Fundamentals (part 36)

Tobias Boje (1908) - Spanton (1995)
Gausdal Elo 2007

White has just captured on f5 - who stands better?

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The position is dead-equal, according to the analysis engines Komodo10 and Stockfish10.
28...Ke7 29.Kg4 c5?
Advancing and, if possible, centralising the king is usually a priority in pawn endings, and this one is no exception. Here 29...Kd6? loses to 30.Kh5, eg 30...Ke7 31.Kg6 Kf8 32.e7+! Kxe7 33.Kxg7 etc, so sensible was 29...Kf6, which maintains the balance.
30.f4?
White offered a draw.
But winning is 30.Kh5 Kf6 31.e7! Kxe7 32.Kg6 Kf8 33.f6, eg 33...gxf6 34.Kxf6 e4 35.e5 etc, or 33...e4 34.fxg7+ Kgg8 35.Kf5 Kxg7 36.Ke5 etc.
30...e4 31.Kg3 d4 32.Kf2 b5
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33.Ke2
White seems to have a draw with 33.b4! c4 34.c3! although Komodo10 reckons Black is winning. After 34...dxc3 35.Ke2 there seems no way for Black to convert his pawn advantage, although Komodo10 for a long time continues to believe Black is winning. However eventually Komodo10 agrees with Stockfish10's assessment of equality, one line running 35...Kd6 36.Ke3 h5 37.h4 Ke7 38.Ke2 when there is no way to make progress.
33...a5 34.Kd2
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34...e3+?
Black wins with 34...b4, eg 35.a4 h5 36.h4 Kf6 37.Ke2 c4! 38.Kd2 (if 38.bxc4 then 38...d3+ 39.cxd3 b3 etc) c3+ 39.Ke2 Ke7 40.Kd1 d3 41.cxd3 e3! 42.d4 Kd6 43.d5 Ke7, or 35.axb4 axb4 (35...cxb4 also wins) 36.Kd1 c4! 37.Kd2 (if 37.bxc4 then 37...d3 38.cxd3 e3! etc) c3+ 38.Ke2 h5 39.h4 Kf6 40.Ke1 d3 42.cxd3 e3! etc.
35.Ke2 c4 36.b4 a4 37.h4 h5 38.Kf3 Kf6 39.Ke2 c3 40.Kd3 Ke7 ½–½