Is it possible to hold as black or does white have a winning advantage?
White to move
The game continued 38.Re2
White has a extra pawn that is doubled. His isolated h-pawn is a source of counter play for black. Black has a tough defensive task especially in a blitz finish. The following variations is what I would consider sample lines to atleast try and shed some light on the position.
One good way to test endgame positions is to play against a computer as both colours using the endgame as the starting point.
Interesting for white is 38.e5 Rb3+ 39.Kg4 Kg7 (39...h5+? 40.Kg5 Rxh3 41.f5 gxf5 42.Kf6 Rh2 43.Ra8+ Kh7 44.Kxf7 Rg2 45.e6 Rg7+ 46.Kf6 Rg6+ 47.Kxf5 Rg7 48.Kf6 Rg6+ 49.Ke5 Rg7 50.Kd6+-) 40.Ra7 Rb2 41.Kg3 (41.f3 Rg2+ 42.Kh4 h6 Black keeps his rook on the g-file and white is unable to make progress.) 41...h6 42.h4 (42.e6? Re2 43.e7 Kf6=) 42...Re2 43.f3 Kf8 44.Rd7 Kg7 45.h5 (45.Rd5 Re1 46.f5 gxf5 47.Kf4 Rh1 The importance of playing h6 blocking white's King off from making any real progress can be seen here. 48.Kxf5 Rxh4 49.f4 Rh5+= Black's defence task has eased and the position is probably drawn. ) 45...gxh5 46.Rd5 f6! 47.Rd7+ Kf8 48.exf6 Re6 49.f5 Rxf6=
38.Kg3 Kg7 39.Ra6 Rc5 40.f3 h6 41.Rd6 Rc1 42.Rd5 Rg1+ 43.Kf2 Rh1 44.Kg2 Re1 45.f5 Kf6 46.h4 Re2+ 47.Kg3 Re1 48.fxg6 fxg6 White has undoubled his pawns but his winning chances have not increased. 49.Ra5 Rc1 50.f4 Rg1+ 51.Kf2 Rg4 52.Ra6+ White does have still practical chances to win so of course why not torture black further. With best play the position is drawn.
The game continued
38...f5!? 39.e5 Kf7 40.Ra2 Rb7 41.h4
A) 41...Ke7?! Black has to be careful not to walk too far away from his pawns as can be shown from the following variation. 42.Kg3 Rb3+ 43.f3 Rb7 44.Ra6 Rd7 45.h5 gxh5(45..Kf7 46.e6++/-) 45...Kf8 46.Kh4 Rd8 47.Kg5 h4 48.Kxf5 h3 49.Rh6 Rh8 50.Ke4+-
B) 41...Rd7 Black can just sit and wait. 42.Ra6 Rb7 43.Kg3 Rc7 44.h5 Rb7 45.Kh4 When white starts to get his King inot the position only then does black worry about active counterplay. 45...Rb1 46.Rf6+ Kg7 47.hxg6 hxg6 48.Kg3 (48.Kg5 Rg1+ 49.Kh4 Rg4+=) 48...Rb3+ 49.f3 Rb1 50.Rd6 Kf7 51.Rd7+ Ke6 52.Rg7 Kd5 53.Rg8 (53.Rxg6 Rg1+ 54.Kh4 Rxg6) 53...Ra1 54.Kh3 Rh1+ 55.Kg2 Rh4 56.Kg3 Rh6 57.Kf2 Black has defensive resources but they are not at all easy to find and white can torture black for a long time if he also plays accurately.
39.Kg4 h5+ ?!
39...f5+! 40.exf5 Rxf5 Black's life would be much easier now that white has 3 isolated pawns.
40.Kg3 Kf6 41.Rc2
Here is where I stopped recording the moves, but thanks to pictures availabe at nzchessevents.myphotoalbum.com. I was able to reconstruct another interesting Rook ending.