Tuesday, December 21, 2010

Ruan-Hou (Game 2): the Rook Endgame

Today in the second game of the final of the Women's World Chess Championship, Ruan Lufei and Hou Yifan reached a rook ending in which Black had a substantial advantage:

Ruan Lufei - Hou Yifan
Women's World Chess Championship, Round 6.2 (2010)
Position after 36...Rxa4

Black is up two pawns, which would normally be an easy win, but rook endings are notoriously drawish.  Here, White's slim chances of a draw are enhanced by the passive position of the Black rook (tied to the defense of the b4-pawn), the active positions of the White king and rook, and the facts that (1) if the b-pawn were removed, the game would be a draw and (2) an ending with just Black's f- and h-pawns will usually be a draw.

37.h4 Kf8 38.Re4 f6 39.Rd4 Ke7 40.Rd4 Ke6 41.Ke4 Ke7 42.Kf4

White is asserting that Black cannot make any progress.  She will just shuffle her king between e4 and f4.  Black can try to make progress by taking one of these squares away from the White king: if she plays h6 and g5, then f4 is off limits.  Thus 42...h6 43.Ke4 Ke6 (so that ...g5 comes with check, preventing White from answering it with h5) 44.Kf4 g5+ 45.hxg5 hxg5+ 46.Ke4 Ke7, and White has to give way, either allowing the rook to shift away from a4 with check or allowing the Black king to advance to the queenside.

42...h6 43.h5?!

Position after 43.h5?!

While Black was making progress after 43.Ke4 (as described above), this is a forced win for Black.


Another attempt was 43...g5!?  If White plays actively with 44.Kf5?, Black wins: 44....Ra5+ 45. Kg6 Rb5 46.Re4+ (46. Kxh6 b3 47. Kg7 [47. Rd1 b2 48. Rb1 Kf7 -+] 47... b2 -+) 46... Kf8 47. Kxf6 b3 48. Re1 b2 49. Rb1 Rb6+ 50. Kf5 Kf7 and Black wins.

Analysis Diagram

White seems to hold the draw, however, with 44.Ke4 Ke6 45.Rc4 Kd6 46.Kd4.  If Black tries to break through with 46...f5!?, then White can just hold the draw: 47.gxf5 g3 48.Ke3 g3 49.Kf3 Ke5 50.Kxg3 Kxf5 51.Rc5+! Ke4 52.Rc6 b3 53.Rxh6 Rb4 54.Rf6 Ke5 (54...b2?? 55.Rf4+ +-) 55.Rf1 b2 56.Rb1 Kf5 57.Kg2 Kg5 58.Kg3 Kxh5 59.Kg2 Kg4 60.Kf2 Kh3 61.Rh1+ Kg4 62.Rb1 and Black can't break through.

Analysis Diagram

44.gxh5 Kf7 45.Re4 Kf8

Position after 45...Kf8

46.Kg4?  This move makes things too easy for Hou.  It would have been more tenacious to play waiting moves that don't allow Black to get the rook behind the b-pawn: 46.Rc4 Ke8 47.Rd4 Ke7 48.Rc4.  Another possibility was the direct 46.Kf5!, which seems to hold the draw: 46...Ra5+ 47.Kxf6 Rb5 48.Re2 b3 49.Rb2 Rb6+ 50.Ke5 Kg7 51.Kd4 Kf6 52.Rg2! Rb5 (52...b2?? 53.Rg6+ +-; 52...Kf5 53.Kc3 Kf4 54.Rg6 Rb5 55.Kb2 Rxh5 56.Kxb3 is a tablebase draw) 53.Kc3 Kf5 54.Kb2 Ke4 55.Rg6 Rxh5 56.Kxb3 is another tablebase draw.

46...f5+! 47.Kxf5 Ra5+ (The point: the rook gets behind the passed b-pawn.) 48.Kg6 Ra6+ 49.Rh7 Rb6

Position after 49...Rb6

Now it is all over.

50.Rf4+ Ke7 51.Rf1 b3 52.Kg7 b2 53.Rb1 Ke6 54.Kxh6 Kf5+ 55.Kg7 Kg5 56.Kf7 Kxh5 57.Ke7 58.Kd7 Kf3 0-1

UPDATE: Analysis at Chessdom suggests that White could have drawn with 48.Kf6!: 48... Rb5 (48... Ra6+ 49. Ke5 Rb6 50. Kd4 b3 51. Re1 ) 49. Re2 Rxh5 (49... b3 50. Rb2 Rb6+ 51. Ke5 Kf7 52. Kd4 Kf6 53. Rg2! Rb5 54. Kc3 Kf5 (54... b2 55. Rxb2 = ) 55. Kb2 Kf4 56. Rg6 Rxh5 57. Kxb3 is a theoretical draw ) 50. Ra2! (this wouldn't work with the white king somewhere else) 50... Ke8 51. Ke6! Kd8 52. Kd6! Kc8 53. Kc6! Kb8 54. Ra6! Rh4 55. Rb6+ Ka7 (55... Kc8 56. Ra6! ) 56. Rb7+ Ka6 57. Rb8! Rc4+ 58. Kd5 Rf4 59. Kc6 =

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