The Elusive Win in Kramnik-Carlsen (Part 2)

As a commenter pointed out, I have not addressed Black's moves other than 69...hxg5 in response to the proposed 69.g5.  I attempt to fill that gap here.  As a reminder, here is the position we are looking at:

There are two sorts of alternatives to 69...hxg5 to consider here: 69...h5 and various waiting moves with the Black king.  Before I begin, though, I should note that I focused on 69...hxg5 because it seemed the most direct way for Black to achieve his goal: eliminating the remaining White pawns.  As we will see, however, this is not the only way that Black can achieve a draw in this ending.

a) 69...h5

It seems foolish at first sight to leave White with the advanced pawn on g5, but Black has a very specific goal in mind.  If Black can capture the pawn on g2, force White to advance the other pawn to g6, and get his King back in time, then he achieve the following fortress position:

White cannot force Black's king away from e7 and f8: if White's king gets too close, then it is stalemate.

The Elusive Win in Kramnik-Carlsen

Today at the London Chess Classic, Vladimir Kramnik and Magnus Carlsen played a fantastic game. At move 62, Kramnik exchanged down into what he must have thought would be an easily-winning piece-up endgame. At move 65 the players reached the following position:

Carlsen saw a clever drawing idea, however: he would send his king deep into White's position. If White tried to push his own king forward, Black would attack the White pawns from behind. There thus followed:

65...Kd4 66.Kf3 Kd3 67.g4 Kd2 68.Be6 Kd3

Here Kramnik played 69.Kg3 and Carlsen defended marvelously to achieve the draw.

In this post, I want to examine the alternative 69.g5, which I believe was winning.