Last time we looked at one of Grandmaster Barcza's rook endings. Here is another less-complicated one (see the first diagram).
Most endings of rook and pawn vs rook and pawn are drawn with best play from both sides. The exceptions occur when one of the pawns is much closer to its queening square. If the inferior side cannot set up a blockade, the correct defensive strategy is to give up the rook for the pawn (or new queen) and then try to promote one's own pawn. The superior side will of course try to prevent this, and the game becomes a race in which the outcome can depend on a single tempo.
In the starting position White has the advantage but with correct play it will not be enough to force a win.
51.g6 Rh3+ 52.Kg4 Rh1 53.Rf7+ Kd6 54.g7 Rg1+ 55.Kh5
It isn't necessary to calculate variations to see that this move must be wrong. White is queening by force, so Black has to be ready to advance his own pawn as quickly as possible. After the self-blockade, Black will have to spend another move getting his king out of the way, which in this case is enough to turn a draw into a loss.
Correct was 55...Kd5! 56.Kh6 (after 56.Rd7+ Black can safely change plans with 56... Ke5 because his king gets to f6, where it interferes with White's king: 57.Kh6 Kf6 58.Kh7 e5 59.Kh8 (definitely not 59.g8Q? Rh1#) 59...e4 60.g8Q Rxg8+ 61.Kxg8 Ke5 and Black draws easily) 56...Rh1+ 57.Kg6 Rg1+ 58.Kh7 e5 59.g8Q (or 59.Rf6 e4 60.Rg6 Rh1+ 61.Kg8 Rf1 and White cannot make progress) 59...Rxg8 60.Kxg8 e4 61.Re7 Kd4 and White will have to give up his own rook in order to stop Black's pawn.
56.Kh6 Rh1+ 57.Kg6 Rg1+ 58.Kh7 Rh1+ 59.Kg8 Rg1
This is a rather serious error at the grandmaster level. Instead of taking two moves to win Black's rook, White takes three moves to do the same thing. In this way he returns the tempo that Black wasted earlier, which is enough turn the game back into a draw.
The winning line is 60.Kf8! Kd4 61.Rd7+! (an important technical device that gains a tempo for White) 61...Kc4 (Black also concedes a tempo if the king moves in front of the pawn) 62.g8Q Rxg8+ 63.Kxg8 e5 64.Re7! Kd4 65.Kf7 e4 66.Kf6 Kd3 67.Kf5 e3 68.Kf4 e2 69.Kf3 and White successfully captures the pawn.
Or 61.Kf7 e5 62.g8Q Rxg8 63.Rxg8 e4 and the e-pawn will cost White his rook.
61...Ke4 62.Kf7 e5 63.g8Q Rxg8 64.Rxg8 Kf3 65.Ke6 e4 66.Rf8+ Kg2 67.Kd5 e3 68.Re8 Kf2 ½–½