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Why is the pawn hook not problematic ?

a3 creates a potential hook whith a castled king , people often say a hook pawn with a castled king is bad , why is it here not bad ?
Bild 18.09.26 um 00.41.png

a3 creates a potential hook whith a castled king , people often say a hook pawn with a castled king is bad , why is it here not bad ? ![Bild 18.09.26 um 00.41.png](https://image.lichess1.org/display?fmt=png&h=0&op=resize&path=iiLDr9Hz0Lv5.png&w=864&sig=423a80215596760111be9f0cbc737e7421f47145)

Black was ready to play b4 and a3 stops that.

Black was ready to play b4 and a3 stops that.

Nc3 is such a good defender that keeping it there is worth creating a hook over.

If Black could quickly push ...a5 to play ...b4, then a3 would lose its value. As it stands, White's pieces are pressuring b5 and Black's are not supporting it.

Since Black's only play on the kingside is their Pawns, shutting them down means that Black has to create something new, which will take time, and White will use that time to attack Black.

Nc3 is such a good defender that keeping it there is worth creating a hook over. If Black could quickly push ...a5 to play ...b4, then a3 would lose its value. As it stands, White's pieces are pressuring b5 and Black's are not supporting it. Since Black's only play on the kingside is their Pawns, shutting them down means that Black has to create something new, which will take time, and White will use that time to attack Black.

my guess would be it takes black too much time opening the a file and creating a queen rook battery and white can in that time create some kind of attack in the center

my guess would be it takes black too much time opening the a file and creating a queen rook battery and white can in that time create some kind of attack in the center

You don't need to guess - just play through some variations. See what happens, can you find a line where black actually makes something out of the hook and how it works out for them? Also check what happens if white allows b4 without doing something active instead.

You don't need to guess - just play through some variations. See what happens, can you find a line where black actually makes something out of the hook and how it works out for them? Also check what happens if white allows b4 without doing something active instead.

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