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I'm playing recently the English opening. specifically this line in the two knights variations
[FEN ""]
1.c4 e5 2.Nc3 Nf6 3.g3 Nc6 4.Bg2
But I find it difficult to see when it's advantageous to go queen side with a3 b4 idea rather then play in the center with e3 maybe d4 later on.
Any thoughts ?
This is a tough question and depends a lot on where the f8 Bishop is going (b4, c5, e7, or even g7), as well as where is the Knight g1 is going (e2 or f3).
In the position of the diagram the most common move among top players is 4...Bc5. Then after 5.e3 with the idea to place the Knight g1 in e2 and to control the square d5 with the Bishop in g2, Black can still react by temporarily sacrificing a pawn with 5...d5 6.cxd5 Nb4 and a wild game. If Black prefers a more positional battle with 4...Bc5 5.e3 a6, then White prefers to expand on the queen-side: 6.Cge2 a6 7.0-0 0-0 8.a3 Ba7 9.b4 with a very flexible play.
Check this nice game between Nakamura and Grandelius at Gibraltar in 2015 (even if the move order is more subtle)
I am not a chess master so take this with a grain of salt. However, I also play the English quite often. Without taking a look at any computer, what I often play is as you suggested e3 to prepare d4 but probably first play Nf3.
I think that playing those moves or preparing a queenside expansion pretty much depends on the position, but in this particular position I would not consider doing this (a3 b4) at least for now. Note also that in some position a3 (not necessarily followed by b4) might be convenient to avoid the jump of the Black knight to b4, however, now (with the absence of Black bishop from f5) that does not look particularly dangerous.
