[FEN ""] 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 g6 6. Be3 Bg7 7. f3 O-O 8. Qd2 Nc6 9. O-O-O d5 10. exd5 Nxd5 11. Nxc6 bxc6 12. Bd4
What is White's plan & idea behind 12. Bd4 move?
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One of the main purposes of playing f3 at the Yugoslavian attack against the dragon is to put pressure on black's king by pushing the kingside pawns (g4, h4-h5).
However the black strong bishop defender should be eliminated in order to put black's king in troubles.
Normally this is done via Bh6.
In this line white is putting pressure on c3 knight, so Bh6 doesn't work.
This is the continuation of Stockfish if Bh6, winning a pawn.
[FEN ""] 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 g6 6. Be3 Bg7 7. f3 O-O 8. Qd2 Nc6 9. O-O-O d5 10. exd5 Nxd5 11. Nxc6 bxc6 12. Bh6 Nxc3 13. Bxg7 Qxd2+ 14. Rxd2 Nxa2+
If Nxc3 bxc3 Qa5!, a classical on Dragon, starts a strong attack on queenside (Stockfish gives -8).
[FEN ""] 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 g6 6. Be3 Bg7 7. f3 O-O 8. Qd2 Nc6 9. O-O-O d5 10. exd5 Nxd5 11. Nxc6 bxc6 12. Bh6 Nxc3 13. bxc3 Qa5
As said, the idea of this move is not only exchanging bishops but also reducing pressure on the diagonal; Nxc3 is a threat.
Something that instantly stands out to me is that 12. Bd4 challenges black's strong fiancettoed bishop.
Black must submit to trading pieces or weaken his bishop.
Also,12. Bd4 removes pressure from the c3 knight. This piece is in a bit of a weak position, especially since one of its defenders is a pawn next to the king that we don't really want to move, and definitely don't want to double up.
Finally, 12. Bd4 could help white control the d-file. Black's queen could step out of the way much more easily and allow the d1 rook to push the d8 queen off of the open d-file. (For example: Knight takes knight, queen takes knight, bishop takes bishop, rook takes bishop.) The queen is also free-er to move along the "up-and-to-the-right" diagonal.
Regarding other future ideas:
A move like Bc4 might be in order soon: it develops a piece, unites the back-rank rooks, attacks a strong but weakly-defended piece, and has the chance to participate in a kingside attack, eventually. It also protects the hanging a2 pawn.
In the line with 9.0-0-0 d5, by contrast with 9.Bc4 or 9.0-0-0 Bd7, the center gets open and White is more often aiming for play in the center than on the h-file.
White wants to neutralize the strong Bg7 and any possible counterplay on the b-file and exploit the weaknesses on c6, c5, d6 and the open d-file.
After the usual 12...e5 (12...Bxd4 13.Qxd4 Qb6 is more solid but passive) 13.Bc5 Be6!, White does best not to take the offered exchange but to build up her pressure with Ne4, Kb1, Bc4, and often g4-h4 and/or b3-a4.
Black chances are linked with threats against a2 or b2 or activating his pawn majority on the kingside with ...f7-f5.
Fixing the pawn structure, even by closing the kingside (g4-g5 met by ...h6-h5) is good for White because Black would lack levers to create counterplay and White minor pieces all have good active and safe posts near the d-file: c4,c5,e4.
A dream scenario for White:
[FEN ""] 1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 g6 6. Be3 Bg7 7. f3 O-O 8. Qd2 Nc6 9. O-O-O d5 10. exd5 Nxd5 11. Nxc6 bxc6 12. Bd4 e5 13.Bc5 Be6 14.Ne4 Re8 15.h4 h6 16.g4 a5 17.g5 h5 18.Bc4 Nf4 19.Qc3 Qc7 20.a4