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Is h3 really a bad move?

I play h3 fairly often in the Queen's Gambit to give my dark space bishop the h2 square in case of an opposing knight, but stockfish always docks me advantage points when I analyze the game. I can't figure out why, so I'm hoping someone out there can enlighten me. Thanks!
Generally speaking h3 is a bad move, as it does not develop any pieces and as it weakens the king's side especially after you play O-O. It is different in case you intend O-O-O, then you often can launch an attack with g4.

It is true that a bishop is worth more than a knight, about 3.25 pawns for a bishop versus 3 pawns for a knight, depending on the position and circumstances. So it is worth saving the bishop.

On the other hand a tempo is worth about 0.33 pawns depending on position and circumstances, more so at the start of the game and less so later in the game. So if your opponent plays Nf6-h5xf4 or xg3 he spends 3 moves while with hxg3 or fxg3 of exf4 you spend only 1 move. So he loses 2 tempi i.e. about 0.66 pawn worth to gain 0.25 pawn bishop versus knight advantage, so that is a bad trade for him especially at the start of the game. By recapturing with a pawn you get doubled pawns, but that may be compensated by the open h, f or e-file you get for your rook on h1, f1 or e1.

Another consideration is that you bishop on f4 is your bad bishop, i.e. it stands on the color of your pawns f2-e3-d4. It is not that bad as it stands outside the pawn chain, but it is worth less than its colleague on e2 or d3, which is your good bishop.

Later in the game, when all pieces are out at good squares, it may be worthwhile for black to play his Nf6 to h5 to capture your bishop. When that is the case it may be worthwhile for you to prevent that with h3.





In each of these games black could have won a pawn with dxc4 and defended it with the help of the extra tempo you gave them with h3.
If you want to save the bishop you might want to play the London (2.Bf4) with a quick h3.
I think that works.

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