Black to move. Win or draw?
There are two equal winning lines. They are a6 and Ka3. I spent 40 minutes to work out the solution. I stumbled over the twelfth move. I had to repeat moves. The end of my solution is very beautiful. The white is in zugzwang and the black wins because of it.
It's a winning position for black.
I think 1.....Ka3 wins. It is possible that black can transpose with 1......a6, too, but I am not sure. The key, though, is a6- time is critical, and a6 does force the white king to go around through d5 if he wants to attack the a-pawn while drawing away the bishop with f8(Q). The line I gave above is the critical one, and it definitely wins- I verified in multiple lines after liquidating the white a-pawn. A very interesting ending!
Obviously, black cannot win with 1......Bxf4- while this exchanges down to a K vs K+P ending for black, as long as white makes black win the b-pawn up the board on b4 or b5, white's king can make it back to the corner. My first instinct was that this was drawn- it seemed to me on first glance that white would push the f-pawn through to f7 and then bring the king over to threaten the black a-pawn, but now I have some doubt. In some of the lines I am looking at, black might be able to work it that the pawn is on a6 rather than the more "obvious" a5, cutting off the b5 square to the white king while the bishop guards f8 and cuts off b4 and c5 thus costing white a tempo in getting to the a-pawn in time before black wins the queenside pawns and reconnects with his a-pawn. The line I am thinking of is 1.....Ka3 2.f5 a6! 3.Kd3 Bb4 4.Kc4 Be7. Needs more work, though- maybe white has a better defense than I see right now.