Could black have won this endgame?

I offered a draw in this position, which my opponent accepted. Was there a way for black to win? I couldn't see one.

I would have offered a trade with moving that pawn next to your bishop on the white diagonal so the white pawn there can either accept or deny it. either way if he didn't accept it it would have turned out bad for them

There was surely a way for black to win bez Black can create a passed pawn with b5 , his king is v active this position though is winning for black even though material is equal

Probably a draw if you're not an engine, but still, offering a draw was unwise. Only black has chances to win here, it was worth pressing on.

If it's black to move in that diagram, 1...Ke4 seems to give black excellent winning chances: Much more active king, better minor piece, possibility of forcing an outside passed pawn. Is there a forced win? Search me! But you have every advantage. You don't need to have the whole win mapped out, you just have to keep carefully improving

In general: yeah, this endgame should heavily favour black. Knights aren't great pieces when they have to defend on both sides of the board. You might find it interesting to do a little study of bishop vs knight endgames with pawns on both sides of the board. In this case, the position is even better, because the black king is really active, the white knight is really passive and the weaknesses on b3 and a4 are fixed on the color of your own bishop, which means they're really vulnerable.

Tactically speaking, I wonder if 1. ... Bd5 is not immediately winning. If white plays 2. Ne3+, I play Ke4. 3. Nxd5, Kxd5 is a winning king and pawn ending, as black can play ...f5, then create a passer with c4, which can be 'sacrificed' at the right moment for a run to the kingside. If 3. Nc4, we trade as well and follow up with ...f5 with an even easier win. Winning the b-pawn for nothing would mean that the a-pawn falls too and is a trivial win.

David Hooper Practical Chess Endgames
p89 to p94

The general idea is the bishop can cover both sides of the board and the knight not.
Five pawns each helps the bishop
Seven pawns each helps the knight.
If the knight has no central *outpost* that side is toast.

1. Ke3 Bd5 2. b4 cxb 3. Kd4 Bb3 4. Ne3+ Ke6 5. f5+ Ke7
That is pretty hopeless for white.

1. Ne3+ (stopping Bd5) Ke4 2. Ke2 Bd7 3. Nc4 b5 4. Nd2+ Kd4
5. axb axb Now what can be done about ... Kc3
6. Nb1 Bg4+ 7. Kd2 b4
and the black king enters either side.

1. Ke2 b5 (want a passed pawn) 2. axb axb 3. Nf2 b4
4. Kd3 Bd5 5. Kc2 c4 6. bxc Bxc4
Don't see white holding that as black can always gain/lose
a tempo with ... Bf7 / ... Bg8

Example games:
Chekhover v Lasker Moscow 1935
Reshevsky v Woliston US Championship 1940

How much time have you got?
Have you studied master games?

I've seen a lot of master games, but almost every endgame is unique. I would have found a way to misplay this, anyway. I've lost endgames when I had an extra piece. After Ne3+ I would have played Ke6 instead of Ke4, which is clearly better than Ke6.

I see Paul. 
What you need is a set of rough principles.
In a knight end game rook pawns are better.
In a rook end game centre pawns are better.
In bishop end games pawns that queen on the bishop's colour square are better.
In bishop v knight pawns on both sides are better.
In pawn end games opposition is better.

And so on.

White to play it is a draw, Black to play loses.
That is the *opposition* principle.

Does this post help?

Yes, thank you.

My guideline: If you wouldn't agree to a draw against an opponent rated 300 points below you, then you shouldn't offer or accept a draw.

As others have noted, black has a clear advantage. In this sort of position, where the center of the board is open and there are pawns on both sides, the bishop is definitely better than the knight. Maybe you can win it, maybe you can't, but you should at least try.

If you want to learn how to play these endings better, you need to play them out. You don't learn anything by prematurely agreeing to draws.

+1

A quick glance shows that the white knight can't protect the backwards pawn on b3 for three moves.  And so 1. ..Ke4! 2. Ke2 Kd4 3. Kd2 Bd5! 4. Kc2 Be6!! and white is in zugzwang, Kd2 drops the b-pawn, any pawn moves loses that pawn, and any other king or knight move allows Ke3, which wins all the kingside pawns.

The key to these kind of endgames is penetrating with the king (which is a stronger attacking piece than the bishop or the knight) and the key to that is identifying targets.  The b3 pawn should pop out as a huge weakness in white's position.

Don't be too quick to assume black is winning. Yes, black has an edge, and it may be enough to win, but white has resources as well. If black's king strays too far towards the queenside, white can create a passed pawn with g5 - even if black has already played f5.

I won't pretend to calculate it all out. Maybe there's nothing there. But black needs to keep an eye on the possibility.

Anyway, we pretty much all seem to agree that black should have played this out.

This was one of the things I was worried about, and why I wouldn't have played Ke4 after Ne3+.