. It's like GMs expect it's obvious to everyone when I really only see players around 1800 or 2000 even thinking in the proper terms.
I've been thinking about making a youtube video explaining some simple logical shortcuts.
Anyway, for example, imagine that neither color complex around you 0-0 king matters. That is to say, if you play h3 and "weaken" g3 it doesn't matter. If you play g3 and "weaken" h3 and f3 and doesn't matter. Also it's not important to protect g4 (with h3) or f4 (with g3) or anything like this.
But it's time to create luft. Which is better? h3 or g3?
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Example / question #2:
Imagine you have knights on c3 and f3. The center pawns are locked in some formation or another. Specifics don't really matter. It may be just the e and d files. It may be c, d, e, and f files. Or only 3 files.
In general though, which knight is better? The knight looking at your pawns, or the knight looking at the enemy pawns?
In this kind of situation, in general, would you prefer your knights on the c and f files? Or on the e and d files?
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Example / question #3:
Imagine a rook and pawn endgame (one rook for each player). Both sides (for some reason) recently 0-0. The only open files are the b and e files. White to move. Which is better in general? Re1 or Rb1?