Defending in the endgame

Black to move

a) How would you evaluate the position? Can black draw the game?
b) How would you defend with Black?

lichess.org/editor/8/p6B/5k2/3p4/3P2P1/4K2n/P7/8_b_-_-_0_1

I saw the first move, Kf7! But i failed to see the defending idea when white King goes to h4. Interesting Endgame.

The white king can march to h4, but he has to take a roundabout route. Meanwhile black can capture pawn d4.

@theoriefritze @tpr my book says black can draw with Kf7, but I analysed it with the engine and it looks that white has many ideas and he can always win, so I'm not sure

My Stockfish gives >+10 which seems pretty clearly winning. E.g. after Kf7:
2.Bd3 Ng5 3.Bf1 Ne6 4.Bg2 Nc7 5.Kf4 Ke6 6.g5 Nb5 7.Bh3+ Kf7 8.Ke5 Nc3 9.Bg2 Kg6 10.Bxd5 Na4 11.Kd6 Nc3 12.Ke6 Kxg5 13.Bc4 Nd1 14.Bb3 Ne3 15.d5 Nf5 16.Ke5 Ne7 17.Kd6 Ng8 18.Ke6 Nh6 19.d6 Nf5 20.d7
+- (13.28 ++) Depth: 29/45 00:00:18 115MN, tb=204203

On Kf7 Ld3 Kf6. Black must guard the black squares.

@CrushKing, @MoistvonLipwig you are right. it is won. I just calculated 2.Bc2 with idea Bb3.

No on Bd3 black just plays Kf6, not Ng5. Black must not allow the white king to enter Kf4 Ke5 on the black squares.

@tpr



This refutes 2...Kf6. Bishop is well placed on g2, king will break through or black will lose d5 pawn.

There exists a fortress when white pushes pawn to a6. Then black knight sac against d+g and king to b8 is a fortress. But black can not enforce it.

Interesting.
Maybe 2...Ke6 idea 3 Bf1 Ng5 4 Kf4 Kf6 5 Bg2 Ne6+ and ...Nc7.