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Why is maintaining the pin bad?

I'm curious about the move 8. Bh4, stepping the bishop back from the previous pawn move 7. .. h6.

Why does the computer say that maintaining the (psuedo) pin on the knight is an inaccuracy?

Because taking the knight leads to an advantage, while maintaining the pin doesn't. Accurate play would press the advantage.

The advantage is Bxf6 Bxf6 cxd5 exd5 Qb3. Now white wins one of the d5 or b7 pawns. With Bh4, you give black the time to defend them (e.g. Nbd7).
Is that the *only* reason? That there is a forced sequence of captures leading to the win of material?

Man, that's hard (for me) to see that many moves into the future. Would it also be related to the fact that the pin is actually not a pin anymore?
It really is mostly that, yes.

Certainly, it's also related (slightly) to the fact that that pin isn't doing much otherwise. You're not threatening to win the knight, the knight can actually move since the Be7 is defended... the pseudo-pin is good, but only one tenth as good as winning a pawn.

The inaccuracy is failing to win the pawn. If it hadn't been for that opportunity you missed, Bh4 would have been a perfectly correct move.
"If it hadn't been for that opportunity you missed, Bh4 would have been a perfectly correct move."

That's very helpful. Thank you for your input! I'll try to keep an eye out for these kinds of tactics.

Out of curiosity, is that a tactic that higher ranked players see very easily? Or would it have flown under the radar for most?

Edit: and! how would one notice that tactic? I would argue that I wouldn't have seen that tactic within a reasonable amount of time.
I could very well have missed it if I hadn't paid attention, especially given that I never play d4.

That being said, b7 has been undefended for a while now, and Qb3 is a fairly common move after c4, and the crux of the queen pseudogambit opening is the d5 spot, so... yeah, it's kinda easy to spot. The tactic is called "don't leave your pieces and pawns undefended, or they fall victims to double attacks", and this is a straightforward double attack (after the mandatory captures, and yes, strong players always consider positions in terms of "how does this behave after mandatory captures").
This is a very standard tactic in the Queen's Gambit. You should try to memorize it.

The basic pattern/chunk is: If Black plays ...Bf5, he leaves b7 undefended, and very often [cxd5 exd5] Qb3 will win a pawn by attacking both b7 and d5 (which you already attack by c4 and Nc3). In this case, White needs to insert the trade on f6 first, but that's the easy part once you know the underlying tactic.

Another instance would be 1 d4 d5 2 c4 c6 3 Nc3 Bf5?! 4 cxd5 cxd5 5 Qb3! [or even 4 Qb3!], for example.

In that sense, a "high ranked player" will not discover such a tactic on the fly as you would. He will already know in advance that ...Bf5 is a risky move against the QG and is prepared to refute it by this tactic.
ProfDrHack, thank you very much for your input. I really appreciate it!

While I am familiar with the Qb3 move, sometimes I am nervous of my queen getting trapped if Qxb7 with some kind of fancy rook or knight move. I will certainly be more on the look out for this kind of tactic in the Queen's Gambit.

It is similar to black playing the Caro Kann in the advance Variation with the black queen going to b6. Just rattling off some moves, something like...

1. e4 c6 2. d4 d5 3. e5 Bf5 4. Nf3 e6 5. Bd3 Ne7 6. Bxf5 Nxf5 7. O-O c5 8. c3 cxd4 9. cxd4 Nc6 10. Bg5 Qb6

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