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I have faced this fairly often in quite a few openings, but there seems to be a theme with players putting their Bishop on a square like h6, supported by a queen and attacking the fianchettoed Bishop next to the castled King. What are the ideas behind this? Is it something I should be bringing into my own gameplan and if so is taking the fianchettoed Bishop a good thing to do? It seems to me to be the only point in putting it there.

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There are two reasons for doing this and immediately taking the fianchettoed bishop is not one of them:

  • Provoke Black into playing BxB when you hope to follow up with Ng5, drive the f6 knight away and then mate on h7
  • Prevent black from playing h5 until you have been able to play h2-4-5 to pry open the black king's position.

It can even be worth sacrificing the exchange with h5, Nxh5 Rxh5 to smash open the black citadel.

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    This seems like it only applies in cases where opposite castling has occurred. While the strategies you give certainly happen, most of the time Bh6 is played for the purpose of carrying out an exchange. Commented Nov 22, 2019 at 22:14
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There are a few benefits behind exchanging off the fianchettoed bishop. For this example, I'll assume the stage is Black's kingside after ...g6 and ...Bg7 are played.

  • Weakening the surrounding squares. Without the fianchettoed bishop, the squares weakened by pushing the pawn (such as h6 and g7 when Black plays ...g6) are less protected.
  • Making the enemy king more vulnerable. Without the bishop, Black's castle is slightly compromised due to pushing ...g6 and having no piece on g7 to fill the gap.
  • Minimizing the opponent's influence along the long diagonal. A bishop on g7 often exerts strong pressure along the h8-a1 diagonal.

But there are also drawbacks behind doing the exchange for you:

  • It takes time. Often you must spend two whole tempi (e.g., Qd2, Bh6) to exchange bishops. In a time sensitive position, this may be a bad idea.
  • It's possible your bishop is better than your opponent's, which means exchanging actually favours them. For example, say you have a White bishop on e3 that is unobstructed along the c1-h6 and g1-a7 diagonals. Meanwhile, assume Black's g7-bishop is blocked in by a White pawn on e5. Here your bishop is clearly superior, so the benefits of exchanging off the fianchettoed bishop may not be worth it.
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    I gave both you and Brian an upvote. Both ideas are possible, but yours is much more common between stronger players. Commented Nov 22, 2019 at 22:34
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As an additional note related to the idea of weakening squares around the king, it is only worth spending the tempi if the pawn adjacent to the "fianchetto triangle" is pushed. So, for example, if black fianchettoed its dark bishop and pushed the e pawn to e6 or e5, it's worth it to trade the bishop because the dark squares around black king are permanently weakened. On the other hand, if his pawns are e7-f7-g6-h7, that e pawn sitting on its original square, will normally compensate for the bishop's absence in dark-square protection duties.

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