when is it a bad idea to trade a bishop or a knight for 3 pawns?

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Shivsky

In the opening or middle-game, where piece-play dictates the game, I would rather have a piece than the three pawns. In an endgame, I would prefer the pawns if they were connected and/or advanced far enough.

Once again, it is suicidal to rely on a catch-all thumb rule for a material-imbalance condition such as this, but it helps to know that the different stages of the game indicate a different way to look at the material on the board.

Elubas

I can give some general rules, but don't cling on to them as if your life depended on it. If there's nothing special about the pawns you're getting, then they probably won't be too dangerous and the side with extra force could probably end up winning some of them. So I think it's more likely the piece will be better.

A situation that would be good for the three pawns is if they're far advanced, connected (preferably) central, mobile, well supported, and are passed or could become passed. In that case the pieces would probably be pushed back and the piece would be of much less value, meanwhile the three pawns are a big threat. They also often have more potential in an endgame, simply because a big part of the endgame is getting the pawns pushed, so there would be a lot of time for that. But they need to be mobile; if they're not mobile that's not good.

Blackadder

As pointed out: you cannot rely on any rule of thumb, instead, I'll give you a list of stuff to think about before making such a trade:

 

  • Consider the remaining peices/material balence:  a 3pawn+K vs B+K endgame, for example, is always going to favour the pawns (the best a bishop could possibly do is draw). On the other hand, if Rooks, Queens, etc are alive and kicking then you might miss the peice.
  • Consider pawn structure: three isolated trippled pawns are probably going to be more of a weakness than there are a strength.
  • Consider pawn structure in relation to the remaining peices: For example, if the position is closed then you might miss trading your only knight. Can your pawns be blockaded and/or can you defend them? And what if the 3 p 4 bishop trade opens files for their peices (which you cannot contest)?...you might end up with two useless rooks!
  • Consider how advanced the pawns are and where the enemy king is: two very advanced pawns can overpower a rook, however, it is also true that advanced pawns can be a liability (hard to defend), thus you need to work out how vunerable or threatening your pawns will be.
  • Consider what you are giving up: while a bishop for three pawns might not always be a great idea, a "bad-bishop" for 3 pawns is probably going to be, in most circumstances, a good idea.
  • Consider weather those pawn are going to be dangerous: If those 3 pawns are passed and conected, trading a bishop for them is probably a good idea, but on the other hand, if those pawns where threatening (or likely to threaten) nothing then what was the point? (i.e if He has isolated trippled pawns do you really want to give up a bishop or knight for that?)