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After playing the following game, Stockfish advised me to play ...Nxd2 after white played Nd2 (which I did not play during the game).
However, I am not sure why. Certainly, in the worst case, this is just an even exchange of material. But is there any point in that move beyond that? Wouldn't moving the knight back to g5 be better as it controls the center?
[fen "r1bqkb1r/ppp1pppp/2n5/8/3Pn3/2P5/PP1N2PP/R1BQKBNR b KQkq - 2 6"]
Computers have complex reasons for their move choices, however, in this position there is a simple rationale for exchanging knights.
You need to think of two factors: are pieces moving to better (or worse) squares, and tempo (who is to move).
In this position, if you play Nxd2, White gets to play Bxd2. So, you keep the move and White improves his bishop slightly and opens C1 for the rook. If you move the knight to f6, then nobody improves, but you lose the move. Note that you cannot play Ng5 because of h4.
In this position losing tempo would be less desirable because White can use his move to play Ngf3 which stops you from playing e5! which is the key move in this position. If you keep tempo, then you can play 1...Nxd2 2. Bxd2 e5! This will improve your position by allowing you to challenge the center.
If you play Nf6 and White stops e5 by playing Ngf3, then White definitely has the advantage because of having more places to put his pieces by virtue of controlling the center. You could easily find yourself in a lost position if White continues to dominate the center.
You are a Pawn up, so it is generally to your advantage to exchange pieces and head for the endgame.
You dont control a great deal of space. If you retreat ..Nf6, your pieces will get in each others way. Exchanging helps to free your game,
White hopes for an attack to compensate his lost Pawn. Exchanging gives him less to attack with
You dont have much choice. Ng5 does not lose the Knight, but it has no strong stable square to go to. It is just a liability. ..Bf5 might be playable, but you get pushed around after Bd3.
You dont have much to worry about. After ,,Nxd2 Bxd2 Bf5 you have no weaknesses and easy development. e6, Bd6, Nf6, 0-0, c5 are all natural and good and you cant really be prevented from playing them.
