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The opening shown here is quite common. Is it generally a good or a bad idea to give up a kKnight and a bishop for the castled Rook and the f-pawn? In terms of their "standard" value, both pairs are generally considered as being worth 6 points.
[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1.e4 e5 2.Nf3 Nf6 3.Bc4 Bc5 4.Ng5 O-O 5.Nxf7 Rxf7 6.Bxf7+ Kxf7
This whole sequence is bad for white. The minor pieces are stronger at such an early stage of the game. White has virtually no development, while black now has more development and tempo. Almost any player should value 2 pieces over 1 rook. Just continue developing instead of the overly optimistic Ng5.
This may be acceptable in the dilworth attack or Open Ruy Lopez where black sacrifices 2 pieces for a rook on f2
That early in the game, it's a bad idea. White is now very behind in development and won't be able to take advantage of the misplaced black king.
Consider this: black is ahead by the ♞f6 and the ♝c5. White is ahead by the ♖a1 and ♙f2. Which pieces are the most useful? Black's, definitely.
I think this exchange is considered inferior in most cases, that is, it's a good idea when it leads to a powerful attack on the lone king, but no less. It'll often be easy for Black to capture the pawn back, with his “piece advantage”.
I do enjoy these exchanges, as they tend to unbalance the games (and I hate draws), but it's only a reasonable option if White's rooks can be quickly put to good use.
An interesting line after the Sozin attack (or Fischer attack) 6.Bc4 in the Scheveningen has gained popularity in the last years, and presents a similar concept:
[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 e6 6. Bc4 Be7 7. Bb3 O-O 8. Be3 Nbd7 9. Bxe6 fxe6 10. Nxe6 Qa5 11. Nxf8 Bxf8
The sacrifice of two smaller pieces for a Rook and two pawns is not uncommon and the position reached after the exchange proposed here is considered "dynamically balanced"
The mere "pawn value" is not enough to determine which side is better, one has to take into consideration the positional (relative) value of the remaining pieces.
A knight and bishop together are worth SEVEN points, not six, at least in early part of the game because of the synergies. (Or, if you will three and half for the minor pieces).
Also, to make this sequence work, the knight and bishop make more moves, so White is actually sacrificing MOVES. Note that Black has two pieces developed, White none.
World Champion JR Capablanca once let E Canal exchange a rook and pawn for a bishop and knight and still won the endgame. But this was because the exchange of queens was forced as a result, increasing the power of Black's rook.
And then he was Capablanca.
