Knight endgame

I reached the following endgame position as black in a recent OTB tournament:

My opponent offered a draw which I of course accepted. We both thought that this endgame would be a draw in the end, but later I've come to think that it may be a win for white after all.

I think that white could win by marching over with his king to the queen side and grab the pawn while black's knight cannot win the a-pawn alone. Black needs his king to protect the a pawn, and this would leave his pawns on the king side vulnerable.

But perhaps black has some possibilities for counterplay that I don't see?

What are your thoughts on this specific position, and on knight and pawn endgames in general? I find knight and pawn endgames very difficult to understand and calculate, much more so than rook or bishop endgames.

This is not necessarily winning for white, but Black's defence is extremely difficult and unpleasant. Knight endings tend to have many similarities with King endings. If you put the knights out here, the endgame is easily winning for White, right?

My very brief analysis: white has an extra pawn and so he has winning chances.  Your opponent let you off too easy

"Knight endgames are pawn endgames"  -Botvinnik

Which means, many of the same rules apply.  Passed pawns (or an extra pawn) are often decisive and things like king activity, sacrificing for a breakthrough, and zugzwang are common ideas.

And also, as you noted, they're tough to play.  This is because (like pawn endgames again) good moves require concrete calculation to back them up.  Where endgames are the least forgiving phase in general, knight endgames are one of the least forgiving endgames.

In the diagram you give, white's general idea should be to advance his kingside to make a passer.  White's king wont be too effective on the queenside, plus that will take a lot of time.  The black knight is close to winning the a pawn by the way, after Nc4 followed by a5 and Nb2/6

pfren: is it really easily winning for white if we take the knights out? I think it looks like a draw. Sure, white will create a passed pawn on the king side, but the remaining pawns are rook pawns, and will white have enough time to win the a-pawn and prevent black's king from reaching c7 or c8?

wafflemaster: sure, black can win the pawn, but only at the cost of white winning the black a-pawn as well (1...Nc4 2.a4 a5 3. Nd4 Nb6 4. Nb3 Nxa4 5. Nxa5). Still, it's white to move in the diagram which allows him to protect the pawn with the knight.

What if we removed the rook pawns and just imagined a scenario with knights and 2 vs 3 pawns on the same side. Is that usually a win for the side with an extra pawn, or can the side with a pawn down usually sacfifice his knight for the last pawn?

pfren: Nevermind, I see the winning technique now, I think (with no knights). White moves his king to the queen side. If black then uses his king to take out whites king side pawns, white will promote long before black. And if black uses his king to prevent white from taking his a-pawn, white's king side majority will create a passed pawn. Am I right?

In the position in the diagram above, you stated that defence will be unpleasant and difficult. I understand that it's impossible to tell me specifics without pages of analysis, but can you give me any general guidelines for the defence of such a position?

The pawn ending is a draw only if Black manages to push his a-pawn to a4. Else, Black has not enough time to return to the queenside.

I would've played this ending out as White on GP - General Principle, namely that I'm a pawn up and should have nothing to lose with careful play, although I might not win. Without the Rook pawns the ending is probably drawn but even at that why let Black off the hook without trying to win?

Try playing this ending out vs a PC and see what happens and/or just analyze it yourself and see what you come up with. Letting a PC play the ending by itself might be instructive too. If possible I'd invest in a decent one vol endgame book such as Basic Chess Endings by GM Fine, which will cover the general principles of this type of ending.

pfren: I'm sure you're right, but I don't understand why black needs to get his pawn to a4.

Nimzoroy: I would have done the same if I were white. This was the last game out of seven in a weekend tournament so I was happy to accept the draw. :) I'll try playing it out vs an engine later, and I might try your suggestion as well, to let the computer play itself.

I already have Silmans complete endgame course and I've worked through it so that I know the material up to what he calls expert level fairly well. But there is very little on knight endgames in that book, only holding a basic draw with K+N vs K+P and such. And there is also almost nothing on more complicated endgames with several pawns plus pieces on each side. Still, with the material I have studied, I feel very confident in the endgame compared to most other players at my level.

What I feel I'm missing the most in my endgame technique at the moment is  general strategic principles for such endgames as this, not specific endgame positions. Is this covered in the book you mention?

Think of something like that:

This is a draw, because white can't prevent the Black kings march to b8.

Ah, I see. Thank you!

Yes, this is a win, as Black is a whole tempo down. However, I cannot find how such a position can be forced.