In the second tiebreak game of the fourth round match between Vladimir Potkin and Alexander Grischuk from the World Cup, Potkin voluntarily entered the following king and pawn ending:
(Potkin-Grischuk, round 4.4. Position after 39.Kxe1.)
It seemed lost to me before I knew the result or checked with an engine. He did indeed lose, and the one part of it I did check with an engine before writing my summary article on the tiebreaks confirmed my suspicions. What I checked was whether White could hold the position if he refrained from playing b4 (after a3), and when I worked out to my satisfaction that he couldn't, I just assumed that it was a simple win and that the course of the game bore it out.
Wrong! Grischuk won, and the position was objectively won, too, but it wasn't trivial. In fact, Grischuk erred and let the win slip, only to have Potkin give away the half point on his very next move. In a slow game, with a reasonable amount of time to think, Potkin would have worked out the draw though Grischuk wouldn't have given him the opportunity in the first place. All the same, it's a good exercise for the diligent reader to try to work out the ending from the diagram.
The first crucial moment, alluded to two paragraphs ago, comes after 39...Ke6 40.Kd2 Kd5 41.Kc3 Kc5 42.a3 Kd5.
How does Black win if White refrains from 43.b4, and chooses instead 43.h3?
Second, after 43.b4 axb4+ 44.axb4 h6 45.h3 h5 46.h4:
How should Black continue? Try to work it out to the end.
The game, with my fairly deep analysis of the pawn ending, is here.