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Draw I think.
f5ch might win as the king must retreat (if Bxf5 then Nh4ch wins the bishop without black having the prospect of winning or exchanging the white pawn) and then f6 etc. it is difficult to see black keeping his bishop
f5+ Bxf5 draw.
To expand a bit on Susan's comment:1. f5? Bf5!2. Nh4 Kg5!3. Nf5 h5!And your mission, should you choose to accept it, is to show how white can make progress. If white moves the knight to any square other than h4, black can push h4 to force the exchange of the last white pawn, and if white plays 4.Nh4, black puts the king on g4 and retreats to g5 when white puts the knight back on f5 to protect the pawn. For illustration:4. Nh4 Kg45. Nf5 Kg5 etc.Finally,4. Ke4 Kg45. Ke5 Kg5 etc.This is clearly drawn after 1.f5.
I have to say, right now I don't see a way for white to win this. White can check from h4 on the first move, and I think black has to put the king on h5 which allows f5 and f6:1. Nh4 Kh5 (K to 7th rank 2.f5)2. f5 Kg5 (keeping eye on f6)3. f6 Bc4 (forced)Now, can white make progress from here? If he moves the knight, the black king regains access to g6, and he can't move the king without losing the f-pawn, so I think this line is drawn.Now, I can't see how other knight moves at move 1 will really help, so I think we are left with king moves and g4:1. Ke6 Bf5Black may well have other moves here that are better, but the idea behind Bf5 is drive the king away from supporting f5, if white returns to Ke5, then he makes no progress in this line:2. Ke7 Be43. Nh4 Kh5! (clearly only move)4. f5 Kg4 (or Bd5 ok?)5. f6 Bd56. Ng2I see nothing better here for white. He can win the bishop with f7, but will drop the g3 pawn and all winning chances. Continuing:6. .....Kg37. Ne3 Bb38. Nf5 Kg49. Nh6 Kg510.Nf7 Kg611.Ne5 Kg512.Nc6Aiming to bring the knight to e6, but.....12. ....Bd513.Nd4 Bg8! and I just don't see how white can ever advance that pawn safely.If there is a win, I am missing it right now.
I went to chessbomb, and white played 1.f5 here and the draw was soon agreed to. The chess engine suggested 1.Nd2 here, and evaluates that line as +1.35 for white, but if you play that line out to the end, it basically finds positions similar to the ones I think are drawn, and I verified the final position on that line is drawn in the Nalimov tablebase (white has given up the second pawn so it is reduced to a 6 man problem. My final verdict is draw.
This is a draw. White can get a position with the knight vs. king and pawn, or king and pawn vs. king and pawn without the proper opposition, or a KPNKPB in which the f pawn's advance is completely blocked. All of these are drawn.
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