I'm playing white and I've been unable to get the black king out of the corner. Does black have a guaranteed stalemate or is there some way to force him out the corner?
[fen "5K1k/6R1/7P/8/8/8/2b5/8 w - - 0 1"]
2 Answers
This position is in fact drawn (which you can confirm e.g. by looking the position up in an online endgame tablebase). The key for Black's defense is to maintain the bishop on the b1-h7 diagonal, which prevents White from doing things like (1) moving the king to g6 (for threatening an eighth rank mate) or (2) pushing the pawn to h7 to threaten checking the black king out of h8 and queening the pawn. Black is able to keep the bishop on this diagonal, or at least be able to come back to it after moving away, and this keeps White from making any progress.
Here is just one line illustrating how White could win if Black were to go wrong with the placement of the bishop. After 1...Ba4?? White has a won position, but only by the move 2.Rg2! which keeps the bishop from returning to its defensively optimal diagonal. And that's the idea behind White's play in the rest of the line given: keep the bishop from coming back to that diagonal (e.g. with 4.Re2, 5.Rd2, 10.Re5 denying the bishop's return) until it's too late and the pawn push has already been arranged.
[fen "5K1k/6R1/7P/8/8/8/2b5/8 w - - 0 1"]
1.Kf7 Ba4?? 2.Rg2! Bb3+ 3.Kf6 Bd5 4.Re2 Bc4 5.Rd2 Bb5 6.Rd4 Bc6 7.Kg5 Bb5 8.Rd8+ Kh7 9.Rd5 Bc6 10.Re5 Ba4 11.Re7+ Kh8 12.h7 Bc2 13.Kh6 1-0
Draw. The white king can never occupy g6/7/8, and thus there is no way to attack both h7 & h8 at the same time, thus no way to chase the black king off the h file, nor any way to support the advance of the pawn to h7, which much be covered twice for it to advance as the black bishop can stay on that diagonal.
h4instead ofh6. In this endgame you need to chase the king out of the corner before advancing the pawn across the middle line.