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In some openings, i.e. the Stonewall Attack / Maroczy Bind, the opponent gets an iron grip over a particular square (e5 / d5) by controlling it with two pawns, and they can stick a knight there. People are often very reluctant to trade this knight off, even if it's a very powerful piece that controls a lot of squares in the opponent's territory. In concrete terms, why would trading off for the knight (via capturing on e5 / d5) generally be bad for Black?

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  • Connected passed pawn?
    – user27142
    May 21, 2021 at 17:58
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    Chess is not that simple. There is no answer to that type of question. If there were, you'd be able to buy a book titled something like "The Strategic Principles of Chess" and you'd become a Grandmaster after you read it. Unfortuantely, there's no meaningful answer that doesn't boil down to "when it's good for your position".
    – David
    May 21, 2021 at 18:53

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Then only strategically relevant reason, that could reasonably be attached to the concept you presented, is in my opionion, that the subsequent change of the pawn structure is unfavourable for the defender. Reasons would vary wildly with the concrete pawn structure. E.g.:

  • In the maroczy structure white may play Nd5 after preparation and if black captures the knight, white can capture with the e-pawn and make the e7 pawn backwards. Or white captures with the c-pawn, opening the c-file because he suddenly can invade over it.

  • In the stonewall structure black plays often Ne4 and if white would take, black would normally recapture with the f-pawn, having a half open f-file and driving a knight on f3 away. This may lead to an attack or if not that could force white to take prophylactic measures with f3, leading possibly to simplifications. Hence white often avoids the exchange altogether and prepares to kick the knight with f3 and a further e4.

  • If white has an isolani on d4, he often play Ne5 or even Nc5. If the knight is taken on c5, this leads to a passer. If the knight is taken on e5, white strenghten his pawns and again may become attacking chances.

Your questions makes absolutely sense to me, but if you want to study chess seriously you can only answer it in on a case by case basis. Stockfish is your friend.

Old FM Roese at your service (https://lichess.org/@/fiskaren)

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  • Since "only" is a bit harsh ;-): Just assume that the black-square bishop captures, g6 already has been played and the white black-square bishop becomes a monster on f6 (Black has only the white-square bishop). Then rather a monster on e5... May 22, 2021 at 9:15
  • It is (deliberately thaught) provoking written and rest assured i am very well aware of the dangers of field weakness and of many other problems a mere trade could have. It is just so, that in my opinion, this problems should not(!) be directly attached to the concept of "outpost" but merely to the concept of "trade" and subsequently should not be discussed in this context. Also consider that i have emphasized that every position must be considered only(!) on a case by case basis and i mean it.
    – user27863
    May 22, 2021 at 9:56

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