In these R+p endings after f6+g5 defence when is gxh4 safe?Kantorovich/Steckner (DEM 9-144)
In Kantorovich/Steckner DEM 9-144 after 1.Kd4 g5! 2.Kd5 as well as Poghosyan's draw by 2…g4 we have Aagaard's draw by 2…Kg6 intending f6,Kf5
You must not preface Aagaard's draw with 2…gxh4? 3.gxh4 since Black loses (Poghosyan mentioned this in his 2…g4 draw) 3…Kg6 4.Kc6 f6 5.Ra8 Kf5 6.Kb6 Rb2+ 7.Ka7 Rxf2 8.Rb8 Kg4 9.Rb4+ Kg3 10.Kb6 Ra2 11.Kb5+-
So White holds up Black's kingside play by defending the lone h4 pawn with Rb4 but, crucially, with g-pawns still on the board the Black King attacks the White pawn on g3.
It turns out this subtly of not exchanging on h4 after f6+g5 occurs in other Rook & pawn endgames although it is often missed!Akopian-Kir. Georgiev (DEM 9-166)
After 1…Ra1?! 2.Ra6! Ra2 3.a4 Ra3+?! 4.Kd4
Dvoretsky criticises further Black moves but all lines in DEM from here win for White (two wins in some lines!) but I believe the position is still drawn.
The game continued 4…f6 5.Ra7+ Kh6 6.a5 g5 7.Kc5 gxh4 8.gxh4 Kg6 9.a6 Ra2 10.Ra8 losing similar to 2…gxh4? line above (Kc5 instead of Kc6 irrelevant)
Instead of 7…gxh4? there is 7…Ra2! (not 7…Kg6? 8.Kb4+-) 8.a6 Kg6! 9.Ra8 Kf5! 10.Kb6 Rb2+! 11.Ka7 Rxf2 and 12.Rb8 Kg4 is drawn with g-pawns still on
If White deviates his plan with 10.f3 or 10.a7 then 10…gxh4 11.gxh4 Kf4 draws and if 10.hxg5 fxg5 11.f3 h4! 12.a7 hxg3 draws
Dvoretsky also considers 4…Ra2 5.a5 transposing to Krakops-Dautov (reversed)
Krakops played 5…f6 when Dvoretsky recommends 6.Ra7+ Kh6 7.a6 g5 8.Ra8 gxh4 9.gxh4 Kg6 10.Kc5 winning as in 2…gxh4? line above
But again instead of 8…gxh4? there is 8…Kg6! 9.Kc5 (9.f3 gxh4! 10.gxh4 Kf5= or 9.a7 Kg7=) Kf5 with identical draw to Akopian-Kir. Georgiev 7…Ra2! line above
I believe Dautov line played of 6.f4 analysed to win in DEM can also be countered but it does not fit into this topic so I will leave that for another thread.
In these Rook & pawn endings logical captures such as gxh4 (as with Rxf2) must sometimes be avoided until…, until it is correct! Just keep checking White's hxg5.