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Anyone would sacrifice their queen if it meant an irresistible mate. It's one of the most beautiful ways of winning a chess game. And the earlier in the game, certainly the more amazed we are at the player's brilliance. But if mate is not irresistible, what and when would you trade your queen for, confident it's a winning move. In general, a queen is worth 9 pawns, a rook is worth 5 pawns, and our minor pieces (bishop and knight) worth three pawns, although earlier in the game they can be valued as 3.5 pawns. Towards the end game, pawns and rooks increase in value. So generally speaking, you would not want to trade your queen for just two pieces, unless of course you gained a favorable position. Three pieces? Yea, I'd trade for three pieces. Here's a game where I did just that.
[Event "Live Chess"] [Site "Chess.com"] [Date "2015.12.05"] [White "Hannahdog22"] [Black "Pontiac49"] [Result "1-0"] [WhiteElo "1373"] [BlackElo "1404"] [TimeControl "15|10"] [Termination "Hannahdog22 won by resignation"] 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 b5 5.Bb3 h6 6.O-O Nf6 7.Re1 Be7 8.c3 d6 9.h3 O-O 10.d4 exd4 11.cxd4 Bb7 12.Bc2 Nb4 13.e5 Nxc2 14.Qxc2 dxe5 15.dxe5 Be4 16.exf6 Bxc2 17.fxe7 Qd3 18.exf8=R+ Kxf8 19.Ne5 Qf5 20.g4 Qe6 21.Bd2 f6 22.Ng6+ Kf7 1-0