Two rooks and bishop versus two rooks

The diagram shows the position after Black's 66th move, when the last pawn has just been captured on f5. This 7-man ending, unusually, is pawnless: two rooks and bishop versus two rooks. Since a single rook and bishop versus rook is hard to win, and is usually a theoretical draw, it is in the interest of Black to avoid a rook exchange.

This was a very long game which lasted until late in the evening, but the critical phase saw Black miss at least three opportunities to win. The course of the game shows how hard it is for even one of the world's leading players to play such positions for a win against the defence of a highly skilled and determined opponent.

Ding,Liren - Giri,Anish
Bilbao Chess Masters, 28.10.2015

1.d4 Nf6 2.c4 g6 3.g3 c6 4.Bg2 d5 5.Nf3 Bg7 6.0-0 0-0 7.Qb3 Qb6 8.Nc3 Rd8 9.Na4 Qxb3 10.axb3 Na6 11.Bf4 Ne8 12.Nc3 Nac7 13.Ra5 Be6 14.Ra4 a6 15.Rfa1 h6 16.h4 Nd6 17.e3 Rac8 18.Nd2 f6 19.Ra5 dxc4 20.Bxd6 exd6 21.bxc4 f5 22.R5a4 c5 23.Ne2 Rb8 24.b4 b5 25.cxb5 Nxb5 26.bxc5 dxc5 27.Rxa6 cxd4 28.Nxd4 Nxd4 29.exd4 Bxd4 30.Rf1 Bb6 31.Re1 Bxf2+ 32.Kxf2 Rxd2+ 33.Kg1 Bf7 34.Ra3 Rbb2 35.Bf3 g5 36.hxg5 hxg5 37.Rae3 g4 38.Be2 Bd5 39.Bf1 Rh2 40.R1e2 Rh1+ 41.Kf2 Rb1 42.Re1 Rb4 43.Re7 f4 44.Rc1 Rb2+ 45.Ke1 Rb8 46.gxf4 Bg2 47.Kf2 Bxf1 48.f5 Kf8 49.Ree1 Rb2+ 50.Kg3 Rh3+ 51.Kxg4 Rb4+ 52.Kg5 Rg3+ 53.Kf6 Bc4 54.Rcd1 Bd3 55.Rc1 Bc4 56.Rcd1 Rb8 57.Rd7 Bb3 58.Ree7 Rc3 59.Rd6 Kg8 60.Rg7+ Kh8 61.Rg5 Rh3 62.Ke5 Bg8 63.Kf6 Rh6+ 64.Rg6 Rh5 65.Ke5 Rb5+ 66.Kf4 Rhxf5+ 67.Kg4? Ding Liren perhaps wanted to keep the K away from the enemy bishop but moving towards the edge of the board is rarely a wise policy when defending pawnless endgames. [The tablebase says that after 67.Ke4 which is the best move, "Black mates in 67" with the first capture occurring at Black's 50th move. This means that with perfect play Black can win but in practice White should be able claim a draw under the 50 move rule if he is keeping score. White's first move in the ending has already made his opponent's task easier: now mate in "only" 55 moves.] 67...Rf1? It is of course very hard for a human to play such an ending. Nevertheless it is somewhat surprising that Anish Giri did not seek to improve his bishop's position. According to the tablebase only two moves are sufficient to retain the win here. [67...Bf7 was by far the best move according to the tablebase. The g6-R is very short of squares. 68.Rgf6 (68.Rh6+? Kg7 and now it's only 32 moves to mate.) 68...Rg5+ 69.Kf4 Kg7 70.Rb6 Ra5 71.Ra6 Rae5 White cannot propsoe a rook exchange here, and after 72.Rfb6 Ref5+ 73.Ke3 Bg6 (73...Rg3+ 74.Ke4 Bg6 75.Rd6 Kh6 Black is gradually improving the position of hsi pieces and their coordination.) ; 67...Kh7 wins in 123 moves!] 68.Rh6+? [68.Rb6! is the unique drawing move.] 68...Kg7 69.Rdg6+ Kf7 70.Rb6 Re5 71.Rhc6? A serious mistake; now Black can mate in only 27 moves. [71.Rb7+ is best to force the king to the back rank, after which mate should take 61 moves.; 71.Ra6 is almost as good and several other moves are much better than the text.] 71...Re7?! Giri protects his second rank but this is only the third best move. [71...Ke7! reduces the task to 27 moves says the tablebase (considerably faster than the ChessBase notes said). White can check the king to the back rank but soon afterwards Black will give a bishop check and drive the king to the fatal edge. 72.Rc7+ Kd8 73.Rcc6 (73.Rg7 soon loses material: 73...Be6+ 74.Kh4 Rh1+ 75.Kg3 Rg1+ 76.Kf4 Rf5+ 77.Ke4 Rxg7 etc.) 73...Kd7 74.Rd6+ Ke7 75.Rd2 Be6+ 76.Kg3 Rg5+ 77.Kh2 Bd5 78.Re2+ Kd7 when Black threatens mate on the move and the useful checks are at an end.] 72.Rc3 Kg7 Now it is mate in 44. 73.Rbc6 Be6+ 74.Kg3 Bd7 75.Rd6 Be8 76.Rf3 Rfe1 77.Rd2 Bc6 78.Rc3 Rg1+ 79.Kh2 Rh1+ 80.Kg3 Rh6 81.Rd4 Re2 82.Rg4+ Kf7 83.Rcc4 Rg2+ 84.Kf4 Rf6+ 85.Ke5 Re6+ 86.Kf5 Rge2 87.Rgf4 Rg6 88.Rcd4 Re7 89.Rh4 Bd7+?! A bad slip. [89...Rf6+ As many commentators pointed out, 90.Kg5 Re5+ 91.Kg4 Kg7 92.Rc4 Bd5 Black's coordination is excellent again, denying checks and forcing White into a tight corner. 93.Rd4 Rf1 94.Rd3 Kg6 95.Kh3 Rg5 threatening mate on h1 96.Rg4 (96.Rd2 Rh1+ 97.Rh2 Bg2# ) 96...Be6 winning the exchange, after which the end will come soon. 97.Rd6 Rxg4 98.Rxe6+ ] 90.Kf4 Rf6+ 91.Kg3 Re3+ 92.Kh2 Re2+ 93.Kg3 Re3+ 94.Kh2 Bf5 95.Kg2 Kg6 96.Kf2 Rc3 97.Rhf4 Rc2+ 98.Kg3 Re6 99.Rd8 Ree2 100.Rg8+ Kh7 101.Rd8 Be6 102.Rdd4 Kg6 [102...Rg2+ is the quickest route to a win (29 moves).] 103.Rfe4 Rg2+ 104.Kf4 Rgf2+ 105.Ke5 Bf5?! A win is still possible to force (but for the 50-move rule) but [105...Rc6 or 105...Rf6 were better.] 106.Re3 Ra2 [106...Rc5+ is six moves faster (34 moves).] 107.Rd6+ Kg5 108.Rg3+ Bg4? Now White can force a draw thanks to the pin on the bishop. [108...Kh4! is clearly best, attacking the rook, and Black could mate in 38 moves.; 108...Kh5 also preserves the win but is much slower.] 109.Rd4! This will lead to a forced exchange of rooks in order to preserve the bishop. 109...Ra5+ 110.Kd6 Ra6+ 111.Kc5 Rf5+ 112.Kb4 Rb6+ 113.Kc4 Rc6+ 114.Kb4 Rf4 115.Rxf4 Kxf4 116.Rc3 Now it is a drawn rook and bishop against rook ending. Giri tried to win but Ding defended well. 116...Rg6 117.Rc4+ Ke5 118.Rc5+ Kd6 119.Rc4 Be6 120.Rd4+ Bd5 121.Kc3 Ke5 122.Rd3 Rc6+ 123.Kd2 Be4 124.Rc3 Rh6 125.Ke2 Rf6 126.Ke3 Rf8 127.Ke2 Kd4 128.Ra3 Bc2 129.Rh3 Rg8 130.Kf3 Be4+ 131.Kf4 Rf8+ 132.Kg5 Ke5 133.Rg3 Bf3 134.Kh4 Ke4 135.Rg7 Rf5 136.Kg3 Ke3 137.Rg8 Rh5 138.Rg7 Be4 139.Rg8 Rh1 140.Rg5 Rf1 141.Kg4 Bf3+ 142.Kf5 Kd4 143.Ke6 Rh1 144.Rg6 Be4 145.Rf6 Rh8 146.Kd6 Ra8 147.Ke7 Ra5 148.Rd6+ Bd5 149.Kf6 Ra7 150.Kf5 Re7 151.Rf6 Re1 152.Kg5 Be6 153.Kf4 Re3 154.Rf8 Bd5 155.Rf6 Re1 156.Kf5 Re5+ 157.Kf4 Be6 158.Kf3 Re3+ 159.Kf4 Re4+ 160.Kf3 Bg4+ 161.Kg3 Ke3 162.Rg6 Bf3 163.Rg5 Ra4 164.Re5+ Be4 165.Kg4 Ra1 Ding could have claimed the draw now but was perhaps afraid of miscounting; an incorrect claim would have given two minutes extra to hois opponent. So he played a few more moves to be certain. If he had never claimed the arbiter would have been able to step in after 75 moves (move 190) to declare the game drawn. 166.Rg5 Rf1 167.Kh4 Bf5 168.Rg3+ Kf4 169.Rg4+ Ke5 170.Rg3 Kf6 171.Ra3 Rg1 172.Ra4 1/2-1/2

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