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Endgame where I can't see how to make progress even though eval says -4

#1

Skip to move 42.

Any suggestions on how to make progress in this endgame? His king guards my 2 connected passed pawns and my king guards his passed pawn. So, how am I supposed to make progress? I tried to check the engine and it just shuffles the kings around and it plays a5 and then a4, which I don't understand.
My opponent suggested that one way would be to allow him to get a queen, get a queen myself and have a more active king.
I'd appreciate any tips.
#2
I'm interested, too. I let this play through on Lc0 while I had some other things to do. Started after 45. h3.

Lc0 walked the d and e pawns down to get promoted, but white was able to promote, too. By move 95, it was K/Q/P vs K/Q. Lc0 puts blacks odds of winning at 97%. There is no quick end in sight, though. On move 95, Lc0 shows at least 62 moves left with best play on both parts. Black's pawn is on the 3rd rank, and there are no more pawn moves in the next dozen moves it's considering.

I think the best strategy is not to blunder as black. Play solidly and hope for a mistake on white's part. It's psychologically more taxing to defend when you're down material, so with solid play, white might buckle. I'd say it's probably more honorable to draw than to hope for time pressure on one side causing a blunder, but that's also a valid strategy. :)
#3
Yeah, pawn endgames are tricky :/ The concept here is "corresponding squares", so I'm guessing what the engine is trying to do is manueuver the king such that Black's king is on a certain square when White's king is on another "corresponding" square, putting White in zugzwang.

http://charlottechesscenter.blogspot.com/2017/06/endgame-strategy-corresponding-squares.html

To understand the corresponding squares in your position, we need to know the concept of the opposition and triangulation.

Opposition is when two kings are facing each other, with an odd number of squares between them. So for example, a King on c4 and a king on c6. Kings 3 files apart from each other, eg. King d8 and King d4, is a distant opposition. The reason why this is so important is because since kings cannot move immediately adjacent to each other, neither king can advance, creating a mutual blockade, which happened in your game.

I'm not sure how to post diagrams, so I can't really give a good example of how this works in a practical endgame. You can read about it here though: www.ragchess.com/endgame-theory-opposition-triangulation-and-trebuchets-explained/#:~:text=Opposition%20occurs%20when%20the%20kings,to%20white%20in%20this%20situation (this article covers triangulation too)

In your position, the opposition is very important - If you can manuever your king such that you have the opposition, and white is forced to move back, then you can push pawns and win.

Let's skip to move 48. 48...Kc6! wins for Black. The idea is that if White just toggles between the d4 and e3 squares we get:

48...Kc6 49. Kd4 Kd7 50. Ke3 Kc8! 51. Kd4 Kd8! (getting the opposition) 52. Ke3 Ke7 53. Kd4 Ke6 54. Ke3 Ke5! and we have the opposition, white cannot move to d4. We win since the King is forced back and then we push pawns.

And if White moves the king off from d4-e3 then we can probably push our pawns and win.

Hope this helps :)

EDIT: it's important to note that his passed pawn can't really be pushed, since our king is close enough to win it.
#4
@ericmsd Thanks for the interesting analysis through leela. You're right on the psychological aspect. I definitely would have pushed further in a more serious setting.

@ke21-0
I knew about opposition, but not about triangulation, even though I kind of used it in the game (47...Kc7) which was what allowed me to push the pawns one square forward. I just didn't see how I could replicate it again without moving too far from the white passed pawn's box.
I learned a lot from the links you shared, even though the first one was a little too complex for me. I understood the examples, but I couldn't solve the exercises by myself, since I don't know how to figure out the winning zone or all the corresponding squares, but I suppose that would require me to properly study the endgame with books. I will look into some youtube videos on the topic to try to figure it out as it seems very important for this sort of positions.
The continuation you suggested makes a lot of sense, considering these concepts and it would allow me to reach the situation my opponent suggested with both of us queening and my king being more active.
Thank you very much for the insightful answer.

Edit: While reviewing the game, I realized that Stockfish plays a5 and then a4 before pushing the pawns probably so that a6 isn't an instant threat right after white queens on c8.
#6
Endgame Manual by Dvoretsky I highly recommend for your endgame needs, especially if you need help with corresponding squares, triangulation, opposition etc ( which all this is in the first chapter)
#10
Well, to win this endgame, @Noiserv71523, all you have to do is to stop that dangerous white passed pawn on c5. That's easy, it's just with your king. Then, you have to bring your king to the game, that is, f5. The white king can't go to d4 and capture the d5 pawn, because it loses to Kd4 Ke7! Kxd5 e3 Kd4 e2 Kd3 e1 = Q. So it's a winning position. And I'm sure you know how to promote a pawn in these 2 pawn + King vs King endgames. Hope this helps! :D

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