The Importance of Elementary Endgames

I was playing a blitz game online and got into a pretty bad position as can happen. I was then let off the hook in the endgame which I thought I'd take a look at.

It is white to play and the win is fairly instructive. White has to advance the king threatening to exchange rooks by Rf7 simplifying into a winning king and pawn endgame. Like this:

1.Kd3 Ra7 [1..Ra3+ 2.Kc4 Ra4+ 3.Kb5 Ra7 4.Kb6 Re7 5.Kc6 Ra7 6.Rf7+! Rxf7 7.exf7 Kxf7 8.Kd7

with a winning position as white's king will be able to win the g-pawn] 2.Rf7+! Rxf7 3.exf7 Kxf7 4.Kd4 Ke6 5.Ke4 with a winning opposition:

With white to move this is a draw, but with black to move white wins. 5..Kd6 6.f5 Ke7! [6..gxf5+ 7.Kxf5 Ke7 8.g6 (8.Kg6 also wins) 8..Ke8 9.Ke6! (but not 9.Kf6? Kf8 =) with another winning opposition]

7.f6+! [7.fxg6? throws away the win 7..Kf8 8.Ke5 Kg7 9.Kf5 Kg8 (Straight back, ignoring the fact there are doubled pawns) 10.Kf6 Kf8 11.g7+ Kg8 and white's spare pawn move is useless as it will lead to stalemate] 7..Ke6

8.f7! Kxf7 9.Kd5 [This outflanking manouvre works as black's pawn is on the 6th rank so when white captures it, they will have a winning position. Note that this wouldn't work further down the board] 9..Ke7 10.Ke5 [Opposition] 10..Kf7 11.Kd6 Kf8 12.Ke6 Kg7 13.Ke7 Kg8 14.Kf6 Kh7 15.Kf7 and black must abandon the pawn and the game.

Unfortunately in the first position white decided that the pawn endgame is won immediately and went straight to it.

1.Rf7+? Rxf7 2.exf7 Kxf7 3.Ke3

[This position is a win with white to move, but a draw with black] 3..Ke7! [Opposition] 4.Kd4 Kd6! 5.Ke4 Ke6!

[We already saw this position as a win with black to move, but here it is white to move] 5.f5 gxf5 6.Kf4 Kf7 7.Kxf5 with a draw as white's king is not in front of the pawn.