In the previous post I presented an endgame study. The solution is below the fold. First a digression on this type endgame. The original position was
It was White to play, though that's probably not critical for assessing the position. We thought this was probably a draw, as it looks like Black should be able to construct a fortress easily enough. But we decided to consult Garry's 2003 revised edition of Reuben Fine's Basic Chess Endings. The section "Queen vs. Rook and One Minor Piece" said the following:
Without Pawns the ending is a draw, though it is to be expected that there will be problem positions where one side or the other may win.He then follows it up with three examples, all of which have pawns on both sides of the board, or asymmetric pawns. Thus they were all useless for properly assessing our situation.
With Pawns, the Queen is equivalent to R+B+P. If the Pawns are even, the Queen will win (though not without difficulty); but R, B and two pawns are required to conquer the Q.
Where the pawns are even, the win is easier for the Q if they are not balanced. For then the superior side will be able to set up a passed Pawn and capture one of the opponent's pieces or tie him up so badly that some other part of the board will be defenseless.
When I got home, I checked Muller & Lamprecht's Fundamental Chess Endings, but that book was silent on the issue, as were Dvoretsky's Endgame Manual and Paul Keres's Practical Chess Endings. Fine states that this is a win, and in 2003 Benko agreed with him. No one else says anything about it. (If anyone can consult Averbakh's endgame encyclopedia, or something from Informant, let me know.) So how to go about winning a position like the one above? I have no idea if the R+B side plays correctly. Feel free to give it a try, and add any research in the comment section below. Alternately, present it at the club. But this one is a bear.
I will also look in my database for similar positions, but not tonight as it's already passing 2am. Maybe Paul or Connor will do it for me!
Now for the solution to the study I gave in the previous post.