When It Paid To Trade Down To A Pawn Ending

I MENTIONED in my post on Sunday at the end of Hastings (https://beauchess.blogspot.com/2020/01/hastings-concluded.html) that the materially-weaker side in an endgame should nearly always avoid exchanging into a pawn-ending.
I added that I could only recall one instance off the top of my head when I successfully traded down to secure a draw, although that was against an international master.

A pair of rooks has just been exchanged on e2 in Spanton (2096) - Viesturs Meijers (2418), Lausanne 1999

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33...Rb6
The analysis engines Komodo10 and Stockfish10 reckon Black should start with 33...g5!?, but I do not see how this helps Black after the obvious 34.hxg5 hxg5 (but read on to see why they are probably right).
Latvian IM - now GM - Meijers tries a different approach.
In general it can be said that if the black rook were defending the extra pawn from somewhere on the a file, this position would be drawn (at least if I am reading Reuben Fine correctly in Basic Chess Endings).
However, James Howell says in Essential Chess Endings that the situation can be very different if the extra pawn is being defended from the side. "The key to success," he writes, "is to arrange his pieces so that his rook is not only defending the passed pawn but also the base of his pawn-chain on the other wing. [White] might try to create counterplay by advancing his king and pawns but in principle there shouldn't be anything stopping the [black] king coming over to shepherd the pawn home."
That would suggest Black should start here with 33...Kf8. But 34.Ra8+ Ke7 35.Ra7+ Kd8 is met by 36.g5, forcing the black rook to give up defending either f7 or a6. Now I understand why the engines recommend 33...g5.
34.h5 Kf8
In my original notes to the game, I suggested Black should try 34...g6. I suspect my idea was that 35.hxg6 fxg6 would give Black hope of creating a second passed pawn. However, the engines reckon the position is dead drawn, presumably because the black king is cut off on the back rank. They reckon Black gets a slight edge by recapturing with 35...Rxg6, although it is hard to see this position being seriously dangerous for White.
35.Kd3 g6 36.hxg6 fxg6
The engines still prefer ...Rxg6, but give Black little chance of converting.
37.Rh7
Ruling out any possibility of the black h pawn becoming passed.
37...g5 38.Kc4 a5 39.Ra7 Rf6 40.Rxa5 Rxf3
My annotation to this move 20 years ago reads: "Fritz5 now has Black at plus over minus, verging on winning, and yet the position looks very drawish." I was right, according to Komodo10 and Stockfish10.
41.Ra6 Rf4+ 42.Kd3 Kg7
White has a much easier draw after 42..Rxg4 43.Rxh6.
43.Ra7+ Kg6 44.Ra6+ Rf6 45.Rxf6+!
VM's body language suggested he was very surprised by this move - he presumably took it as granted White should keep rooks on.
In my original notes I point out that 45.Ra4? h5 46.Ke3 hxg4 47.Rxg4 Kh5 46.Ra4 g4 "is a win according to Fine," and this is confirmed by Nalimov (at least after 46...hxg4 or 45.gxh5+). But it is quite possible other rook moves, eg 45.Ra8, also draw.
45...Kxf6

What are the keys to White's defence?

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The first point is that if the black king can ever get to e5, the white king must be able to oppose it by occupying e3. The second point is that if Black organises the sequence ...h5, gxh5+ Kxh5, Black only wins if his king can get to f3, g3 or h3.
46.Ke4
From the above, it can be seen 46.Ke2 also draws, but 46.Ke3?? is a gross blunder as the black king gets to e5 with White to move.
46...Kg6 47.Kf3 Kf7
Or 47...h5 48.gxh5+ Kxh5 49.Kg3=.
48.Ke3 Ke7 49.Ke4 Ke6 50.Kd4
The only move to draw. Note that the sequence 50.Kd3?? Ke5?? 51.Ke3 also draws, but in this case Black wins with 50...Kd5.
50...Kf7 51.Ke3 Kg7 52.Ke4 Kf6 53.Kf3
Another only move. Note that this time Kd3?? loses to 53...Kg6 54.Ke3 h5 55.gxh5+ Kxh5 56.Kf3 Kh4 57.Kg2 Kg4 as the black king gets to h3 or f3.
The similar blunder 56.Kd4?? (the position was reached with three more moves on the scoresheets) was played in Murat Eren Aytekin (2063) - Georgi Petrov (2207), EU Amateur U2300 Championship 2007. The game finished 56...Kg6 57.Ke4 h5 58.gxh5+ Kxh5 59.Kf3 Kh4 60.Kg2 Kg4 61.Kh2 Kf3 62.Kh1 Kg3 63.Kg1 g4 0-1.
53...Ke5
This position, but with Black to move, was reached in Friedrich Dicks - Ludger Lautenschütz, Recklinghausen 2002, and Omran Al Hosani (2101) - R Ashwath (2250), Sharjah Masters 2018. In both games, Black won quickly by outflanking White with ...Kd4.
54.Ke3 Kd5
In Vladimir Anchikov - Lazar Ivic (1648), World Schools U9 2013, Black tried 52 ...Kf6 (the position was reached with two fewer moves having been played), when White blundered with 53.Kd4??, either forgetting, or being unaware, that Black could win down the h file. The game concluded 53...Kg6 54.Ke3 h5 55.gxh5+ Kxh5 56.Kf2 Kh4 57.Kf1 Kh3 58.Kf2 g4 59.Kg1 Kg3 60.Kh1 Kf2 61.Kh2 g3+ 62.Kh1 g2+ 63.Kh2 g1=Q+ 64.Kh3 Qg3#.
55.Kd3 Ke5 ½–½