| AylerKupp: <coolconundrum> Here is an unnecessarily detailed answer (I can’t help it, it's my nature), and if all you have is a hammer everything looks like a nail. First, of course, White has to win the black bishop (and there is more than one way to do that) and then he has to mate the Black king. After White succeeds in winning the Black bishop in exchange for the White d-pawn, there are only 6 pieces left and so the winning procedure can be determined by the 6-piece Nalimov tablebases This is the position after 45.Bg6:
click for larger viewHere is the earliest that the 3 engines suggest in their Principal Variation (best play by both sides), that White win the Black bishop: Houdini 4, d=13: 45...Bc8 46.Kf4 Kg8 47.Ke5 Bg4 48.Kd5 Bd7 49.Kc5 Kf8 50.Kb6 Be6 51.Kc7 Kg8 52.d7 Bxd7 53.Kxd7
click for larger viewKomodo 9.02, d=36: 45...Kg8 46.Kf4 Kf8 47.Ke5 Bg4 48.Kd4 Bd1 49.Kd5 (49.Kc5 shortens the line by one move) 49...Bf3+ 50.Kc5 Bg2 51.Kb6 Bh3 52.Kc7 Kg8 53.d7 Bxd7 54.Kxd7
click for larger viewStockfish 6, d=18: 45...Kg8 46.Kf3 Kf8 47.Ke4 Bg4 48.Kd4 Be6 49.Kc5 Bd7 50.Kb6 Bh3 51.Kc7 Bg4 52.d7 Bxd7 53.Kxd7
click for larger viewSo all 3 engines arrived at essentially the same position, except that Stockfish ends with the Black king on f8 and Houdini and Komodo end with the Black king on g8. And Komodo could have shortened its move sequence by 49.Kc5 instead of 49.Kd5, arriving at its final position on move 53 instead of move 54. And here is how the Nalimov tablebases then indicate the quickest way for White to win following the winning of the Black bishop by each of the 3 engines. There is a stalemate possibility that might succeed if White is in terrible time trouble (or maybe not, remember Hammer's 74.Kc6 against Topalov): Houdini and (improved sequence) Komodo: Mate in 9 moves: 53...Kf8 54.Ke6 Kg8 55.Ke7 Kh8 56.Ke8 (of course not 56.Kf8?? – stalemate!) 56...Kg8 57.Bf7+ Kh8 58.Kf8 Kh7 59.Bg8+ Kh8 60.Kf7 g6 61.hxg6 h5 62.g7#
click for larger viewStockfish: Mate in 9 moves: 53...Kg8 54.Ke8 Kh8 55.Ke7 Kg8 56.Bf7+ Kh8 57.Kf8 Kh7 58.Bg8+ Kh8 59.Kf7 g6 60.hxg6 h5 61.g7# - same final position as above So, to answer your original question, a winning approach from the final position (there may be others) is: 1. Bring the White king to c7, preferably along the dark squares only. 2. Advance the d-pawn and, after the forced ...Bxd7, capture the bishop with the king. 3. Force the Black king to h8 with the White king on f7 and bishop on g8, avoiding the stalemate by Ke7-f8?? . This leaves Black in zugswang with no choice but to advance its g-pawn. 4. After either ...g6 or ...g5, hxg6 followed by g7#. And I suppose that the winning engine is Stockfish since it found the mate one move earlier than either Houdini or Komodo, although it took Stockfish on my computer at least half a second to win the Black bishop in its Principal Variation while it took Houdini less than half a second to accomplish the same thing. | 
Kibitzing
