How to make progress?

 

White to move

5b2/2p2k2/1p2p1p1/p1p1P2p/P1P2P2/1P2BKP1/7P/8 w - - 0 32 

Let's first see what Stockfish has to say:

Stockfish at 39 ply deep

Remarkable is that the move 32.h3, which is proposed in the The Strategy Instructors Volume 1: Pawn Majority & Minority doesn't seem to be winning at all. Btw, I'm going to promote this book at Chessable shamelessly, since I hope they will be inspired to write a volume 2 at some moment.

In a sense that might be good news. It shows that even grandmasters tend to be failure prone in the endgame. Let alone mere mortals. The bad news is that I have to think for myself.

The first 9 moves seem to score equally well. Which moves make progress and which moves do nothing more than not giving the win away?

Let's see what theoretically might lead to progress. The black king is powerful on the white squares. He can blockade the black king from invasion. What can drive the black king away from the white squares?

White has no piece to drive the black king away. So the only tools he has are:

• put the black king in zugzwang
• luring away the black king
• drive the black king away with a pawn

This gives a good insight in the stages before this position. Which pieces do you want to trade? A knight or rook would be handy right now, since these can be used on the right squares. But it is too late for that now.

After 32.g4 Be7 33.Kg3 c6 34.Kh3 Bd8 35.Bf2! we get the following position:

Black to move

3b4/5k2/1pp1p1p1/p1p1P2p/P1P2PP1/1P5K/5B1P/8 b - - 3 35

This is the plan: bring the white bishop to d8 and bind the black bishop to the defense of b6. Note that black cannot permit the exchange of the bishops, since then the white king invades via g5. He kan force black in zugzwang due to the spare moves h3-h4. Just try it with Stockfish until you are convinced.

35...Bc7 36.Bh4 hxg4+  37.hxg4 Kg7 38.Bf6+ Kf7 39.Kg5 and black is in zugzwang.

Black to move

8/2b2k2/1pp1pBp1/p1p1P1K1/P1P2P2/1P6/7P/8 b - - 4 39 

From here I don't follow the exact game due to repetition in time trouble and mutual errors which compensate each other. That obscures the method.

To be continued. . .