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1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 g6 5.Nc3 Bg7 6.Be3 Nf6 7.f3 O-O 8.Bc4 e6 9.O-O a6
Here is a line from a game of mine. I made the movee 10. Qd3, but my computer program says Qd2 would have been a much better move. Why is that?
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1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 g6 5.Nc3 Bg7 6.Be3 Nf6 7.f3 O-O 8.Bc4 e6 9.O-O a6
Here is a line from a game of mine. I made the movee 10. Qd3, but my computer program says Qd2 would have been a much better move. Why is that?
One of Black's development plans will include moves like Nd7 intending Ne5 hitting the Q and Bishop if the Q is on d3. This will cost White an important tempo in this dynamic opening.
Black's plans revolve around control of the c4 square hoping to place a piece on this square. Depending on White's particular move order Black may play b5, Bb7, Nd7, Nb6, Nc4, Rc8.
To counter this Q side action of Black, White needs to get active on the K side: Qd2 allows the B to h6 plan to exchange off the key defensive Black B. In due course after completing development White can plan a pawn storm against the B King.
Qd2 is used in these lines to support the Be3, which is typically played to h6 to exchange for the Bg7, followed by a pawn attack on the king-side.
Without giving a long, drawn out explanation, the simple answer is that you're decreasing the mobility of the queen. The queen only has three legal moves from d3 and all of them waste time. Qd2 loses a tempo since you could have played Qd2 the move before. Same with Qe2. Qd1 wastes two moves.
The value of moves comes from the value of the pieces and the value of the pieces comes from their mobility.
The queen on d2 allows for a future Bh6 exchanging the bishops and preparing a h4-h5 push with a strong attack for White.
With Qd3, you are exposing it to attack (...Nc6-e5 is a typical maneuvre in this type of posiiton). You also prevent your bishop from going to c4 which is a typical square where it's placed.
Also note that Black's ...e6 is a very bad move, as it does nothing to further development, weakens the d6 square and prevents the c8 bishop from developing to e6.