Pawn endgame transitions

In endgames there is often the opportunity to exchange the last pieces or to offer exchanging them, and we have to calculate or at least evaluate the resulting pawn endgames. Today I had two such games in the 158th Rapid League, and while the 7+5 time control is quite slow by online standards for me this was not enough time to properly look at every relevant line. Here are the crucial moments.

In the first game I was looking for a way to breach White's defenses, and 41... Be4 came to mind. Is that a good idea?

In the second game my opponent had offered to exchange rooks. Should I do that? Spoiler: this is quite a difficult decision.

Game 1: No, 41 Be4? g3+ loses the winning advantage.
Game 2: Yes, 30...Rxd1+ simplifies to a won pawn endgame.

@tpr said in #2:

Game 1: No, 41 Be4? g3+ loses the winning advantage.
Game 2: Yes, 30...Rxd1+ simplifies to a won pawn endgame.

Both answers are correct, if rather terse. I have updated the first game and added the variations, but the second one is really complicated. In fact the automatic fishnet analysis calls 30... Rxd1+ an inaccuracy and recommends Ra5 instead.

I followed up correctly with 31... g5 (the only winning move, otherwise White plays 32. h4), but went astray later on.

#3
In game 2 30...Rxd1+ is the human way. It may be that 30...Ra5 wins faster for an engine, but from a human perspective that looks more complicated.

@tpr said in #4:

#3
In game 2 30...Rxd1+ is the human way. It may be that 30...Ra5 wins faster for an engine

No, the reason why 30... Rxd1+ is criticized by the fishnet analysis is insufficient depth. After running SF 16 in my local browser for a while it prefers to exchange rooks.

but from a human perspective that looks more complicated.

Not to me, but maybe the winning process is easy to see for you and you can describe it?

#5
To me winning the rook endgame looks difficult.

The pawn endgame looks straightforward: play ...g5 with the later threat ...f4 with either two connected passed pawns e4 - f4 or a protected passed pawn f3. Meanwhile approach the king to stop the candidate passed pawn b2.

@tpr said in #6:

The pawn endgame looks straightforward: play ...g5 with the later threat ...f4 with either two connected passed pawns e4 - f4

This is the right plan, but you need to be sure that these connected passers queen faster than White's pawns on the wings.

or a protected passed pawn f3. Meanwhile approach the king to stop the candidate passed pawn b2.

I managed to do that, but then got stuck. Note that White will put the queenside pawns on b3 and a3 to stop the black king from entering there.

#7
"you need to be sure that these connected passers queen faster than White's pawns on the wings"

• The question is not to queen faster, the connected passed pawns or the protected passed pawn tie up the white king.
  The black king is free to move. The black king may need some triangle to put white in Zugzwang.

"White will put the queenside pawns on b3 and a3 to stop the black king from entering there."

• But the white king will be tied to the protected or connected black passed pawns, while the black king is free to move.
  He does not need to enter and can make triangles to create Zugzwang for white.

@tpr said in #8:

#7
"you need to be sure that these connected passers queen faster than White's pawns on the wings"

• The question is not to queen faster, the connected passed pawns or the protected passed pawn tie up the white king.

If White takes on f4, it becomes a race because White has a passer on the h-file and the queenside majority.

"White will put the queenside pawns on b3 and a3 to stop the black king from entering there."

• But the white king will be tied to the protected or connected black passed pawns, while the black king is free to move.
  He does not need to enter and can make triangles to create Zugzwang for white.

Yes, but how exactly do you do that?

#9
"If White takes on f4, it becomes a race because White has a passer on the h-file and the queenside majority."

• Black must not advance ...f4 too soon, first centralize the king. The black king can easily hold off the b-pawn, while the white king is tied. White can play defense b3-a3 as you said, but then these pawns are tied and cannot move either. Likewise black must keep his pawn at a7 for defense.

"Yes, but how exactly do you do that?"
I start with Rxd1+ Kxd1 g5, then you can play b3 and a3 while I approach the king. Now what? How will you defend?