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"Black's rook occupies a good position on b5 as it hinders the advance of White's king: <1. Rg6+> After 1. f5 Black can give checks from behind: 1 ... Rb1 2. h6+ Kh7 3. Kg5 Rg1+ 4. Kf4 Rf1+ 5. Ke5 Re1+ 6. Kf6, and then: a) The immediate 6 ... Kxh6? runs into 7. Kf7+! Kh7 8. Ra2 Rh1 (8 ... Kh6 9. f6 Rb1 10. Rh2+! Kg5 11. Kg7 ) 9. f6 . b) 6 ... Rb1! is correct: Black draws after 7. Re6 Kxh6 =. <1 ... Kf7 2. Rg5> In "Batsford Chess Endings," Speelman draws attention to Kopaev's idea (see ECE 582) 2. Kh4!? with the plan of Rg3 to cut Black's king off from the h-pawn (he argues that therefore 1 ... Kh7 might even be preferable to Smyslov's 1 ... Kf7). Black must now find 2 ... Rb1! (2 ... Ra5? 3. Rg3 Ra1 4. h6 Rh1+ 5. Kg5 Ra1 6. f5 Rb1 7. Rg4 Ra1 8. Rh4 Rg1+ 9. Kf4 Rf1+ 10. Kg4 Rg1+ 11. Kf3 Rg8 12. h7 ) 3. Kg5 Rg1+ 4. Kh6 Rf1 5. Rg7+ Kf6 6. Rg8 Kf7 7. Rg4 Rh1 = in order to draw. <2 ... Rb1!> The south-west corner is the right place for the rook. It can give check from the side or behind depending on White's winning attempts. <3. Rc5> 3. h6 Ra1! (3 ... Rg1+? 4. Kf5 Rh1 5. Rg7+ ) 4. h7 (4. Rh5 Kg8 5. h7+ Kh8 6. f5 Ra4+ 7. Kg5 Ra6 =) Rg1+ 5. Kf3 Rh1 6. Ra5 Kg6 7. Ra7 Kf5 =. <3 ... Kf6 4. Rc6+ Kg7!> This decision is of crucial importance. After 4 ... Kf7? Black's king is driven to the back rank: 5. Kg5 Rg1+ 6. Kf5 Rh1 7. Rc7+ . <5. Kg5 Rg1+! 6. Kf5 Ra1 7. Rc7+ Kh6 8. Re7 Rb1 9. Re8 Kg7 10. Re5 Ra1 11. Rd5 Rf1> 11 ... Rb1 =. <12. Rd4 Ra1 13. Rd6 Ra5+ 14. Kg4 Ra1> 14 ... Rb5!? 15. Rg6+ brings us to the same position that arose after 1. Rg6+. <15. Re6 Rg1+ 16. Kf5 Ra1 17. h6+ Kh7!> Now Black's king has to go to the h-file so that it can take the h-pawn when necessary. <18. Rd6 Ra2 19. Kg5 Rg2+ 20. Kf6 Kxh6! 21. Ke7+ Kh7> Or 21 ... Kg7 22. f5 Re2+ 23. Re6 Rf2! 24. f6+ Kg6! (24 ... Kg8? 25. Re5 ) 25. Rd6 (25. f7+ Kg7! =; 25. Re1 Ra2 26. Rg1+ Kh7 27. f7 Ra7+! =) 25 ... Rf1 =. <22. f5 Re2+ 23. Re6 Ra2 24. f6 Ra8! 25. Kf7 Kh6 26. Re1 Ra7+! 27. Re7 Ra8> 27 ... Ra1 28. Kf8 Kg6! 29. f7 Kf6! 30. Kg8 Rg1+! =. <28. Rd7 Kh7 29. Rd1 Ra7+! 30. Ke6 Ra6+ 31. Rd6 Ra8 32. Rd4 Kg8 33. Rg4+ Kf8 1/2-1/2> You should study the role of Black's king in detail. It must avoid being confined to its back rank and can stay on g7 until White plays Rg6+ or h6+. After Rg6+ both ... Kf7 and ... Kh7 draw, but h6+ forces it to go to h7."

Smyslov had this type of endgame six years earlier (Smyslov vs Bondarevsky, 1941 ) and undoubtedly learned how to master it after studying that game. He also had advantages over players of today: after Black's 41st move and again after White's 66th move, the game was adjourned. Nowadays, games are finished in one session, and when the players reach such endgames, they are frequently playing at a very fast rate and more errors are made.

In an effort to win, White usually sacrifices the h-Pawn in an attempt to promote the f-Pawn. But if Black wants to draw, it is important to know what to do in the following position:

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Smyslov's 106...Ra8! is the only move to draw in this position. For an example of a different (=losing) move see Onischuk vs S B Hansen, 2006 after White's 83rd move.

E. 1
Black to move. Last: 63.Rxg6

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The rook ending has now transformed to 2 pawns against 1 pawn.

FinalGen considers the position as a win for White.

E. 1.1
If Black plays 63...h4 then only 64. g4 wins

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Stockfish after 25-minute analysis after 63...h4 64. g4:

1) +4.32 (31 ply) 64...Kf7 65.Rh6 Kg7 66.Rxh4 Rd5+ 67.Kf4 Kg6 68.Rh5 Rd4+ 69.Ke3 Ra4 70.Rd5 Ra3+ 71.Ke4 Ra1 72.f4 Re1+ 73.Kf3 Rf1+ 74.Ke3 Kf6 75.g5+ Kg6 76.Rd6+ Kg7 77.Rb6 Ra1 78.Ke4 Rd1 79.Kf5 Rd7 80.Rh6 Rd5+ 81.Kg4 Rd1 82.Rb6 Rd4 83.Kf3 Ra4 84.f5 Rd4 85.Rb8

2) +4.32 (30 ply) 64...h3 65.Rh6 Rd5+ 66.Kf4 Rd4+ 67.Ke5 Ra4 68.g5 Ra5+ 69.Kf4 Ra2 70.Rxh3 Rb2 71.Rh7+ Ke6 72.Rh6+ Kf7 73.Kf5 Kg7 74.Rh3 Rb3 75.Kg4 Rb1 76.f4 Kf7 77.Rh6 Kg7 78.Rd6 Rb4 79.Rd7+ Kg6 80.Rd5 Kg7 81.Kf5 Rb7 82.g6 Re7 83.Rd6

E. 1.2
Game instead continued with 63...Rd3
White to move.

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Now White could have won with 64. Rf6!

Also, the great endgame specialist, Poghosyan, analyzed the above position years earlier and had come to the same conclusion as FinalGen that the attacker (White) wins.

See Diagram D. 5, it is on the bottom of the article of
f- and g-pawns versus h-pawn rook endings

'https://www.chesspub.com/cgi-bin/ch...

E. 1.3
Black to move. Last: 64.Rf6

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Stockfish after 15-minute analysis:

1) +11.75 (35 ply) 64...Rd1 65.Rf4 Rh1 66.Rh4 Rg1 67.Kf4 Kf7 68.Rxh5 Rb1 69.Kg4 Rb6 70.f4 Rg6+ 71.Kh4 Rc6 72.f5 Rc5 73.Kg5 Rb5 74.g4 Kg7 75.Rh6 Rd5 76.Rb6 Rd7 77.Rg6+ Kf8 78.Rh6 Rg7+ 79.Kh5 Rd7 80.Rh8+ Kg7 81.Rb8 Kh7 82.Kg5 Rd2 83.Rb6 Kg8 84.Kg6 Kf8 85.Kf6 Ke8 86.Kg5 Rd7 87.Rb8+ Kf7 88.Rb6 Kf8 89.Rg6 Rd1

2) +12.04 (35 ply) 64...Rd8 65.Rf4 Ke6 66.g4 Rg8+ 67.Kxh5 Rh8+ 68.Kg6 Rg8+ 69.Kh7 Rg5 70.Kh6 Ra5 71.Kg6 Ra3 72.Rf6+ Kd7 73.f4 Kc7 74.Kh5 Kb8 75.Kg5 Ra4 76.f5 Kb7 77.Rh6 Kb8 78.Rh8+ Kb7 79.Rh5 Ra5 80.Rh7+ Kc8 81.Kh4 Kd8 82.Rh6 Ke7 83.Kg5 Kf7 84.Rh5 Rb5 85.Rh7+ Kf8 86.Rh8+ Kg7 87.Rh6 Rc5 88.Rb6 Kf74

3) +11.74 (34 ply) 64...Rd2 65.Rf4 Rh2 66.Rh4 Rg2 67.Kf4 Rd2 68.Rxh5 Rb2 69.Kg4 Rb4+ 70.f4 Rb3 71.Kh4 Rb1 72.f5 Ra1 73.g4 Rh1+ 74.Kg5 Ra1 75.Rh8 Kf7 76.Rh7+ Ke8 77.Kg6 Ra6+ 78.Kh5 Kd8 79.Kg5 Ra5 80.Kh4 Ra1 81.Rh6 Rh1+ 82.Kg5 Ra1 83.Rg6 Rf1 84.Rb6 Rd1 85.Rf6 Re1 86.Rd6+ Kc7 87.Rh6 Re8 88.Rh7+ Kb8

64...Ra3 can be met by 65. g4 or Rf5 or Rf4 or Kg6

Stockfish 15-minute analysis after 64...Ra3 65. Rf5:

1) +11.2 (31 ply) 65.Rf5 Ra8 66.Kxh5 Rh8+ 67.Kg5 Rg8+ 68.Kf4 Rc8 69.g4 Rg8 70.g5 Rg7 71.Kg4 Rg8 72.Rf4 Ke8 73.Kh5 Rh8+ 74.Kg6 Rg8+ 75.Kh6 Rh8+ 76.Kg7 Rh3 77.Rf5 Kd8 78.Kf6 Ke8 79.Kg6 Ke7 80.Rf6 Rh8 81.Kf5 Rc8 82.f4 Ke8 83.Kg6 Ke7 84.Rf5 Rg8+ 85.Kh7 Rd8 86.Kg7 Ke6 87.Re5+ Kd6

E. 1.4
64...h4 is met by 65. gxh4 - Black's king is cutoff <Poghosyan>
Shredder confirms this a win for White

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I don't have any engine analysis but as g15713 indicated after 63.Rxg6 FinalGen considers the position as a win for White. This is also the first position that's amenable to Lomonosov 7-piece tablebase evaluation, and they also consider the position as a theoretical win for White, White mating in 36 moves. So since after 63.Rxg6 the position is considered to be a theoretical win for White and the game's final result was a draw, I would conclude that somewhere between moves 63 and 115 White missed the win.

You can use the Lomonosov tablebases to quickly determine where White missed the win between 63.Rxg6 and 115.Rg4+ by using a binary search. I got the following results after each of the following White moves:

(1) 63,Rxg6+ White mates in 36
(2) 89.Rc7+ Draw
(3) 76.Kg4 Draw
(4) 70.Rg2 Draw
(5) 67.Kf2 Draw
(6) 65.Rg5 Draw
(7) 64.Kf4 Draw

So it looks like White missed the win immediately after 63.Rxg6 since after 63...Rd3 the tablebases indicate that White mates in 35 after 64.Rf6, so 64.Kf4 apparently threw away the win, although there might have been other blunders by White and Black in between the tablebase positions I checked. And, of course, this would only be a theoretical win since it would require that White played the best move for the following 35 moves and that might very well not have happened, although if it did then Black probably would have resigned before then.

It would also be instructive to find out when White could first theoretically win. The first position that's amenable to FinalGen analysis is the position after 55.Kxe3 since this is the first position that contains only one piece for both sides besides kings and pawns.

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Unfortunately, as chess user <AylerKupp> points out, FinalGen estimates that it would require about 2 TB of disk space when I only have 1 TB SATA drive (865 GB workable space). Instead of waiting to buy a new computer let us try to break down the position.

Game continued:

55...h5 56. Ra6+ Kf5 57. Ra5+ Kf6

F. 1.1
58. Kf4 was now played as in the game

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I propose 58...h4!? as a solid defense and after 59. Ra6+ Kf7 seems to draw according to Stockfish.

F. 1.2
White to move. Last: 59...Kf7

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Stockfish 15-minute analysis:

1) +0.11 (51 ply) 60.Ra2 Kf6 61.Kg4 Rc4 62.Ra6+ Kf7 63.Kxh4 Rxd4+ 64.Kg5 Rd5+ 65.Kf4 Rb5 66.Kg4 Rc5 67.Ra4 Kg7 68.Ra7+ Kf6 69.f4 Rd5 70.g3 Rb5 71.Ra8 Kg7 72.Ra4 Kf6 73.Ra7 Rd5 74.Ra8 Rb5 75.Rf8+ Kg7 76.Re8 Kf6 77.Re4 Rd5 78.Rc4 Rb5 79.Rc8 Kf7 80.Rc3 Kf6 81.Re3 Rd5 82.Ra3 Rc5 83.Ra6+ Kf7 84.Ra7+ Kf6 85.Ra1 Rd5 86.Ra6+ Kf7 87.Kf3 g5 88.Ke4 Rb5 89.f5 Rb3

2) +0.08 (51 ply) 60.Ra5 Rc2 61.Rg5 Kf6 62.Rg4 Re2 63.d5 Re7 64.d6 Rd7 65.Ke4 Rxd6 66.Rxh4 Rd2 67.Rf4+ Kg5 68.Rg4+ Kf6 69.Kf4 Rd5 70.Ke3 g5 71.Ra4 Re5+ 72.Kf2 Re6 73.Ra7 Rb6 74.Kg3 Kg6 75.Kh2 Rd6 76.g3 Rd3 77.Kg2 Kf6 78.Ra6+ Kg7 79.Ra1 Kg6 80.g4 Rd2+ 81.Kg3 Rd3 82.Ra5 Kf6 83.Rc5 Kg6 84.Rc6+ Kf7 85.Rh6 Rd4 86.Ra6 Rd2 87.Ra5 Kg6

3) +0.08 (50 ply) 60.Ra4 Rc2 61.g4 h3 62.Ra7+ Kg8 63.Kg3 h2 64.Ra1 g5 65.Rh1 Rd2 66.Rxh2 Rxd4 67.Rh5 Rd5 68.Kf2 Kg7 69.Ke3 Rb5 70.Kd2 Rd5+ 71.Kc3 Kf6 72.Rh8 Ra5 73.Kd3 Ra3+ 74.Ke2 Ra2+ 75.Ke3 Ra3+ 76.Kf2 Kf7 77.Rh6 Ra5 78.Rh7+ Kg6 79.Rd7 Ra2+ 80.Ke3 Ra5 81.Rd2 Ra3+ 82.Ke4 Kf7 83.Rd5 Kg6 84.Rd6+ Kf7 85.Rd3 Ra4+ 86.Ke5 Ra5+ 87.Kd6 Ra4 88.Kd7 Rf4 89.Rd6 Rxf3

Going back to diagram F. 1

After 55...h5 56. Ra6+ Kf5 57. Ra5+ Kf6

F. 1.3
58. g4 is a nice try to win

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F. 1.4
But Black can respond with:
58...hxg 59. fxg Rc1! - only move to draw according to my cursory analysis (Actually, FinalGen says White wins or Draw)

Those with Lomonosov 7-piece tablebases can verify this as they have an advantage as they contain the exact evaluations (draw or moves to mate) for all positions with no more than 7 pieces on the board.

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Example lines after 59...Rc1

60. Ra2 Kg5 61. d5 Kxg4 = (Shredder)

60. g5+ Ke6 61. Ra6+ Kf5 62. Rf6+ Kxg5 63. Rf2 = (Shredder)

Going back to diagram F. 1.1

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After 58. Kf4 the game continued with:

58...Rc2 59. g3 Rd2 60. Ra6+ Kf7 61. Kg5 Rxd4 62. Rf6+ Ke7 63. Rxg6 Rd3

which led to diagram E. 1.2 in an above post of mine

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<"Gligoric played here 1.Kf4? which gave Smyslov the possibility to sacrifice his pawn and to go into a drawn ending with f- and h-pawns: 1...Ra3 2.Rg5 Ra4+ 3.Ke3 Ra3+ 4.Kf2 Ra2+ 5.Kg1 h4 6.gxh4 Kf6 =.

In fact, the position in the diagram is winning, but the correct move was missed by the players during the game and by numerous annotators in their analysis."> Poghosyan (05/23/12)

The capture of the White d-pawn was a red herring which led Black astray while White in turn missed the chance to cutoff the Black king with 64. Rf6.