I'd say there's a good amount of tactical justification. Normally black wouldn't play Bxc3 after 13.a3. Black would retreat to d6 or e7 or even a5 but... (see the 3 variations on move 13)
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So since black has to trade the good bishop for the fairly passive c3 knight, black's position is even worse.
And if you give black time he's able to play Bd6 after a3
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So that's what makes 13.a3 good, but that doesn't answer your question about how I'd look at the position. I'd want to open lines and attack due to some of the things you pointed out like black's kingside looseness and my lead in development... for those reasons lots of moves are good (like Rc1 or 0-0) but they're not as good as the best move because the timing is just right to force Bxc3.
So... that's my answer.
My improvement in this game has come from the understanding of the imbalance system of training while also considering tactical refutations or tactical moves which must go against positional concepts. Can a high rated player please explain what they would do in this position upon evaluating it. This is the type of game where the opponent plays very aggressively.
What I notice in this position:
- White's dark squared bishop is very active
-White has a lead in development
-There is a half-open c-file which the white rooks can use
-The e-file is half-open
-The black king is weaker than the white king
-Black's pawn advances on the kingside have gained space but left a bunch of weak squares (especially on the dark squares) such as e5 square
- Black controls the e4 square and currently has a knight placed there which is an active knight
Some tactical considerations:
-My knight is pinned and both the e4 knight and the b4 bishop put pressure on it
-If the black plays Be7 than I can play Nxd5 when if cxd5 Bc7 traps the queen
- I could sacrifice a piece on e4 in the future to open up the position with Qxe4+. This might or might not be the way to go
Now... upon evaluating the position. In this case I found it difficult to find the top engine move a3. I know that I'm not a computer and playing the best move is impossible all the time but how does one find the logic to play a3 in this case. I understand the other top engine moves Rc1 just places the rook on the half-open c-file (the only good home really) and overprotects c3 and 0-0 places the king to safety, but a3 I don't get apart from the fact that is asks black what he wants to do with the bishop.
Can a 2000+ rated player or please evaluate this position and explain the move(s) they would play and the logic behind them