TWO MINOR PIECES vs. ROOK AND PAWN(S)
All of the above applies with even more force to the case of two minor pieces vs. rook and pawns; the side with the rook wants very much to trade major pieces, even if he is a bit behind in material. Why this should be so is subject to debate; my explanation is that having more than one major piece is somewhat redundant - in many games there may only be time to employ one major piece on an open rank or file. Having at least one major piece (preferably a rook) to bring to an open line may be critical, but having two may be wasteful.
All in all, this section is a very important one; imbalances involving the Exchange are fairly common, and the effect of major piece trades on the evaluation is quite significant. While nearly everyone above novice level knows the value of the bishp pair, I suspect that even many masters are unaware of the above "principle of the redundancy of major pieces." As for rook and knight vs. two bishops and pawn, with nothing else but pawns on the board, the rook's side has a mild advantage, but add a rook to each side and the game is dead even. In general, with other pieces on the board, this imbalance should be considered even, with only a trivial edge for the rook's side.
How about the common situation of rook and pawn(s) vs. two minor pieces? My data shows equilibrium at 1½ pawns (slightly less when both minors are knights), assuming no bishop pair advantage. When the side with the minors has the bishop pair advantage, two pawn makes things about even (slightly better for the rook's side if he has one bishop, slightly worse if he has none).
For a good example of the accuracy of this statement, look up the main line of the Dilworth variation of the Open Ruy in any opening book. I think this evaluations are in agreement with the majority of grandmaster comments. As in the case of the Exchange, extra major pieces favor the minors, as do extra pawns. Here too we can adjust the fair value down by a quarter pawn when queens and one rook have been exchanged and up by a quarter when no major pieces have been traded.
By illustration, after 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.O-O Nf6 5.Ng5? O-O 6.Nxf7? (often seen in novice games) 6...Rf7 7.Bxf7+ Kxf7 material is even by traditional count, but the above considerations put Black a pawn and a quarter ahead, which is a fair assessment of the true [DH: material] situation. Actually the situation is even worse for White because no pawns have been exchanged, so the rooks' relative value is less than the average value would indicate. I have seen this exchange criticized on the grounds that White is trading off his developed pieces, but in my opinion this explanation is almost totally wrong, since the exposure of Black's king roughly compensates for the loss of a tempo or two by White [Here I must disagree with Larry. In fact, if anything White's king is in more danger since the open f-file gives the Black rook access to the kingside and Black has far more pieces ready to attack White's king, which is a primary reason for a king's lack of safety! And White lost more than a tempo, more like two or three since it took five bishop and knight moves to make the captures and Black did not lose a tempo with castling and only made two capturing moves with his rook and king. I discuss this position also with, of course, a similar conclusion to Larry's in my Novice Nook A Counting Primer.]
http://home.comcast.net/~danheisman/Articles/evaluation_of_material_imbalance.htm
17 Dec '09 14:55
rook and a pawn for a knight and a bishop
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