Rook vs. Bishop: Ending 2
and the task was to determine how White is supposed to win.
It does look easy: all we need is get the rook to the back rank and it's mate! Black can use stalemate tricks, sure, but if we put the king on h6 and the rook on the 7th to protect the pawn (if we have to), what resources could Black have then? So let's try it:
Hitting the h7 pawn forces White to play 2.Ra7, because the pure rook vs. bishop ending is generally a trivial draw when the king is in a corner of the opposite color of his bishop.
and now, the key move:
This move isn't terrific because it's showy; its strength comes from its preventing White from repositioning the rook on a different file. It's also the only move: 2...Bc6? 3.Rf7; 2...Bd5? 3.Rd7, etc.
There's no other way to attempt progress: if the rook retreats, the bishop simply returns to e4.
3...Be4+ 4.Kf7 Kxh7=
J. Vancura, the composer of this 1924 study, gave the unnecessarily fancy but also more thematic 4...Bg6+ 5.Kf6 Bxh7 6.Ra8+ Bg8= as the continuation. It works too! And either way, 1.Kh6 fails to win - but then how could White have any winning ideas here at all?
A first clue comes if we consider the position after 1.Kh6? Be4! 2.Ra7 Bb7!! Since it's a mutual zugzwang, White's win, if it's possible, will involve some tempo-gaining maneuver. White needs to get the rook off the a-file, for starters, and to do so without dropping the h-pawn. He can't move the rook yet, though, because of 1...Be4+, either winning the pawn or leading to stalemate, so by process of elimination, we get this:
It's not at all clear how this wins, but it's at least certain that it doesn't hurt anything, as the obvious/familiar Black tries 1...Kxh7, 1...Be4 and 1...Kg7 lose to 2.Rh4+, 2.Rxe4 and 2.h8(Q)+ Kxh8 3.Rh4+ and 4.Rxh1, respectively.
Turning to subtler lines, carefree bishop moves demonstrate the winning procedure. Thus
(A) 1...Bc6 2.Rc4 Bb5 3.Rc7 Bd3 4.Kh6 Bf5 5.Rf7 wins.
(B) 1...Bd5 2.Rd4 Bc6 3.Kh6 Be8 4.Rd6 (zugzwang) Bd7 5.Rf6 wins.
(C) 1...Bb7 2.Rb4 Ba6 3.Kh6 Bc8 4.Rb6 Bb7 5.Rd6 wins.
In each case, White is able to win by improving the position of the rook, and that becomes possible by attacking the conveniently relocated bishop. So Black's best try involves playing hide and seek with the bishop:
Now what? Attacking the bishop on the g-file, in correspondence to the method of lines A-C, appears pointless, while 2.Kg6 Be4+ and 3...Bxh7 or 2.Kh6 Be4 3.Ra7 Bb7 both draw. Worse news still: if the rook leaves the fourth rank, then 2...Be4 wins the h-pawn, drawing.
Thus, even though it looks pointless, we see by process of elimination that White's only attempt is
Fortunately, it's also a good move! Black now has two options: to return the bishop to the h-file or not.
(i) 2...Bh3 3.Re4! (Taking advantage of Black's inability to capture on h7 when 4.Rh4+ would pick up the bishop) Bd7 4.Kh6 Be6 5.Rb4 Bc8 6.Rb6 (zugzwang) Bb7 7.Rd6 wins.
(ii) 2...Bc6 3.Kh6 Bd5 4.Rd4 wins.
Subtle? Yes. Difficult? Quite - but not impossible. But it's also elegant and instructive, and though the path to improvement comes not so much from mastering particular positions like this (though it's a component of one's skill), it does come (a) from the chess-specific cognitive development and (b) the feeling for the pieces one acquires by attempting to solve such positions. So if you haven't done so yet, give positions 3 and 4 a try before I present their solutions. It's worth it!