Attacking the accelerated dragon What are the best moves for white after the following moves

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1. e4 c5 2. Nf3 Nc6 3. Nc3 g6


One aggressive choice here is 4. h4.

which can potentially damage the pawn structure or harass the bishop if he is deployed to g7. Is this a fairly good move? What are other alternatives in this position?
The two sources I'd depend upon to answer this question are actual games played by GM's (best), and engine analysis, carried to a depth of at least 24 ply (12 moves by each side).

Here's what I get:

Actual Games

Move     Games  Win %  Latest  Players
4 d4      2947  57.3    2016   Carlsen, Kasparov, Karjakin, Anand
4 Bb5      513  57.8    2016   Grischuk, Karjakin, Morozevich, Adams
4 Bc4      229  47.2    2016   Vallejo Pons, Movsesian, Lu SHanglei, Zhigalko
4 g3       153  48.4    2010   Mamedyarov, Romanishin, Galego, Biyiasas
4 h4        38  43.4    2012   Hamdouchi, Pilavov, Minasian, Pridorozhni


So, the move is pretty unpopular at the highest levels (about 1% of games), and since Black outscores White by 57%-43% in this line, it's no wonder.



Engine Analysis

Engine parameters: Stockfish 7, QuadCore AMD CPU using 4 Cores, Depth=25/39
Line Move    Eval
 a.  4 Bb5   0.17
 b.  4 d4    0.13
 c.  4 h3    0.13
 d.  4 Rb1   0.11
 e.  4 a4    0.10
 f.  4 Bc4   0.09
 g.  4 a3    0.03
 h.  4 Be2   0.01
 i.  4 d3    0.00




That's 9 lines that are better than 4 h4, and the 9th has an evaluation of dead equal, implying that the move 4 h4 must have a lower evaluation. Note that 4 h4 starts at among the top four moves until the engine reaches a depth of about 15-17 ply, and then falls off the map.  So the blowback seems to occur somewhere between move 11 and move 13.