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Why is exchanging these knights the best move for white? I'm trying to understand how to get better with strategy and tactics.

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    You're winning a pawn – David Feb 12 at 13:41
  • subjectively/personally i find this like, even though an objectively good question (i upvoted), not a bad question but like a wrong question. or maybe a good question like better questions could be asked. i mean, white is already winning, and both moves are still winning for white, so who cares? i think it's better to ask about winning games that were lost/drawn or games that are about even and then there's particular move that swings the evaluation bar. i mean would you bother to continue analysing a game after a point where your opponent should've resigned already? of course in general... – BCLC Feb 13 at 14:15
  • ...you'll benefit from any analysis or question. but i believe we must maximise our benefit given our limited time to play. some questions/analysis may have more benefit than others (eh just some unsolicited non-professional advice) – BCLC Feb 13 at 14:17
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Despite the difference in evaluation, e4 is not really a mistake. White is a rook ahead and will win this game anyway, provided that they don't blunder. Perhaps Nxc4 leads to a victory a few moves faster, almost within the engine's search horizon; that's probably why the engine prefers it over e4.

However, even humans should prefer Nxc4. If you're this far ahead, you should exchange material; every exchange means less chance of threats from your opponent. A two-to-one advantage is much more decisive than an eight-to-seven. Black's knight is also more active than White's, that's another reason to exchange it. (That the engine indicates that Black should exchange knights after e4 is surprising, but it only underlines how bad Black's position actually is.)

The advice about exchanging when you're ahead is of course not a rule set in stone. You should always keep in mind the (potential) activity of the exchanged pieces. And if you're only a pawn ahead, that doesn't need to be decisive enough for the win. Rook endgames and endgames with opposite bishops are notoriously drawish, and there are more examples out there, but you don't have to worry about them for now.

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  • Should you really consider white a full rook ahead in this position? I feel that the bishop at h8 is basically dead. (But I do not play chess) – Taemyr Feb 12 at 7:53
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    @Taemyr: it's not at all dead, it isn't under attack and can safely go back to e5. – RemcoGerlich Feb 12 at 9:03
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    The engine isn't completely wrong. White exchanging knights isn't an exchange but wins a pawn outright as soon is the bishop is safe. – Joshua Feb 12 at 18:48
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    The engine is probably suggesting black exchange knights because it's an even exchange while allowing white to do so costs a pawn. – Loren Pechtel Feb 12 at 21:09
  • But why is trading with the only Knight the best option? I would rather keep a Knight and a Bishop than two Bishops. So I guess my question is, why is trading black's Knight with the Bishop not equally as good as trading with the Knight? – RoundHouse Feb 13 at 3:13
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Strategy aside, Nxc4 also simply wins another (center!) pawn, while developing the light squared bishop to a nice square (assisting to continue to attack Black's kingside).

On top of limiting Black's options for counterplay, as the other two answers correctly state.

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Look at the engine line! After your move, black voluntarily exchanges knights and plays ...f6, trapping your dark squared bishop. Now, white is still completely winning since you're up so much material and I don't see a direct way for black to try and win the bishop, but you're allowing black unnecessary ideas.

Instead, the suggested best line to play f4 after an exchange of knights forces Nf6 as there's no other way to defend the knight for black. Now you can trade bishop for knight, trading down even more material and getting you closer to a completely winning endgame. (You could also go Bxc4 first like the engine suggests, then trade the h8 bishop for knight later.)

This answer is not comprehensive, the other answers also raise excellent valid points, of course.

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e4 is still winning but not necessary because you are giving away the f4 square to Black's knight, which gives them some counterplay. There is no good reason to give f4 to your opponent.

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