Queen plus pawns versus Rook plus Bishop plus pawns, Part 2 [UPDATED]

Update is below the fold.

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.

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.

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.

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.

(This part has been redone.)


My initial winning try was INCORRECT! In the original line, Garry and I both missed the key move in this line, which is 5 a4!! (Note that this time I haven't attached any analytical marks. That's because I'm not clear enough on all the moves yet to use the Nunn Convention, which is my preference for endgames.)

The problem, though, is that Black has a much better second move: 2 ... Be5! Black will then be able to build a fortress, e.g. 3 Qe8 Bb8 4 Qe4 Rc7+ 5 Kd8 b6 etc. Oops!

(Last night I forgot to look at this line, so I initially posted that our first attempt had been correct. Not so. Thanks to Jim McTigue for pointing this out tonight at the club.)

Here was the first, incorrect attempt.

However, the initial position IS winning. White can force the exchange of R+B for the Q without allowing Black the opportunity for ... Be5. Instead of 2 Qc8, White plays 2 Qg7! Now the rook is attacked along the diagonal, so the bishop can't move to e5 to protect the rook. The main line runs: 2 ... Rc4 3 Kc8 b5 4 Qxc7+ Rxc7+ 5 Kxc7 a5 6 a4, as in the earlier failed solution.

The rook can't leave the c-file without dropping the bishop, save for the g3 square. But 2 ... Rg3 runs into 3 Qf6 and now either the bishop falls or retreats to b8 which offers no salvation: 3 ... Bb8 4 Kc6 Ka8 5 Kxb6 and Black is helpless

This position gives some idea of how the win might be achieved, but Black can play better between the position at the top of the column and the one at the start of the study. In the study White starts off in almost an ideal situation with regards to the placement of both Kings and all the other pieces. That isn't so in the position at the top. Maybe some database research will turn up similar examples, so we can figure out if there is a winning procedure, or if each case is largely independent.