|Position 1: White to play and draw|
This one is dead easy. White uses a stalemate threat to force Black's king into the open, before employing the back-rank defense.
Not 1. Rb8?? Ra3#
1... exf2 is stalemate
Black cannot escape the barrage of back-rank checks, while 2... Ra1+ 3. Kf2 and White will just shuffle along the 1st and 2nd ranks.
Our 2nd position:
|Position 2: Black to play, can he save the game?|
At first glance 1... Ke8? seems to draw, because after 2. Kf6 Kd7 Black has what looks like an Inverse Philidor. However, this is not the case because Black's king is on the long side of the board: 3. Rh7+ (better than 3. Kf7 Re7+) 3. Ke8 4. Rh8+ Kd7 5. Ra8 Rb1 6. Kf7! (Black can no longer employ the side-rank defense because his king gets into the way) 6... Rf1 7. Ra7+ Kc6 8. f6 and White is on his way to creating a Lucena Position.
Instead, Black saves the game by denying White access to the f6 square (which allows him to shelter from checks):
No better is 2. Kg6 Rf1 where Black has an Inverse Philidor: 3. Ra3 Rf2 4. Ra7+ Kf8 5. f6 Rg2+ and White can't hope to win.
3. Rh7+ Kf8
Now repeated checks make no progress since Black can just shuffle his king along the 7th and 8th ranks.
4. Kg6 Rg1+
Our 3rd position is the most interesting:
|Position 3: White to move, can he win?|
The position arose in Ponomariov vs Polgar, Sofia 2005 after Black's 35th move. Both sides have their rooks tying the enemy king down to defending the pawns, but Black has another important defensive asset. The pawn on h5 denies White of too much central space, and discourages him from pushing g4 (which would lead to a pawn exchange favourable for Black). As such, this position should be a draw no matter which side to play.
As the stronger side White wants to gain as much centre space as possible. Black's defense is long and tedious, but don't worry: What matters here is that we understand the basic concepts.
If Black plays 36... f6, White's best chance will be to play 37. Rb5 (hitting the undefended pawn), but after 37... g6 38. Rb7 Rd2 39. Kh2 Rc2 (note how Black's rook ties the enemy king to the g-pawn) 40. Kg3 Rd2 41. Rb5 Kg7 42. Rd5 Rb2 (Not 42... Rxd5?? 43. exd5 +-) 43. Rd7+ Kg8 (43... Kh6? 44. Rf7 Rb6 45. Kf4 and White stands much better) the position is very much similar to the main line: As long as Black's rook remains on the 2nd rank, it will continue tying down White's king to the backward pawn.
37. Kh2 Kg7
38. Kg3 Re2
The basic idea is to keep the rook on the 2nd rank and make White's king babysit his pawn.
39. Rb6 Kf8
40. Rb1 Kg7
41. Rg1 (D)
|Position after 41. Rg1|
Freeing the White king, but Black has other plans.
42. Kf4 Rb2
43. g3 Rb4
Once again, the concept of active rook play is very important.
44. Rd1 Ra4
45. Ke3 Ra2
46. Rd4 Rg2!
It turns out White's g-pawn still needs protection after all!
47. Kf4 Rg1
48. e5 Re1
Hoping to entice Black into 49... Rxe4+?? 50. Kxe4 where the resulting king-pawn endgame is much better for White.
No way that a GM like Judit Polgar would fall for this!
50. Re3 Rg2
51. Re1 Rf2
White doesn't want to do a pawn trade favourable for his opponent, but there is no other plan; 52. Ke4 Rg2 is not going to help at all.
53. Kxg4 (D)
|Position after 53. Kxg4|
We now have a three vs two position.
54. Kh3 Rf2
55. Kg3 Ra2
56. Rd1 Re2
57. Rd5 Re1
58. Kf2 Rh1!
With the g-pawn gone, Black now turns her attention to... the h-pawn!
59. Rd4 Rh2+
60. Kg3 Re2
61. Re4 Ra2
62. Re3 Ra1
63. Rd3 Re1
64. f4 Rg1+
Another strong line is 64... Ra1 65. Kf3 Rh1 66. Rd7 Kf8 (wisely avoiding 66... Rxh4? 67. e6! where the pin causes problems for Black) 67. Kg4 Rg1+ and White can't do much.
65. Kf3 Rh1
66. Kg4 f5+
67. Kg3 Rg1+
Just look at how Black's rook dances around in enemy territory. As I repeat: Active play!
68. Kf3 Rh1
69. Rd7+ Kg8
70. Kg3 Rg1+ 71. Kh2 Rg4 72. e6 Kf8 and White has too many weak pawns to defend.
71. e6 Kf8
72. Kd4 g5
73. Ke5 gxf4
74. Rf7+ Ke8
75. Rxf5 Rh1
76. Rxf4 Ke7
|Position after 76... Ke7|
Looks like an upcoming Philidor Position? Only here it is easier, because Black can use a simple tactic to win back the pawn.
77. Rf2 Re1+
78. Kd5 Rxe6
In tedious and seemingly complicated positions like this, what matters is no longer memorization, but the understanding of concepts. I'll leave this link here for you to revise what we've covered: http://nushsblackknights.blogspot.com/2014/11/rook-pawn-endgames-four-vs-three.html
Hopefully I will be able to post up more positions for y'all to challenge yourselves further in the future!
"Chess Endgame Training" by Bernd Rosen
"Silman's Complete Endgame Course" by Jeremy Silman