Why is the f7-g6-h5 pawn complex so important for black in rook endgames?

Question

I was watching the chess24.com video on endgames with Mark Dvoretsky, and the video “Plus-equal mode | Part 1” covered the game Tony Miles-Simon Webb, Birmingham 1975, and we quickly get to the double-rook endgame.

 [Event "Birmingham Zetters"]
 [Site "Birmingham"]
 [Date "1975.04.08"]
 [Round "11"]
 [White "Miles, Anthony John"]
 [Black "Webb, Simon"]
 [Result "1-0"]
 [ECO "A05"]
 [SetUp "1"]
 [FEN "2r5/p4rkp/5pp1/5q2/3Q4/6P1/P4PKP/1R1R4 b - - 0 23"]
 [PlyCount "82"]
 [EventDate "1975.03.27"]
 [EventType "tourn"]
 [EventRounds "15"]
 [EventCountry "ENG"]
 [EventCategory "6"]


 1... Rc2 2. a3 Qc5 3. Rb3 Qxd4 4. Rxd4 Re7 5. Ra4 Kf7 6. Ra6 Rce2 7. Rb4 Rd7 8. Rba4 Ree7 9. g4 h5 10. gxh5 gxh5 11. R4a5 Kg6 12. h4 Rc7 13. Rg5+ Kf7 14. Rxh5 Kg7 15. Rf5 Rf7 16. Kg3 Rc3+ 17. f3 Rc1 18. Rfa5 Rcc7 19. Kg4 Rc4+ 20. f4 Rcc7 21. Kf5 Rb7 22. a4 Rbc7 23. h5 Rb7 24. h6+ Kxh6 25. Rxf6+ Kg7 26. Rxf7+ Kxf7 27. Ra6 Rc7 28. Kg5 Kg7 29. f5 Rd7 30. a5 Rc7 31. Rd6 Kf8 32. Rd8+ Ke7 33. Rh8 Kd6 34. Kg6 Rc1 35. Ra8 Ke5 36. Re8+ Kf4 37. f6 Rg1+ 38. Kf7 Ra1 39. Kg7 Kf5 40. f7 Rg1+ 41. Kf8 Kg6 42. Re6+ 1-0

Although Webb had the pawn on f6 already, GM Jan Gustafsson mentioned at one point that he wanted to play h5 several times, somewhat setting up the desirable formation. Black hesitated, and white played the common stopping move to that setup, g4! This led to black getting impatient, and playing h5 himself, which led to creating another weakness.

So just why is that f7-g6-h5 setup so important?

P.S. I should have added that the point of this question is "how to draw the 4-3 rook endgame on the kingside, and how that pawn setup is so important." It is also important that it is before the pawns have net and passed each other, as this is very typical in OTB play.

Answer 1

So just why is that f7-g6-h5 setup so important?

Compare the two pawn structures below, one on the kingside where Black has achieved the f7-g6-h5 structure and one on the queenside where White has achieved an advanced equivalent pawn structure.

[FEN "8/p4p2/Pp3Pp1/1Pp3Pp/2P4P/8/8/8 b - - 0 23"]

[FEN "8/p4p2/Pp3Pp1/1Pp3Pp/2P4P/8/8/8 b - - 0 23"]

Now imagine kings on the board and one minor piece, say a knight for each side. White has more space, Black less so White is attacking. How could White win? How could Black defend?

Well, on the queenside Black has to guard against a sacrifice on b6. If White sacrifices on b6 then Black needs to be in the square of the White pawn on a6. That means no closer to the center than c7 or c8. Otherwise the piece capturing on b6 can't be taken.

Now look on the kingside and ask the same question. This time the equivalent sacrifice is on g6 and the Black king has to be no further away from the action than e6 or d6. Note that f5, taking the sacrificed piece with the king, is also possible.

e6, d6 and f5 are much closer to the center of the board than c7 and c8. Clearly if Black faces a situation on one side of the board like that on the kingside with pawns and rooks elsewhere on the board his king will be able to both defend and be much better placed for action, much more active, than if he faces the same situation but with pawns arranged as on the queenside.

Answer 2

This is a very common rook endgame at higher levels, and it is considered very important to know how to defend it at the 2000-rating level and above, and maybe even a little lower.

The answer as to why the f7-g6-h5 formation is so important is that it combines a relatively safe pawn structure for hiding the black king, and it makes it almost impossible with best play for white to obtain a passed pawn without trading down to the last pawn, which is a draw. Sometimes, white is allowed to create a passed h-pawn, but it is still an easy draw. Lastly, with a pawn on f7, in some lines of defense, it provides a black rook with the solid e6 square, keeping the white king from wandering to d7 and then e8 attacking f7.

Consider these classic 4 versus 3 pawns rook endgames as the primary reason.

Here are a couple of rook endgames at the highest level that show the proper classical defense.

 [Event "Moscow Chess for TV"]
 [Site "Moscow"]
 [Date "2019.06.14"]
 [Round "3.2"]
 [White "Dubov, Daniil"]
 [Black "Radjabov, Teimour"]
 [Result "1/2-1/2"]
 [ECO "E12"]
 [WhiteElo "2700"]
 [BlackElo "2759"]
 [SetUp "1"]
 [FEN "8/5pkp/6p1/4P3/1r3P2/R5PP/6K1/8 b - - 0 38"]
 [PlyCount "85"]
 [EventDate "2019.06.10"]
 [EventType "k.o."]
 [EventRounds "6"]
 [EventCountry "RUS"]

 1... h5 2. Kf3 (2. Kh1) 2... Rc4 3. Rb3 Ra4 4. Rc3 Rb4 5. Ra3 Rc4 6. g4 hxg4+ 7. hxg4 Rc1 8. Ra7 Rf1+ 9. Ke4 Rg1 10. Kf3 Rf1+ 11. Kg3 Rg1+ 12. Kh4 Re1 13. Kg5 Re2 14. Re7 Re4 15. Ra7 Re1 16. Ra6 Re2 17. Ra1 Re3 18. Ra5 Re1 19. Ra7 Re2 20. Ra5 Re1 21. Rb5 Re2 22. Kh4 Re1 23. f5 gxf5 24. gxf5 Rf1 25. Kg5 Rg1+ 26. Kf4 Rf1+ 27. Ke4 Re1+ 28. Kd5 Rf1 29. f6+ Kg6 30. Kd6 Ra1 31. Rb7 Ra6+ 32. Kd5 Ra5+ 33. Ke4 Ra4+ 34. Kd5 Ra5+ 35. Kd4 Ra4+ 36. Kc5 Ra5+ 37. Kd6 Ra6+ 38. Ke7 Re6+ 39. Kf8 Rxe5 40. Rxf7 Re6 41. Kg8 Re8+ 42. Rf8 Rxf8+ 43.  Kxf8 Kxf6 1/2-1/2

And a second game.

 [Event "ESP-chT Div Honor"]
 [Site "Monzon"]
 [Date "2016.10.02"]
 [Round "7.4"]
 [White "Bacrot, Etienne"]
 [Black "Anton Guijarro, David"]
 [Result "1/2-1/2"]
 [ECO "E17"]
 [WhiteElo "2692"]
 [BlackElo "2630"]
 [SetUp "1"]
 [FEN "2r3k1/5p2/6p1/3R3p/8/2N1P1P1/5P1P/5K2 b - - 0 34"]
 [PlyCount "84"]
 [EventDate "2016.09.26"]
 [EventType "team-tourn"]
 [EventRounds "7"]
 [EventCountry "ESP"]


 1... Rxc3 2. Ke2 Kg7 3. f3 Ra3 4. e4 Kf6 5. Rd3 Ra2+ 6. Rd2 Ra3 7. Kf2 Rb3 8. f4 Ra3 9. Rb2 Kg7 10. e5 h4 11. gxh4 Rh3 12. Kg2 Rxh4 13. Kg3 Rh8 14. Rb7 Re8 15. Kg4 Re6 16. h4 Ra6 17. h5 gxh5+ 18. Kxh5 Rh6+ 19. Kg5 Rg6+ 20. Kf5 Ra6 21. Kg4 Ra1 22. Kg5 Rg1+ 23. Kf5 Rg6 24. Ke4 Rg1 25. f5 Re1+ 26. Kd5 Rf1 27. f6+ Kg6 28. Rb3 Ra1 29. Rg3+ Kf5 30. Kd6 Ra6+ 31. Ke7 Ra7+ 32. Kf8 Kxe5 33. Kg7 Kf5 34. Rf3+ Ke6 35. Rf1 Rb7 36. Rh1 Ra7 37. Re1+ Kf5 38. Re7 Ra6 39. Rb7 Rc6 40. Rxf7 Kg5 41. Rf8 Ra6 42. Rf7 Rc6 43. Rf8 1/2-1/2