Why is h4 much better than h3?

Question

rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1    
[Event "Rated Rapid game"]
[Date "2021.08.09"]
[Result "0-1"]
[Variant "Standard"]
[TimeControl "600+0"]
[ECO "A45"]
[Opening "Indian Defense"]
[Termination "Normal"]
[Annotator "lichess.org"]

1. d4 Nf6 { A45 Indian Defense } 2. Bf4 g6 3. e3 Bg7 4. c3 d6 5. Bd3 Nc6 6. Nd2 e5 7. Bg5 h6 8. Bh4 g5 9. Bg3 h5?! { (0.18 → 0.94) Inaccuracy. Be6 was best. } 10. h3?  (10. h4) 

I (white) played a London system against a kings indian defense. After 10. h3? the engine turns from 1.2 to -0.3. I get that it is better to force black with 10... g4 into a weird pawn structure but I don't see cleary what is that wrong with h3. Could somebody explain the evaluation of the engine?

Answer 1

Why is h4 much better than h3?

It's very simple. The prospects for the bishop are much better on g3 than h2. On h2 the bishop does nothing useful and it will take a lot of moves to get it back into the game via g1. Black will exert iron control over f4 with pawns on e5 and g5 making the freeing move f2-f4 impossible.

On g3 the bishop has a role protecting the pawn on h4. Black will have to push the g pawn to g4 loosening control over f4 and giving white more targets. If the h2-b8 diagonal remains blocked then re-entry via f2 or e1 later on is much easier.

Answer 2

After 10.h4 g4, the kingside pawn structure is more favorable for White. Black's g- and h-pawns are blocked, they are too far advanced and feel more weak than strong. Black doesn't have possibilies for a kingside attack because of the blocked pawns. White's king will be safe on g1 after castling short. This is the most important factor. Far advanced pawns also often leave weak squares behind, this is the case here as well.

After 10.h3 h4 11.Bh2, Black has gained space on kingside and his g- and h-pawns are mobile. If White castles short, then Black can castle queenside and White's king is not safe since Black has ...g4 pawn breakthrough. Most likely ...g4 should be played already earlier. For example, 11...g4 12.hxg4 Nxg4 and White loses the bishop pair. The character of the position is much different than in the 10.h4 g4 variation.