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What are some common tactics or ideas that arise when black has played h6 (or white has played h3) in front of his castled king?

An example I have in mind is, in this position, white can win a pawn with Bxh6, gxh6, Qxf6:

white can win a pawn

A less concrete but still important idea is, with a bishop on the a2-g8 diagonal (pinning black's pawn on f7), white often plans to sink his king's knight into g6 in a couple of moves:

g6 is weak

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Two basic ideas:

  1. Put a knight on f5; Black will have a hard time chasing it away with g6 without losing material.
  2. Storm with your g-pawn to g5. Especially with the black knight still on f6, Black cannot avoid the opening of some lines.

Both plans would work in some circumstances with the pawn still on h7, but are a lot more effective with the pawn on h6.

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In my experience, your second idea, sinking a knight in g6, is not very common. Some more ideas:

  • piece sacrifice on h6 for two pawns and an open king

  • piece sacrifice on g5 (not forced but tempting). If white has a pawn on h4 and rook on h1, the opening of the h file can often be very dangerous for black. This is also known as fishing pole trap

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With usual piece placement for this struture it is good to be careful that with weak 8th rank king can get to serious troubles on h7. Qf5+ with knight on f6 lost after g6, occasionaly Ng5+ hxg5 Qh5#. Also any b1-h7 attack can be often very dangerous. Shelter on g7 is more often safer.

You can think out and write to comment some reasons for that as a training. Or you don't have to trust this statement, but I'm always very careful if my King must run after check to h7.

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To understand this question, we must look at what the move ...h6 does to the protection of the black kingside position once it is played.

When black plays ... h6, he:

  • Weakens g6 - no longer protected by a pawn on both f7 AND h7.
  • Weakens h6 itself and makes it vulnerable to capture sacrifices.
  • Weakens h5 as well because playing g6 now leaves the h6 pawn unprotected.
  • To some extent it weakens ... e6 also, as a sacrifice on e6 and subsequent recapture by fxe6 results in g6 undefended. Do you smell a combination?

Whenever you move a pawn, you change the fundamental structure of the position most of the time, so be very careful. Pawn moves can have far-reaching effects.

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