Rook versus Bishop

When I think that I understand something, I expect to be able to execute the maneuver in mere seconds. Sometimes, my understanding of the patterns is not strong enough. It is well-known that rook versus bishop is usually a draw, but that a few positions favor the rook. One such position is an exercise in my Essential Tactics: Building a Foundation for Chess Skill (2017).

White to move

The tactic is simple. 1.Kf6, forcing the bishop to move. But then, the finish takes me more time than I think it ought. I want to execute the moves to checkmate in ten seconds or less, but find that the calculation can require a minute or more. Each White move must contain a concrete threat of a) checkmate, b) capture of the bishop, or c) the final threat that pins the bishop on the back rank, creating zugzwang. One slip and a drawn bishop versus rook ending is reached.

In rare instances, usually with more pieces on the board, the bishop dominates the rook. This composed problem came to my notice via Mikhail Tal, and Victor Khenkin, Tal's Winning Chess Combinations (1979).

White to move

White need only check the king from a square where the bishop cannot be captured. Alas, both the immediate 1.Bh3 and 1.Bg4 fail. A zwischenzug is necessary to divert the rook from control of these squares.