Why is this the best move?

Question

I was just reviewing my game and was wondering why the AI would think this is the best move. All I see is giving white a free knight.

Answer 1

10 . . . Nxe4 is best because it wins a pawn, while other moves only keep material equality (or worse, give away material).

The move is a typical "desperado" sacrifice, introducing a line where wB and bN try to take as much material as possible before being captured themselves:

11 Bxe7 (or 11 Nxe4 Bxg5 and if then 12 Nxg5 Qxg5)
11 . . . Nxc3! (not Qxe7? 12 dxe4 1-0)
12 Bxd8 (or 12 dxe4 Qxe7)
12 . . . Nxd1 (certainly not Rxd8?? and Black is down a Queen)
13 Rxd1 Rxd8 and Black remains a pawn up.

At the end White can instead play 13 Bxb6 Nxb2, but Black is still up a pawn and the desperado Knight escapes while the Bishop is in danger, e.g. 14 Bc7 (trying to restore material equality) Na4 15 Bxd6 Rd8 16 Bc7 Rd7 and the Bishop is trapped and lost.

Note that the engine already has Black up 1.1 pawns after 10 . . . h5?!, and 1.67 pawns after Nxe4!. That's probably because White is behind on development and needs several moves to castle; that's less of an issue after the Queens come off the board, though meanwhile Black also gains B for N.