[Dark Knight]

THE EXCHANGE

Now let's move on to discussing the Exchange (rook for knight or unpaired bishop). My research puts its average value squarely at 1¾ pawns (a tiny bit more when its a knight). Most authors value the Exchange at either 2 (the standard value) or at 1½ (Siegbert Tarrasch, GM Edmar Mednis, GM Larry Evans), so my value is right in the middle. World Champion Tigran Petrosian actually claimed the Exchange was only worth one pawn, and former challenger David Bronstein said the same when the minor piece was a bishop, but in such cases the bishop pair is often involved. When the side down the Exchange has the bishop pair, my data shows he needs only 1.15 pawns to make things even; perhaps this case is what Petrosian and Bronstein had in mind.

I note for the record that the authors who put the Exchange at 1½ pawns are right on the money if they are averaging in the cases where the side down the Exchange has the bishop pair, but it think it is much better to regard the bishop pair as a separate component of the material balance.

TWO FACTORS

The value of the Exchange is influenced by two factors. First of all, the presence of more major pieces on the board favors the minor piece. In general, with no minor pieces traded, the Exchange value drops to 1½ pawns, and if the minor side has the bishop pair just one pawn makes things even. But with queens and a pair of rooks gone, the Exchange is worth slightly more than its nominal value of two pawns, or about 1½ when opposed by the bishop pair. Also important is the number of pawns on the board, especially when the minor piece is the knight. With most of the pawns on the board the Exchange is worth less; each pawn trade helps the rook. Rooks need open files!

So if you have a rook for a knight and two pawns, even though you are nominally a quarter pawn behind in material, you should try very hard to exchange major pieces, in contravention to the usual rule that the side ahead in material seeks exchanges. I had a game with USCF Executive Director Mike Cavallo in the World Open in which he sacrificed the Exchange for some compensation. I was not at all sure of victory until he allowed me to exchange the extra rooks, after which I won in just a few moves. Had he known this principle, he could have put up a good fight.

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.]

FAMOUS BRILLIANCY

I would like to make reference to a famous brilliancy by Kasparov against Shirov [DH: see 3rd game on linked page.] played in 1994. I consider it one of the greatest games ever because Kasparov sacrificed (successfully!) a full Exchange (rook for knight) for purely positional compensation. Any strong player would have made the sacrifice if it had been the Exchange for a pawn, since Kasparov was left with markedly better pieces and pawn structure, but it seemed to me (and probably to most other masters) that the compensation would not be worth nearly two pawns.

However, considering the principles of this article, since the queen and the extra pair of rooks remained on the board, and since only two pawns had been exchanged (with no files fully opened), the real value of the rook for knight exchange was only about a pawn and a quarter, and since the positional compensation did appear to be worth more than a pawn, I can now see that the sacrifice was at least reasonable, if not clearly favorable. Another example of the above principle is a game I lost in the 1972 U.S. (Closed) Championship to Greg DeFotis. I voluntarily exchanged two minor pieces for rook and two pawns with the queens off, thinking I was getting the better of the deal, and then didn't understand why I lost badly. Since he had the bishop pair, my above guidelines put the material even. Queens were off, which favored my side, but the extra rook pair was still on, which favored his side. One of my extra pawns was a rook's pawn, which favored him.

The decisive factor, which I didn't appreciate then was that all but one of my pawns remained on the board, which meant no open files and reduced value for my extra rook. So even though I was a pawn ahead by the traditional count, I was really behind in true material value, and that (along with Greg's excellent play) is why I lost.

THE QUEEN

Many books say that rook, minor piece, and pawn are equal to or even better than a queen, but Garry Kasparov wrote that the side without the queen must also have the bishop pair to claim equality, which agrees quite well with my statistics. When not opposed by the bishop pair, the queen is worth rook, minor piece, and 1½ pawns. The knight seems to be marginally better than the single bishop in assisting the rook against the queen.

As to which side benefits from the presence of an extra pair of rooks, Karpov wrote in Chess Life that the side without the queen definitely wants to keep the extra rooks on the board, but later when he actually found himself with rook and minor piece vs. queen against Kamsky in their title match both players acted as if the opposite were true. Probably the explanation was that the exchange of rooks makes thte game more drawish (see the 1996 game Topalov-Anand where Anand lost his queen and a pawn for rook and knight but managed to draw rather easily with the other rooks off the board), and since Kamsky was the only one with winning chances in that game. Karpov sought the rook exchange and Kamsky avoided it, ultimately winning.

My statistics mildly confirm Karpov's written statement. Roman Dzindzichashvili [DH: "Dzindzi"] told me that he believes the extra rooks tend to favor the queenless side because a pair of rooks can defend each other against the queen. Note that my principle of major piece redundancy does not help us in this case, since the extra rooks are redundant extra pieces for both sides. In general, if you have a queen you don't need rooks nearly as much as if you are queenless.