White to move. Is it possible for White to win in this position?
8/8/8/8/p3K3/Pb6/5k2/7R w – – 0 2
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I believe white can win, starting with 1. Rh2+, thereby constricting the white black king on either the 1. rank or the g-file, whichever black prefers. After the black king is thus cut off sufficiently far the white king will go to the queenside to take the pawn. As far as I can see, with the black king on the g-file, the white rook will have enough time to come take the pawn: White king on a4, white pawn on a3, and the black king on either f-file or 2nd rank with black to move, black cannot stop white from queening the pawn.
No, g-file isn’t far enough. Instead, I think white wins starting by
1. Rh2+ Kg3
2. Rd2! but I must hurry and cannot calculate it yet.
The idea above is:
1. Rh2+ Kg3
2. Rd2! Be6
3. Rd4 Bb3
4. Rb4 Bc2
5. Kd2 Bb3
6. Rxb3 axb3
7. a4 and now it cannot be stopped.
Sorry I forgot to insert the move Ke3 in that, but triangulations will see the final position emerge… =)
1.Rh2+ Ke1
…
1.Rh3
Both 1.Rh2+ and 1.Rh3 win, as do ten of White’s seventeen other legal moves.
a) Find the only move for White which loses.
b) Find the only White king move which doesn’t win.
black needs either to occupy c4 sq after white takes the pawn or get to a8
1. rh2+
if 1… ke1, the the things are straightforward (keep black the king on the first rank, approach the pawn and win)
1… kg3; after rd2-d4 black either (a) keeps the bishop on a4-d1 diagonal (b) retreats to e8
(a) we reach a zugzwang position w: kd2 rb4; b: kf3 bb3 and win (black king must move out of the square of the pwn and rxb3)
(b) there is a chance to win a tempo 2. rd2 bf7 3. rd4 be8 4. kd3 kf3 (or kf2) 5. rd8 bc6 6. rf8 kg3 and white approachs the pawn and wins
if black moves his king to g5 or g6 (to reach a8 sq after the exchange) it turns out that the diagonal is too short and white wins with pushes the bishop out (cause either b5 or c6 sq will be unaccessibel rof the bishop because of pin or fork)
White can win easily as many people have already mentioned. There are a lot of ways to do it. Basically because of the position of Black’s king any exchange of R for B + P will lead to a win for White. For a much more difficult example of this endgame see this Chessbase article by GM Marin