Why is bishop h6 the best move? Why sacrifice bishop for a knight?


You sometimes have to take an engine analysis with a grain of salt and not worry about why it prefers one move over another. NikkiLikeChikki has a good point, Bxh6 shatters Black's Kingside. I looked at the analysis, Bxh6 is rated +3.6, Bc4 is rated +2.7. To the computer programmer, and probably high-level players, that's a significant difference. I not sure that it is for average players. We can find many ways to mess up a lead, be it 3.6 or 2.7.

This is hardly a sacrifice. It's more like a trade.
But by making this trade, you accomplish 2 big things:
1) You cause serious damage to black's pawn structure: black gets double-isolated pawns on the h-file, which are notoriously weak.
2) You completely shatter the defence of black's king. Now if you manage to bring your queen to h5, this will be devastating and cause serious mating threats against the black king.

My guess without looking at an engine is gxh6, Nxe5!!, fxe5, Qh5+, Ke7, Qf7+, Ke6, O-O-O+, maybe Kc7, Nb5+, Kb6, Nd6, and then maybe the queen can deliver mate after going to d5.
Your analysis is wrong because you're assuming that your bishop is on c4.
If we play the correct move (Bxh6), we're playing that move instead of Bc4, meaning our bishop still sits on the f1 square.

My guess without looking at an engine is gxh6, Nxe5!!, fxe5, Qh5+, Ke7, Qf7+, Ke6, O-O-O+, maybe Kc7, Nb5+, Kb6, Nd6, and then maybe the queen can deliver mate after going to d5.
Your analysis is wrong because you're assuming that your bishop is on c4.
If we play the correct move (Bxh6), we're playing that move instead of Bc4, meaning our bishop still sits on the f1 square.
Correct.
Still, 1. Bxh6 gxh6 2. Nxe5! fxe5 3. Qh5+ followed by Qxe5 forking h8 and c5 wins the piece back immediately, with two Pawns up and a strong attack.
No?

Benefits of the exchange:
- Creates a doubled pawn. (Advantage of a doubled pawn is that it can be easily attacked and captured with proper play)
- It opens the king side. (Your opponent will have to lose a lot of time trying to castle queen side which will help you develop and attack)
- The analisis given by @ToastyPosition (https://www.chess.com/forum/view/for-beginners/why-is-bishop-h6-the-best-move-why-sacrifice-bishop-for-a-knight#comment-52931786)
- Hope this helps!

You have analyzed the wrong position. The engine suggests Bxh6 INSTEAD OF Bc4. You can't have both moves... it's one or the other.

You have analyzed the wrong position. The engine suggests Bxh6 INSTEAD OF Bc4. You can't have both moves... it's one or the other.
sorry I put that bishop there by mistake

You have analyzed the wrong position. The engine suggests Bxh6 INSTEAD OF Bc4. You can't have both moves... it's one or the other.
sorry I put that bishop there by mistake
4. ... Kf7, not f8. Playing it to f8 loses the Queen.
1. Bxh6 gxh6 2. Nxe5! fxe5 3. Qh5+ Ke7 4. Qxe5+ Kf7 5. Bc4+!! is much better, since:
a) 5. ..Kg6 6. Qf5#
b) 5. ..Kf8 6. Qxh8+ Ke7 7. Nd5+ wins the black queen in addition to the h8 rook.
c) 5. ..d5 6. Bxd5+ and now Qxd5 is the only move that avoids forced mate.
The easy conclusion is that 2. ..fxe5?? is a blunder, but black is losing further material with alternatives. For example, 2. ..O-O 3. Bc4+ Kh8 4. Nf7+ wins the exchange. Certainly better than the continuation above, but this shows how tactically strong the initial 1. Bxh6 move really is.

Black has to defend an open position with an exposed king where one inaccuracy is death. White’s position plays itself and white’s king can easily castle to safety.
In theory black is down only 3.6. In practice this should be an easy white win after the trade on h6.

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You sometimes have to take an engine analysis with a grain of salt and not worry about why it prefers one move over another. NikkiLikeChikki has a good point, Bxh6 shatters Black's Kingside. I looked at the analysis, Bxh6 is rated +3.6, Bc4 is rated +2.7. To the computer programmer, and probably high-level players, that's a significant difference. I not sure that it is for average players. We can find many ways to mess up a lead, be it 3.6 or 2.7.
I agree. Characterizing Bc4 as a mistake seems harsh at intermediate skill levels