Typical Good Bishop vs. Bad Bishop endgame - how to decide if stronger side has a definite win Black here has 3 weak pawns; if any one of them falls - he will very likely lose the game as well. If he lets White king break through via c4-c5(d5) - White will also likely win. c5 pawn is a passed pawn, but is not going anywhere. Evaluations like "White is better" are not precise enough - is it possible via analysis to prove that White definitely wins? Or that Black definitely holds? Variations or plans for both sides are welcome.

White to move:

2k5/5b2/p7/P1p2p1p/P4P1P/2K2B2/8/8 w - - 0 64
With new analysis from user AlwaysLearningNewStuff, we can conclude this is a win for white,

The first critical position appears after 1.Be2 Kb7.          

      [FEN "2k5/5b2/p7/P1p2p1p/P4P1P/2K2B2/8/8 w - - 0 1"]

       1.Be2 Kb7


Black defends everything at the moment, but the only moves that keep the position are Kb7-a7-b7. A simple triangle maneuver puts black in zugzwang.

     [FEN "2k5/5b2/p7/P1p2p1p/P4P1P/2K2B2/8/8 w - - 0 1"]

       1.Be2 Kb7 2.Kd2 Ka7 3.Kc2 Kb7 4.Kc3 


Now black is in zugzwang and loses. The following lines illustrate this:

[FEN "2k5/5b2/p7/P1p2p1p/P4P1P/2K2B2/8/8 w - - 0 1"]

1.Be2 Kb7 2.Kd2 Ka7 3.Kc2!+- Kb7 4.Kc3 ( 4...Ka7 5.Bc4 Be8 ( 5...Bg6 6.Be6 Kb7 7.Kc4 Kc6 8.Bd5+ Kd6 9.Bb7+- Bf7+ 10.Kd3 )( 5...Bxc4 6.Kxc4 Kb7 7.Kxc5+- ) 6.Be6 Bg6 7.Kc4 Kb7 8.Kxc5+- )( 4...Bg6 5.Bf3+! Kc7 6.Kc4 Kd6 7.Bb7+- Bf7+ 8.Kd3 )( 4...Be8 5.Kc4 Kc6 6. Bf3+ Kd6 7.Bb7+- Bf7+ 8.Kd3 ) c4! 5.Kd4! ( 5.Bxc4? Bxc4 6.Kxc4 Kc6= ) 5...Kc7 ( 5...Kc6? 6.Bxc4 Bxc4 7.Kxc4+- )( 5...Kc8? 6.Bxc4+- Bxc4 7.Kxc4 Kc7 8.Kc5 ) 6.Bf3! Kc8 7.Bd1!!+- Kc7 ( 7...Kd7 8.Bc2! Be6 9.Ke5+-)( 7...Kb7? 8.Bc2! Be6 9.Ke5 Bd7 ( 8... Bg8 9.Bxf5+- ) 10.Kd5!+- ) 8.Bc2! Be6 9.Ke5 Kd7 ( 9...Bd7 10.Kd5!+- ) 10.Bd1! Bf7 11.Kxf5 Kd6 12.Kf6!+-


The important idea is that after 4...c4! White uses 6.Bf3! to restrict Black king. After 6...Kc8 White repositions Bishop on c2 with the move 7.Bd1!! so the decisive zugzwang can be achieved. After 12.Kf6! the rest is a matter of technique.

The analysis is kept as brief as possible in order to preserve space, since the rest of the winning moves can be easily found with an engine.