3

This is the opening I'm referring to:

[fen ""]
1.d4 Nf6 2.Nf3 e6 3.g3 b6 4.Bg2 Bb7 5.O-O Be7 6.c4 O-O 7.Nc3 Ne4 8.Bd2!?

The other white book moves at this point seem sensible 8.Qc2 or 8.Qd3, or even 8.Nxe4 (which seems to almost always draw). I'm unsure about 8.Bd2, as it seems to give up the bishop pair (and 8...Nxd2 has been played, e.g., Gelfand vs. Radjabov, 2017) and it puts the bishop on a fairly modest square, but it's listed as having 1500+ master games at LiChess.

Question: Why is 7...Ne4 8.Bd2 such a popular line in this variation of the Queen's Indian Defence?

The most popular continuation on LiChess is the following:

[fen ""]
1.d4 Nf6 2.Nf3 e6 3.g3 b6 4.Bg2 Bb7 5.O-O Be7 6.c4 O-O 7.Nc3 Ne4 8.Bd2 f5 9.d5 Bf6 10.Rc1 Na6 11.a3 Nac5 12.b4 Nxc3 13.Bxc3 Ne4 14. Bxf6 Qxf6
2

White wants to avoid doubled c-pawns and all of the moves you mention, Qc2, Qd3, Nxe4 and Bd2 achieve this.

As you note, Nxe4, exchanging knights tends to be drawish, so is not what most white players want.

With the queen moves (Qc2, Qd3) your queen will end up on c3, which is a bit of an unusual square for the queen. Also the c1-bishop is not developed yet, so white would still have to connect his rooks and likely move the queen to a better square.

  1. Bd2 is a modest development move for the bishop, but it does make space for the rooks. Also, if black takes Nxc3, Bxc3 and the bishop has found a very nice square on c3.

I would not be concerned about giving up the bishop pair. The black knight on e4 is a rather strong piece while the dark squared bishop is the weaker of white's bishops due to the pawn structure.

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