Should white be able to win this endgame?

Question

Should white be able to win from the position

[fen "8/5k2/3p1p2/3PnP2/1KP1r1P1/8/3RB3/8 b - - 0 67"]

with black to move?


(A game I was playing ended there when black just let
black's time run out due to having very little of it left.)
Black can take the g4 pawn, but Stockfish evaluates that as being much worse than
black's alternatives, regardless of whether the capture is immediate or after Ke7 Kb5.


Thus, play should presumably continue Ke7 Kb5 Nd7, resulting in the position

[fen "8/3nk3/3p1p2/1K1P1P2/2P1r1P1/8/3RB3/8 b - - 0 69"]

with white to move. ​ From that position, Bd1 is the only way Stockfish sees to make progress.

However, after Bd1, Stockfish thinks black should play Ne5, and then the line it gives is
4. c5 dxc5 ​ 5. d6+ Kd7 ​ 6. Kxc5 Nf7 ​ 7. Bc2 Re5+ ​ 8. Rd5 Rxd5+ ​ 9. Kxd5 Nxd6 ​ ​ ,
which results in a draw since


with white's pawn still on g4, Nf7 will establish a fortress because black can play Ke7 and N(x)g5 and even if white gives up the g4 pawn, white's king can't attack more than one of {h3,e4,h7}
and the only way for the bishop to do that is from g2, which leaves f7 safe for the knight

and

g5 fxg5 gives a tablebase draw, regardless of whether white plays that immediately
or after Ba4+ Ke7, and Ba4+ Ke7 Be8 Nxe8 gives a tablebase win for black


.

(Reminder: ​ My question was at the top of this post.)

Answer 1

White's main threat is c5, which forces a pawn exchange and a passed pawn with king covering queening squares. The bishop is covering the g pawn.

Should black force an exchange of that pawn, white's rook could go to e5 and capture the d pawn, allowing a double passed pawn.

If black defends c5, white first move his king to b4 to cover the next 2 pawn squares, then force black to zugzuang(by moving rook to a file) which forces black to stop defending c5 or move the rook.

If black moves rook to e5, putting pressure on the bishop, white pins black's knight and therefore forces a minor piece exchange, with a more active king, which will then go on and promote pawns.

If black stops pressuring the bishop, the endgame should be easily winnable.

As for Ke7, idea would be the same

For moves that does not either pressurise c5 or protects d6, force an exchange on c5 and you can win easily

Answer 2

Possibly is what my intuition says, but it would take a lot of analysis to know what best play result should be.

OTOH with real people it could easily be a win if they have time pressure in a tournament. Maybe even if not pressure just insufficient time to really do a full scale in depth analysis of all the nuances.

If black takes the pawn and white exchanges B for N then we have a R+P endgame with white a pawn up but black's king in front of the potential passed pawn. That would be very hard to win. But computer analysis might show it is possible.

Answer 3

Stockfish 14.1 NNUE ruled this position as a win. It is indeed evaluated at 4.00 depth =56. After a Rook exchange, a second iteration in the Bishop vs Knight endgame at d=64 returns + 11.15 in favore of White. It seems a win instead, albeit a laborious one.

Answer 4

After 67... Ke7 68.Kb5 Nd7 I think white should try to force to get the king to c6 and next c7. For this a plan is 69.Ra2 with the idea of playing Ra7 next Kc6 that wins on the spot. Black can try to go back 69...Ne5, when 70.Rc2! seems to be good: holds c4 and enables the K to move. Now on 70...Nd7 follows 71.Kc6 and if 71...Ne5+ again, 72.Kc7, with idea c5, winning. Only 72...Nf7 holds f5 a move, but after 73.Rd2 and there is no way to prevent 74.c5 +-

Black can try 69...Re3 70.Ra7 Rb3+ (70...Rxe2? 71.Kc6+-) 71.Kc6 Rb6+ 72.Kc7 Rb2 73.Ra6! is killing e.g. 73... Rxe2 74.Rxd6 +-