The notes to the game are provided by Garry.
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After 54...Rxa7 55.Rh7+ White skewers the rook through the Black king. This is vital endgame technique and needs to be remembered.
Lets take a look at the simplest form of this ending.
This position is a book draw, as long as Black keeps his king on one of his 7 safe squares, shown below.
Black can shuffle his king between h7 and g7 and if White tries to advance his king to help the pawn then the Black rook can check from behind to frustrate White's winning chances. The point is that White no longer has his skewer trick, or a tempo gaining check. So the draw is easy to defend for example:
1.Kf3 Kh7, 2.Ke4 Kg7 3.Kd5 Kh7, 4.Kc6 Kg7, 5.Kb7 Rb1+
Once White moves his king Black can either throw in a few more checks or return his rook to the a-file, there is no way for White to make progress.
From the pure form of these endings we have to try and calculate the difference we may see in an actual game.
here White plays 52.a6 and I would argue that after 52...Kg7 53.a7 we have the book draw. However, White can increase his winning chances by delaying a7, then his plan should be
- walk his king to Ka7
- use the rook to cover the b-file to block checks
- Move the king to b7
- Advance the a-pawn
This plan is discussed by Karsten Muller and Frank Lamprecht in their Fundamental chess endings. Frustratingly they provide an advanced drawing technique for Black in the purest form of the position from a composition by J.Vancura in 1924
Black then has checks from the side to save him, but there are some tough-to-find moves in this defence. Perhaps another time...