This position has been well-known since Kopayev’s analysis of the game Capablanca – Yates (Hastings 1930/31). Kopayev believed that after Black’s last move, Rc4–Rc6, a draw could be secured. However, this assertion was refuted in 2011. Dvoretsky included the winning line (with 10.Ra3 f6 11.Ra7+ Kf8 12.exf6 Rxf6 13.Kg3 Kg8 14.Ra4 followed by Kh4–h5) in the forth English edition of his Endgame Manual (2014). 

At the same time, he accepted Kopayev’s variation 10.f5 Kf8 11.Ra3 Rc1 12.Ra8+ Ke7 13.f6+ Ke6 14.Re8+ Kd5 15.e6 Rc6 as a draw (Dvoretsky’s Endgame Manual, 5th ed., D. 9–120, p. 201). Gelfand also considered 10.f5 a mistake in his Decision Making in Major Piece Endings (2020).

As I recently noted in the thread “Capablanca–Yates (Hastings, 1930) Revisited”, contrary to the prevailing opinion (Kopayev, Dvoretsky, Gelfand), the move 10.f5 also leads to a win - albeit in a more complex fashion.

1.f5?! Rc1

The move 1...Rc1 is Black’s most resilient defense, aiming to transfer the rook to the first rank to harass the White king from behind. Kopayev only analyzed 1...Kf8 2.Ra3 Rc1 3.Ra8+ Ke7 4.f6+? Ke6 5.Re8+ Kd5 6.e6 Rc6 =. Instead of 4.f6+?, the move 4.Ra7+ leads to the main winning line after 4...Ke8 5.f6+.

Shankland analyzed this position in Theoretical Rook Endgames (2023) with Black’s rook on g1 (pp. 188–190).

2.Rd3!

Only by seizing control of the d-file can White hope to win. The importance of this file is illustrated by comparing the lines:
•      2...Rf1+ 3.Ke4! Rg1 4.Rd7! Rxg4+ 5.Kf3! Rg5 6.Kf4! Kg8 7.Rd8+! Kh7 8.e6 fxe6 9.fxe6! Rg8 10.e7+– (Shankland) with
•      2.Ra3? Rf1+ 3.Ke4 Rg1! 4.Ra7 Rxg4+! 5.Kf3 Rg5! 6.Kf4 Kg8! 7.Ra8+ Kh7! 8.e6 fxe6! 9.fxe6 Rg8=.

In the latter, White is forced to retreat, e.g. 10.Ra1, after which Black draws with 10...h5! 11.Kf5 (or 11.Ke5 Rg2 12.e7 Re2+! 13.Kf6 Rf2+! 14.Ke6 Re2+! 15.Kf7 Rf2+! 16.Ke8 Re2=) 11...Rf8+! 12.Kg5 Re8 13.Ra7+ Kg8! 14.Kf6 Rf8+! 15.Ke7 Rb8 =.

2...Kf8 3.f6 Ke8 

Shankland writes: "All White needs to do to win the game is get his rook to the seventh rank without allowing Black’s king to d7. Then, a check on e7, followed by bringing the king to d8, will win. But this is easier said than done! As soon as the rook transfers to a square like b3 aiming to go to b7 next, Black’s king will be free to go to d7. The winning plan for White is as follows: First, he must walk his king to d6. Then he can transfer his rook to the side, threatening mate on the back rank. In order to avoid mate, Black will need to start checking from behind. When he does, the potential for skewers along the d- and e-files makes it impossible for him to get his king to d7. Let’s see how this would look in action". 

However, even once White reaches the setup with the rook on e7 and king on d8, victory is far from obvious, as Black still retains resources for harassment through both lateral and vertical checks.

4.Rd4

"White overprotects his g4-pawn and prepares the king’s journey" (Shankland).

4...Rg1

Black continues to obstruct White’s king. Shankland examines only the passive line 4...Rb1 5.Ke4 Ra1 6.Kd5 Rb1 7.Kd6 Rc1 8.Rd5 Ra1 9.Rb5 Rd1+ 10.Kc5 Rc1+ 11.Kd4 Rd1+ 12.Ke4 Re1+ 13.Kd3 Kd7 14.Rb7+ Ke6 - a weak move that accelerates White's win. Shankland does not consider 14...Ke8, after which the outcome is still unclear (see the main line after 25...Ke8).

5.Kf4 Rf1+ 6.Ke4 Re1+ 7.Kf5 Rf1+ 8.Rf4 Ra1 9.Rb4 Rf1+ 10.Ke4 Re1+ 11.Kd5 Rd1+ 12.Kc5 Rc1+ 13.Rc4 Rg1 14.Kb6 Kd8 15.Kc6 Ke8 16.Kc7 Ra1 17.Rc5 Rg1 18.Kd6 Rd1+ 19.Kc6 Ra1 20.Rb5 Rc1+ 21.Kd5 Rd1+ 22.Ke4 Re1+ 23.Kd3 Kd8 24.Rb8+ Kd7 25.Rb7+! Ke8 26.Re7+ Kf8 27.Kd4 Rd1+

I have analyzed this position in 2013 in “Duras-Capablanca (1913) revisited”, D. 1.-8, after 19.Re7+ Kf8 20.Kd4 Rd1+.

28.Kc5 Rc1+ 29.Kd6 Rd1+ 30.Kc7 Ra1 31.Kd8 Ra8+

31...Rd1+ 32.Rd7 Rg1 33.Rd4 Rb1 34.Kd7 Ra1 35.Rd5 Re1 36.Ra5 Rd1+ 37.Kc6 Rc1+ 38.Kd5 Rd1+ 39.Ke4 Re1+ 40.Kd4 Rd1+ 41.Ke3 Ke8 42.Ra8+ Kd7 43.Rf8 Re1+ 44.Kd4 Rd1+ 45.Kc3 Rc1+ 46.Kd2 Rc4 47.Rxf7++–.

32.Kd7 Ra7+ 33.Kd6 Ra6+ 34.Kc5 Ra5+ 35.Kb6 Ra1 36.Ra7 Rb1+ 37.Kc5 Rc1+ 38.Kd4 Rd1+ 39.Kc4 Rd8

39...Rc1+ 40.Kd3 Rd1+ 41.Ke2 Rd8 42.Kf3 Ke8 43.Ra1 Kf8 44.Kf4 Re8 45.g5 hxg5+ 46.Kxg5 Rxe5+ 47.Kh6 Ke8 48.Ra8+ Kd7 49.Kg7+–.

40.Kb5 Ke8 41.Kb6 Rd1

41...Kf8 42.Kc7 Ke8 43.Ra1 Rd7+ 44.Kc6 Rd8 45.g5 Rc8+ 46.Kd6 Rd8+ 47.Kc7 Rd7+ 48.Kc6 Rd8 49.gxh6+–

42.Ra8+ Kd7 43.Rf8 Rb1+ 44.Kc5 Rc1+ 45.Kd4 Rd1+ 46.Kc3 Rc1+

46...Ke6 47.Re8+ Kd7 48.Re7++–

47.Kd2 Rc4 48.Rxf7+ Ke8 49.Re7+ Kf8 50.Ke3 Rxg4 51.Ra7 Rg1 52.Ke4 Rf1 53.Kd5 Rb1 54.Ke6 Rb8 55.Kf5 Rb5 56.Rh7+–