If you trade a piece for 3 pawns my guess is that your looking for an endgame where your pawns will be worth more , so why would white trade down . It's hard to say anything without the game can you post it?
3 pawns vs piece
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its more games but they follow the same theme i will post theme later.and seeing now its two pawns for a piece but there are double isolated a pawns.
But until then who is the side with the piece supposed to win.
Three connected passed pawns are easily worth a minor piece , even a Rook if they are advanced up the board a bit. .
Three scattered pawns that are either blocked or backward ain't worth a popcorn fart.
All depends on the value of the pawns vs the piece, whichever one is better has the advantage and what phase the game is in could have an impact on the value aswell . What dodger said too . You might want to look at this game where blacks connected passed pawns vs the piece wins http://www.chessgames.com/perl/chessgame?gid=1753385
in the slav defence there is a sacrfice a bishop for three pawns and to top it all of white dosent have a queen then he is playing for a draw but he can force a draw a move earlier with Qf3 i can see that white often wins in that varition how does he win.And here is one of the games i was looking at http://chess-db.com/public/game.jsp?id=3012567109.1400142.139181824.21344
Hi i was analayzing games where black sacrifice a piece for 3pawns and came to the conclusion that white first blockades the pawn next he exchanges pieces and then tries to pick them up one by one any thought