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Why is Bg5 not a mistake or inaccuracy?

In this position
https://lichess.org/editor/r1b2rk1/ppp1qppp/3p1n2/4b3/2B1P3/2NQ4/PPP2PPP/R1B1R1K1_w_-_-_0_11
After white plays Bg5, Black can take the h2 pawn due to tactics. So why is Bg5 not even an inaccuracy? Sorry for the dumb looking question, it just seems weird to me.

In this position https://lichess.org/editor/r1b2rk1/ppp1qppp/3p1n2/4b3/2B1P3/2NQ4/PPP2PPP/R1B1R1K1_w_-_-_0_11 After white plays Bg5, Black can take the h2 pawn due to tactics. So why is Bg5 not even an inaccuracy? Sorry for the dumb looking question, it just seems weird to me.

It's just a pawn, everything else is in White's favour after Bxh2+ Kh1. White has two immediate threats, Nd5 and Bxf6 Qxf6 Kxh2, so Black will be forced to play Be5 back, when Nd5 will spoil Black's kingside pawns anyway (staying in the pin with Qd8 won't do due to Black's poor development, f4 hitting the bishop will be immediately decisive). This gives White enough compensation for the material.

It's just a pawn, everything else is in White's favour after Bxh2+ Kh1. White has two immediate threats, Nd5 and Bxf6 Qxf6 Kxh2, so Black will be forced to play Be5 back, when Nd5 will spoil Black's kingside pawns anyway (staying in the pin with Qd8 won't do due to Black's poor development, f4 hitting the bishop will be immediately decisive). This gives White enough compensation for the material.

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