As clearly black cannot trap the white queen for longer. So, won't Nxd4 be the best move in this scenario? Letting the queen escape and take a piece for his lost rook. Nxd4 will be followed by either Nxc2 or Nxe6. What are the different ways in which white can counter this move?

Q1bq3r/p1ppk1bp/1pn1B1pn/4PpN1/3P4/8/PPP2PPP/RNB1K2R b KQ - 0 1

1... Nxd4
  • After Nxd4 Bb3 black does not regain any material, and he is still losing. I don't think you'll ever be able to trap and win the queen. – TMM Jun 13 '17 at 18:47

This is a funny looking position, which I assume you probably reached out of a poorly played Dutch defense, something along the lines 1.d4 f5 2.Nf3 g6 3.Ng5 Bg7 4.e4 e6 5.Bc4 Nh6 6.Qf3 b6 7.Bxe6 Ke7 8.e5 and so on... (or 1.d4 f5 2.Nf3 g6 3.Ng5 Bg7 4.e4 e6 5.Bc4 Nh6 6.Qf3 b6 7.e5 Ke7 8.Qxa8 Nc6 9.Bxe6) which are very weird looking...

With little analysis I think you convince yourself that black is completely lost here and Nxd4 doesn't come to rescue either. Simply put, white is a clear piece up, the queen isn't really trapped, black's king is a mess, and there's just not any piece coordination to create any counter-play whatsoever. As pointed out by TMM in the comments after Nxd4 white just retreats the bishop to b3 and protects everything, this is the simplest and best move. Or even Bc4 to preserve the bishop and even provoke Nxc2+ which leads to some fun tactics either mating the black king or trapping the queen, for example:

Q1bq3r/p1ppk1bp/1pn1B1pn/4PpN1/3P4/8/PPP2PPP/RNB1K2R b KQ - 0 1

1... Nxd4 2.Bc4 Nxc2+ 3.Kd1 Nxa1 4.Nxh7 Ke8 (4...Nf7 5.Bxf7 Kxf7 6.Qd5+ Ke8 7.Bg5 ) 5.Bg5
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I think if white really wanted to stop Nxc2 and Nxe6, white could play Bb3 (assuming black to move) to stop both options. Since trading is beneficial to white, this looks like a better position for white. However, I think that black can still keep the black queen locked up at a8:

Why doesn't black play dxe6 first? This regains more material than Nxd4, and keeps the queen locked up. Some possible continuations:

1... dxe6 2.Qxc6 Qxd4 threatening 3... Qxe5+ 4. Be3 Qxb2

1... dxe6 2.Nxe6 Kxe6

1... dxe6 2.Nxe6 Bxe6 3. Qxd8 Rxd8 threatening 4... Nxd4 5. Kd1 Nb6+

and black looks better than before.

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  • 2
    After ...dxe6 Qxc6 black hasn't made any progress, and ...Qxd4 O-O is much more likely than white blundering a rook on a1 for no reason. – TMM Jun 13 '17 at 18:46

No. No move will level the game.

Does not really matter as Black is lost.

It is almost zugzwang for black. White is up a rook and can continue developing

After the horsie takes the pawn black can easily protect then get on with finishing white off easily.

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