Basic Rook Endgames

We lost on board count to old rivals Teignmouth in the Peter Rooke Cup at the end of January. One of the last games to finish involved a simple-looking Rook endgame. Just as it was getting crucial, White, short of time, found a time-saving blunder:
[Event "Peter Rooke Semi-Final"]
[Site "Teignmouth"]
[Date "2013.01.25"]
[Round "?"]
[White "Pope, Sean"]
[Black "Gorodi, John G"]
[Result "0-1"]
[ECO "B22"]
[PlyCount "124"]
[EventDate "2013.01.25"]
[EventCountry "ENG"]

1. e4 c5 2. c3 Nf6 3. e5 Nd5 4. d4 cxd4 5. Nf3 e6 6. cxd4 b6 7. Bd3 Bb7 8. O-O
Be7 9. Nc3 Nxc3 10. bxc3 Qc7 11. Bd2 d6 12. exd6 Bxd6 13. h3 Nd7 14. Re1 Nf6
15. Qe2 Nd5 16. Be4 O-O 17. Rac1 Nf6 18. Bb1 Bf4 19. Ne5 Bxd2 20. Qxd2 Nd7 21.
Qd3 g6 22. f4 Nxe5 23. fxe5 Qc6 24. Qe2 Rac8 25. Be4 Qxe4 26. Qxe4 Bxe4 27.
Rxe4 Rc4 28. Re3 Rfc8 29. Rd3 b5 30. Rb1 Rxc3 31. Rxc3 Rxc3 32. Rxb5 Rc1+ 33.
Kh2 Rc6 34. Rb2 Rc4 35. Rd2 Ra4 36. Kg3 Kg7 37. Kf3 f5 38. exf6+ Kxf6 39. Ke3
Ra3+ 40. Ke4 Ra4 41. Ke3 Ke7 42. Kd3 Kd6 43. Kc3 Kd5 44. Re2 Rc4+ 45. Kb3 Rxd4
46. Rf2 a5 47. Rf7 Ke4 48. Rxh7 Rd2 49. Rh4+ Kf5 50. Rg4 e5 51. Ra4 Rxg2 52.
Rxa5 Rg3+ 53. Kc2 Rxh3 54. Kd2 Kf4 55. a4 e4 56. Ra6 g5 57. Rf6+ Ke5 58. Rf8
Ra3 59. Ra8 g4 60. Ke2 Kf4 61. a5 Ra2+ 62. Kf1 Kf3 0-1
So what should the result have been? I discussed it briefly with my friend Bill Ingham. As is often the way, he fancied his side's chances to win, and I hoped for a draw, but the discussion showed how vague we all are about some basic theory. To be fair, some apparently small differences can change the best obtainable result:
--r-----
--------
----k---
--------
--P-----
-K------
--------
---R----
{White to move: draw.} 1/2-1/2
--r-----
----k---
--------
--------
--P-----
-K------
--------
---R----
{White to move: win.} 1-0 So, what was the right result for the Teignmouth game? Before I answer that, I want to decide: regardless of the right result, what is the right approach? You probably know the Philidor and Lucena positions. Philidor showed a draw, with the defending King having control of the Queening square. The defender keeps out the attacking King. White can make progress only by pushing the pawn, the Black shows a draw by sending the Rook a long way away and playing a flurry of checks.
----k---
R-------
-r------
----P---
----K---
--------
--------
--------
Black K has control of the queening square and bR has control of the sixth} 1. Kf5 1... Rc6 { now there is no shelter on the board from the checks for the White King.} 2. e6 Rc1 3. Kf6 Rf1+ 4. Ke5 Re1+ 5. Kd4 Rd1+ 6. Ke4 Re1+ 7. Kd5 1/2-1/2 The 'Lucena' position, shown by Salvio and attributed to Sciapino, is a win for the attacking side. With the defending King cut off by at least two files, the defending Rook has to play the flurry of checks from across the board. The attacker either makes an escape hatch for the King, or 'builds a bridge' so that the Rook can step in at the right moment.
--k-----
--------
----K---
----P---
--------
--------
---R----
-----r--
p{ White has control of the sixth/seventh with the K and the bK is cut off} 1. Ke7 1... Kc7 2. Rc2+ Kb6 3. e6 Rd1 4. Ke8 Rg1 5. e7 5... Rf1 {} 6. Rc4 { the critical manoeuvre: 'BUILDING A BRIDGE'} (6. Rh2 {although the 'bridge' manoeuvre is always emphasised in the books, there is also a win by getting the king out on the short side, e.g.} 6... Kc7 7. Rh7 Rf2 8. Rf7 Rh2 9. Rf8 Rh7 (9... Re2 10. Kf7) 10. Rf1 Rh8+ 11. Kf7 Rh7+ 12. Kf8 Rh8+ 13. Kg7 Re8 14. Kf7 { This is important because the bridge-building manoeuvre may not be available, and vice versa.}) 6... Rf2 7. Kd7 Rd2+ 8. Ke6 Re2+ 9. Kd6 Re3 10. Rb4+ Ka7 ( 10... Ka5 11. Rb8) 11. Rb5 Rd3+ 12. Ke6 Re3+ 13. Re5 1-0 Please note: sending the Rook a long way away. If the defending Rook is too close to the attacking King, the King will be able to chase the Rook away all by itself. This is the idea of checking distance, and will help us understand less clear-cut positions. We all know that the Rook belongs behind the pawn, but that's not true for every position. For example, in this one, the defending Rook has checking distance only in front of the pawn. [White Cheron, Andre]
--r-----
--------
----k---
--------
--P-----
--K-----
--------
---R----
{This is a typical case of an easy draw due to a frontal attack.} 1. Kb4 (1. Rd4 Ke5) 1... Rb8+ 2. Ka5 Rc8 (2... Ra8+ 3. Kb6) 3. Kb5 Rb8+ 4. Ka6 Rc8 5. Rd4 Ke5 6. Rh4 Kd6 1/2-1/2 How does this help us understand the Teignmouth position? Well, the defending King doesn't have access to the Queening square, but there may be checking distance from the side. [chessboard]4K3/4P1k1/8/8/8/8/r7/5R2[chessboard] p{} 1... Ra8+ 2. Kd7 Ra7+ 3. Kd6 Ra6+ 4. Kd5 Ra5+ 5. Kc6 Ra6+ 6. Kb7 Re6 1/2-1/2 [Event Rook ending: checking distance not OK] [chessboard]4K3/4P1k1/8/8/8/8/1r6/5R2[chessboard] 1... Rb8+ 2. Kd7 Rb7+ 3. Kd6 Rb8 (3... Rb6+ 4. Kc7 Re6 5. Kd7) 4. Kc7 Ra8 5. Ra1 $1 {Obtaining a Queen and Rook ending: q.v.} 1-0 Now, when Bill and I were playing around with this position, I managed to persuade him that it might be a draw, because he couldn't escape the flurry of checks, because he didn't approach the Rook with his King. I didn't know the theoretical result, but I did know the best thing to try. It's very well worth your while to play out these positions against a friend or a computer, so that if and when it turns up in one of your games, you won't hesitate to adopt the right approach. A very useful online resource is this implementation of the Nalimov tablebases: http://www.k4it.de/index.php which give the theoretical best obtainable result from any given simple position.

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