From the Complex to the Simple

Here's a theoretical position that I encountered in one of my recent games. Is it a win or a draw? That depends on which side is to move.

If Black is on move, it's a draw. The move 1...b6 (or 1...b5) practically forces the exchange of Pawns. White can't catch the a-Pawn with the King, because it's outside the Pawn's square.

If White is on move, it's a win for White, despite the a-Pawn of the wrong color for the Bishop. White eventually confines the Black King to the corner square with the Bishop on the a7-g1 diagonal and the King on c7. The ensuing zugzwang forces Black to move the b-Pawn, when it's quickly over.

Note that with White on move, the zugzwang only works because the Bishop is on the dark squares. With Bishop on the light squares, the game is drawn.

Another surprising point is that White to move can win if the King starts on h1. While 1.Kg1, reaching the diagram with Black to move, doesn't work, the move 1.Kg2 sets up another maneuver which works because the Bishop is on the long diagonal. After 1...b6, White can stop the a-Pawn with the Bishop because the White King arrives just in time to take over the defense of the b-Pawn.

These observations allowed me to resolve more complicated positions. Reducing from the complex to the simple is one of the basic tools for endgame play.