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Saturday, June 12, 2010

Revisiting Minor Pieces for a Rook - Part 1

I’ve posted on this before as to why it’s generally not a good idea to trade 2 minor pieces (usually a B and N) for a R and P early in the game. The person trading the 2 minor pieces most likely won’t have enough pieces left to conduct a winning attack. The R’s gain a little in strength in the ending though. Of course a lot depends on the number of Pawns.

Purdy can explain it far better than I can and I’m going to let him do so. It’s a little hard to grasp on the first reading and will require some careful thought. Anyway, the reason I’m posting it again is because I just played a 10 minute game where my opponent sacrificed a B and N for a R and P then quickly succumbed to an attack against his K.

When I went over the game with Fritz, it didn’t really suggest any major improvements for me, but in practical play, I kind of disagree with its evaluation as being over 3 points in my favor. I’m not Fritz and it’s entirely possible my play would not have held up in the ending if White had found the correct defense. I give the game because it shows how difficult these positions are to play even if you know how things should shake out!

First Purdy’s explanation, then the game.

The main facts are:

1) In the opening, two Minor Pieces (excluding two B’s) are normally equivalent to a R and two P’s. Two B’s are roughly equal to 2 and a half P’s.

2) In an end-game with P’s but no additional pieces the superiority of the two Minor Pieces (excluding two B’s) over the R’s is less than one P. For two mobile B’s, add nearly a P

So the difference in value (except for two B) decreases by more than a P as exchanges proceed!

The R has least worth in the opening because he is hard to develop. To induce the enemy to give up two pieces for a R and two P’s is usually fairly good business in the opening.

But the biggest jump occurs with the last exchange of pieces just before the ending described in 2) is reached. In other words, add even one piece to each side and the minor pieces' faculty for combining with other forces will appreciably increase their value. Indeed, Fine says in Basic Chess Endings:

"Three pieces versus two Rooks (equal pawns) is normally a draw, but in favor of the pieces because they have more play."

That is true for two B’s and N, the only combination that Fine gives by way of illustration. Two N’s and B are not quite so good; but even if they are barely equal to two R’s in an endgame, that shows that the third piece strengthens its fellows by appreciably more than the endgame value of one minor piece (three P’s). In other words-and this is the great point to remember-

B and N or two N’s without other pieces, are usually a poor team. The two Minor Pieces are much better in combination with at least one other piece.

In BCE, Fine makes the following statements which do not quite tie up.

A) "In the ending, two minor pieces are approximately equivalent to Rook and one pawn."

B) "Rook vs. two minor pieces (equal pawns) will usually be a draw, but tbe two pieces will win more often than the Rook."

If the difference were really about equal to a P on the average, Fine would have to say the ending is usually a win for the pieces. Clearly, a draw might occur fairly often; but a win for the R would be so infrequent as to make the second clause of B) a manifest understatement.

Which statement is slightly out, A) or B)? Probably both-i.e. A) slightly overstates the value of the pieces, whereas B) slightly overstates the value of the R. All of Fine's other remarks and his illustrative positions would tie up better had he changed A) and B) to A1) and B1). Thus:

A1): Substitute our Proposition 2) at the beginning of this article.

B1) R vs. two minor pieces (excluding two B’s) with equal P’s (P’s on both wings) ends in a draw or in a win for the two pieces with about equal frequency. The R may win in very favorable circumstances.

One cannot, of course, reduce chess to arithmetic. In all this, we are speaking in averages. Weak P’s on either side, badly placed pieces, and so forth, are likely to turn the scale; but nevertheless, a knowledge of the average values is a necessary starting point for forming a judgment in any given position.

Got all that? Good! The short version is: it's hardly ever a good idea to trade a B and N for R and P early in the opening. Now take a look at the game in Part 2.

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