QGA 3. Nf3 Bg4 Can I let black double my pawns?

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CNoahSay

Hello again

My question is about this position with white to move:

Now I did check the database and Ne5 seems to score the best and thematic but I am wondering if I should be afraid of this:
I played a game today where I did this and I won nicely:
Maybe after 5. Nc3 if black does not capture than maybe I would continue with 6. Ne5. Otherwise I gain the bishop pair and get to hone in on the weak light squares on his queenside.
 
Also, after 4. Ne5 Bh4, the moves f3 and e4 seem to be played as well. In those cases is my king planning on castling kingside? 
 
Thanks all
 
 

 

Nimzowitsch2017

just play e3

Cali_boy613
Yeah, just play e3. It puts pressure on blacks c4 pawn, and guards the knight with the queen.
aggressivesociopath

Of course there is nothing wrong with 4. Nc3, but why do you want to avoid 4. Ne5 meeting Bh5 with g4 and Bg2? Black will miss not having the bishop on the queenside.