Pawn endgame transitions

@tpr said in #10:

"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?

I'll wait and move the king between e2 and f2. How does the black king approach?

#11
30... Rxd1+ 31. Kxd1 g5 32. Ke2 Kf6 33. Kf2 f4 34. Ke2 Kg6 35. Kf2 Kh5 36. Ke2 f3+ 37. Kf2 Kh4 wins.

Finally you got it. The game went a bit differently, I put my pawn of f3 (which was fine), but the idea to run all the way to the h-file with the king did not occur to me since it looked like White could then advance the queenside pawns. However this is an optical illusion since the king can come back just in time.

#13
White can also defend against ...Kh4 with Kg3. Then black can force Zugzwang with a king triangle. In case white advances his b-pawn, then the black king can go there to stop it.

@tpr said in #14:

#13
White can also defend against ...Kh4 with Kg3. Then black can force Zugzwang with a king triangle. In case white advances his b-pawn, then the black king can go there to stop it.

Right, I have updated the study in the meantime.

first game white can not exchange Bishops but to move bishop on b5, where it supports passed pawns, and it's problem for black , so it's better to get rid of c3 pawn for them first
in second game exchanging rooks allows white to play equal with black by moving their king in the same direction as black and they have a b passed pawn so if black plays on left rank they won't be in time to promote pawns as white do I think, so better move is rook a 5 I think

#16
In the first game black should play ...h4 to fix the weak white pawns on light squares and then invade with the king to g3 wins.

In the second game black trades rooks and plays ...g5 then goes with the king to h4 to capture the pawn. If white tries to prevent it with Kg3, then black makes a triangle with his king to force Zugzwang. If white plays his b-pawn, then the black king marches towards it to stop it. He comes in time, but must not move his defensive a-pawn a7. You can see this: white would need b4, b5, a4, a5, b6, b7, b8 to queen, in that time the black king is there. On the other hand if the black pawn were on a6 instead of a7, then b4, a4, b5, b6, b7, b8 takes one less move and the black king does not arrive in time.

I cannot see a clear plan after ...Ra5. Rook endgames are tricky with many drawing resources. I would certainly simplify Rxd1+ to the pawn endgame.

If White captures on f4, the position turns into a pure race: White will have a passed pawn on the h-file while Black’s queenside majority starts rolling.

However, Black must avoid pushing ...f4 too early; the first priority is to centralize the king. Once the king is active, it can easily contain the b-pawn, leaving the white king tied to defense. Even if White tries the defensive setup with b3–a3, those pawns become fixed targets and lose mobility. Similarly, Black should hold the a7 pawn in place to cover key entry squares.

“Alright, but what’s the concrete plan then?”
“I’d begin with Rxd1+ Kxd1 g5: now after your b3 and a3, I’ll activate my king and start advancing on the kingside. What’s your next move? How do you intend to hold this position?