[Event "74th Tata Steel GMC"]
[Site "Wijk aan Zee NED"]
[Date "2012.01.25"]
[Round "10"]
[White "01.01 Tania, Sachdev"]
[Black "Schut, Lisa"]
[Result "1-0"]
[ECO "D85"]
[WhiteElo "2411"]
[BlackElo "2290"]
[Annotator "Karsten Müller"]
[SetUp "1"]
[FEN "6k1/7R/7K/8/2b5/8/8/8 w - - 0 56"]
[PlyCount "7"]
[EventDate "2012.01.14"]
[EventType "tourn"]
[EventRounds "13"]
[EventCountry "NED"]
[EventCategory "9"]
[Source "Chess Today"]
[SourceDate "2012.01.26"]

{Tablebase revolution in the endgame rook against bishop In general the theory
of chess endgames is fairly stable compared to chess openings. It is very
seldom that the theoretical verdict of a major cornerstone position is
overturned. But the complete solution of all endgames with 7 men or less has
changed several verdicts of course. For example Ken Thompson created a
tablebase in 1983 that proved that in general two bishops win against a knight,
when the 50 move rule is not taken into account, while human theory had
thought that it is drawn, when the defender can reach the Kling and Horwitz
position. Later John Nunn pointed out that queen and g- and h-pawn against
queen is amazingly usually drawn, if the defending king is well placed, while
human theory had assumed that the 2 extra pawns should win. While in those two
cases the evaluation of a whole typ of endgame was changed, I want to
illustrate the influence of the tablebase with rook and pawn against bishop
and pawn on the endgame rook against bishop as a whole. Humans and computer
analysis engines without tablebases have big problems in several important
positions as the dominance duels between rook and bishop can be amazingly deep,
difficult and incomprehensible for the human eye. Even one of the cornerstones
of human theory was broken by computer analysis using the tablebases. I want
to start with a relatively easy pure dominance duel to warm up. Figure 1a:} 56.
Rc7 $5 {White tries the best trick against the standard defense with Black's
king in the corner, which is not controlled by the bishop.} Be6 $2 {
Black falls for it. Among the drawing moves are} (56... Ba2 {and}) (56... Bd3
$11) 57. Kg6 $1 Kh8 $6 {This makes it relatively easy for White.} (57... Bh3 $5
{is the best try, when White has only one way to win:} 58. Re7 $3 (58. Rf7 $2
Bg2 59. Re7 Bc6 60. Re6 Ba4 $11) 58... Kf8 59. Re5 {
, Figure 1b.The central rook dominates the bishop.} Bg2 60. Kf6 Bf3 61. Rf5 {
The rook forces the bishop to leave the shadow of the kings.} Bc6 62. Rc5 Bd7
63. Rh5 Kg8 64. Rg5+ Kf8 (64... Kh7 65. Rg7+ $18) (64... Kh8 65. Kf7 $18) 65.
Rg1 Bc8 66. Rc1 Bd7 67. Rb1 Ke8 68. Rb8+ Bc8 69. Rxc8+ $18) 58. Rh7+ $1 Kg8 59.
Re7 {Figure 1c.} 1-0

[Event "Rio de Janeiro, Interzonal Tournament"]
[Site "?"]
[Date "1979.??.??"]
[Round "8"]
[White "01.02a Timman, Jan. H"]
[Black "Velimirovic, D."]
[Result "1-0"]
[ECO "D30"]
[Annotator "Karsten Müller"]
[PlyCount "205"]
[EventDate "1979.??.??"]

{Position 69w is much deeper and human analysis in principle was confirmed by
the tablebase: Cheron had proved, that White can win this position, but he
needed more than 50 moves. Jan Timman and his second Ulf Andersson were able
to refine the process, so that Timman indeed managed to win the game within
the 50 move rule.} 1. d4 {dtc/m = 10/30m} d5 2. c4 e6 3. Nf3 c5 4. cxd5 exd5 5.
g3 Nc6 6. Bg2 cxd4 7. Nxd4 Bc5 8. Nxc6 bxc6 9. Qc2 Qe7 10. O-O Bd7 11. Nc3 Nf6
12. Bg5 O-O 13. Bxf6 gxf6 14. Rac1 Bb6 15. e3 h5 16. h4 Kh8 17. Ne2 Bg4 18. Nf4
Rac8 19. Bh3 Bxh3 20. Nxh3 Qe5 21. Nf4 Rg8 22. Qe2 Rxg3+ 23. fxg3 Bxe3+ 24. Kg2
Bxf4 25. Qxe5 Bxe5 26. b3 Kg7 27. Rfd1 Rc7 28. Rc2 Bd6 29. b4 Bxb4 30. Rxd5 Kg6
31. Rd4 a5 32. g4 c5 33. gxh5+ Kxh5 34. Rd5+ Kh6 35. Rc4 a4 36. Kf3 a3 37. Rd6
Re7 38. Rxf6+ Kg7 39. Rf5 Rd7 40. Rg5+ Kf8 41. Rg2 Rd5 42. Ke4 Rh5 43. Kf3 Ke7
44. Kg4 Rh7 45. Rf2 Rg7+ 46. Kf5 Rh7 47. Rf3 Kf8 48. Rh3 Rh5+ 49. Ke4 Ke7 50.
Kf4 Kf6 51. Kg4 Kg6 52. Rf4 f5+ 53. Kf3 Kf7 54. Ke2 Ke6 55. Rc4 Kd5 56. Rf4 Ke5
57. Rc4 Kd5 58. Kd3 Ba5 59. Rh1 Bd8 60. Rf1 Be7 61. Rcf4 Bxh4 62. Rxf5+ Rxf5
63. Rxf5+ Ke6 64. Rxc5 {KRP(a2)KBP(a3) =} Bf6 65. Rc6+ Ke7 66. Ke4 Bb2 67. Kd5
Kf7 68. Re6 Kf8 $4 {not ... Kg7?? as in many sources. Figure 2a, 1-0, dtc/m =
36/56m. Ba1/c3/d4/f6/g7/h8 draw.} 69. Ke4 Kf7 70. Kf5 Kf8 71. Kg6 Bc3 72. Ra6
Bb2 73. Ra7 Ke8 74. Kf5 Kf8 {dtc/m = 30/50m} 75. Ke6 Kg8 76. Rf7 Bc3 77. Rf3
Bb2 {Figure 2b, c.f. Cheron (1969) p323, dtc/m = 28/47m; adjournment 3} 78. Ke7
Kh7 79. Rg3 Kh6 80. Kd6 Kh5 81. Kc5 Kh4 82. Rg8 Be5 83. Kd5 Bb2 84. Kc4 Bf6 {
dtc/m = 20/39m} 85. Rg6 Bg5 86. Kd5 Bc1 87. Ke4 Bb2 88. Kf5 Kh5 89. Rd6 Kh4 90.
Rd3 Bc1 91. Rc3 Bb2 92. Re3 Bc1 93. Re1 Bd2 94. Rh1+ Kg3 95. Rd1 Bb4 96. Rd3+
Kf2 97. Ke4 Ke2 {dtc/m = 10/30m} 98. Kd4 Bc5+ 99. Kc4 Be7 100. Rh3 Bd6 101. Kb3
Bf8 102. Rh8 Bd6 103. Ra8 {and Black resigns} 1-0

[Event "JvdH SC-/SC+ line"]
[Site "?"]
[Date "1979.03.07"]
[Round "?"]
[White "01.02b Timman"]
[Black "Velimirovic"]
[Result "*"]
[ECO "D30"]
[Annotator "Haworth, Guy"]
[SetUp "1"]
[FEN "5k2/8/4R3/3K4/8/p7/Pb6/8 w - - 0 69"]
[PlyCount "71"]
[EventDate "2014.??.??"]

{'Line B', the JvdH (1987) DTC-minimaxing line, i.e., SV+C-/SV+C+. Figure 2a:} 
69. Ke4 Kf7 70. Kf5 Kf8 71. Re4 Kf7 72. Re3 Bc1 73. Rc3 Bb2 74. Rc7+ Ke8 ({
'Line D', SV+C-M-/SV+C+M+:} 74... Kf8 75. Ke6 Kg8 76. Rf7 Bg7 77. Ke7 Kh7 78.
Rf2 Bd4 79. Rg2 Kh6 80. Ke6 Bb2 81. Kd5 Kh5 82. Kc4 Be5 83. Kb3 Bd6 84. Rd2 Bf8
85. Rd3 Kg5 86. Kc4 Kf4 87. Kd5 Be7 88. Ke6 Bc5 89. Rc3 Bf8 90. Rh3 Ke4 91. Rh8
Bc5 92. Rh4+ Kd3 93. Kd5 Be3 94. Rh3 Ke2 95. Ke4 Bc5 96. Rh2+ Kf1 97. Kd3 Bf8
98. Kc2 Ke1 99. Kb3 Bd6 100. Rh5 {Figure 2d, dtc/m/ = -4/-24m. Black must lose
the pawn earlier or hasten mate by losing the bishop later.} Bf8 ({
SM-C-/SM+C+ line} 100... Ke2 101. Ra5 Ke3 102. Rxa3 {dtc/m/z = -10/-22/-2m})
101. Rf5 Bd6 102. Ra5 {and Black's last try is} Kd2 103. Rd5+ (103. Rxa3 $4
Bxa3 104. Kxa3 Kc3 $3 $11) 103... Ke3 104. Rxd6 {dtc/m/z = -1/-12/-1m}) 75. Ke6
Kf8 76. Rf7+ Kg8 77. Ke7 Kh8 78. Rf2 Kg7 79. Rg2+ Kh6 80. Kd6 Kh5 81. Kc5 {
and here, Figure 2c, the bishop steps away from the pawn, q.v. Line C} Be5 ({
'Line C':} 81... Kh4 {
maintaining direct defence of the bP at the 'DTC cost' of 15m} 82. Kb4 Kh3 83.
Rg8 Kh4 84. Kb3 Kh3 85. Rg5 Bc1 86. Rc5 Bb2 87. Rc4 Kg3 88. Ra4 Kf3 89. Rxa3 {
KRPKB, dtc/m/z = -7/-10/-2m}) 82. Kb4 Bd6+ 83. Kb3 Kh4 84. Rg6 Be7 85. Kc3 Kh5
86. Rg2 Kh4 87. Kd3 Bf6 88. Ke4 Bc3 89. Kf5 Kh3 90. Rg4 Be5 91. Kg5 Kh2 92. Kg6
Kh3 93. Kf5 Bd6 94. Ra4 Kg2 95. Ke4 Bf8 96. Kd3 Kf3 97. Kc3 Ke3 98. Ra8 Bd6 99.
Ra6 Bc5 100. Kc4 Bf8 101. Ra8 Bd6 102. Rd8 Be5 103. Rd3+ Ke4 104. Rxa3 *

[Event "?"]
[Site "?"]
[Date "????.??.??"]
[Round "?"]
[White "01.03 Noam Elkies 1993"]
[Black "?"]
[Result "*"]
[Annotator "Karsten Müller"]
[SetUp "1"]
[FEN "6k1/1R5p/8/6PK/8/b7/8/8 w - - 0 1"]
[PlyCount "29"]

{In the next example the computer was needed to break the defense: Figure 3a.
Human theory had thought that Black can draw, but this is not the case as the
rook can win the domination duel as Noam Elkies established in 1993:} 1. Rb3
Bd6 2. Kg4 {White has three plans. He can invade with the king to f6 or h6 or
play g5-g6 under the right circumstances. Black can not stop all of them.} Bf8
(2... Bc5 3. Rb5 Bd4 (3... Ba3 4. Kf5 Be7 5. Rb8+ Kf7 6. Rb7 $18 {
and White wins by bringing the king to h6.}) 4. Kh5 Bc3 (4... Bg7 5. g6 h6 6.
Rb8+ Bf8 7. Rxf8+ Kxf8 8. Kxh6 $18) 5. Rb8+ Kg7 6. Rb7+ Kh8 7. g6 h6 8. Kxh6
Bg7+ 9. Kg5 Bd4 10. g7+ Kh7 11. Rf7 Be5 12. g8=Q+ Kxg8 13. Kg6 $18) 3. Kf5 Bc5
4. Rd3 Bb4 5. Kf6 Ba5 6. Rb3 Bd8+ 7. Kf5 Ba5 8. Kg4 Bc7 9. Rb5 Bd6 10. Kf5 Bc7
11. Rd5 {Figure 3b. The central rook dominates the bishop.} Bb6 12. Kf6 Bc7 13.
Rd7 Ba5 14. Rg7+ Kh8 15. Kf7 $18 {Figure 3c.} *



[Event "Amber-blindfold 20th"]
[Site "Monte Carlo"]
[Date "2011.03.20"]
[Round "8"]
[White "01.04 Gelfand, Boris"]
[Black "Ivanchuk, Vassily"]
[Result "1/2-1/2"]
[ECO "D34"]
[WhiteElo "2733"]
[BlackElo "2779"]
[Annotator "Karsten Müller"]
[SetUp "1"]
[FEN "6k1/2R5/4K1p1/7p/8/6P1/1b5P/8 w - - 0 54"]
[PlyCount "72"]
[EventDate "2011.03.12"]
[EventType "tourn (rapid)"]
[EventRounds "11"]
[EventCountry "MNC"]
[EventCategory "21"]
[Source "ChessBase"]
[SourceDate "2011.05.17"]

{The discussion of the next two positions is a slightly expanded version of
Endgame Corner 143 which can still be found in the archives of ChessCafe.com.
The following position is of very high practical importance:Figure 4a. It is
indeed almost certainly a fortress as human theory had claimed. For a 100%
confirmation we of course must wait for the 8 men tablebases, but as an
analysis engine using the 6 men tablebases can not find a win for White it
indeed seems to be almost certain that there is none. But the drawish margin
is not as large as it seems. Black must defend very carefully. It not enough
just to keep the bishop on the long diagonal and wait:} 54. Rc2 (54. h4 Ba1 $11
(54... Bd4 $2 {
Figure 4b. This is a typical mistake, which often occurs in practical play:}
55. Rc4 Bb2 56. g4 hxg4 57. Rxg4 Kh7 58. Kf7 Kh6 59. Rxg6+ Kh5 60. Rg2 {
Figure 4c, and White wins the domination duel in the long run (he mates in 50
moves according to the tablebase), e.g.} Bc3 61. Rh2 Be1 62. Kf6 Bg3 63. Rh1
Bf2 64. Kf5 Be3 65. Rh2 Bg1 66. Rg2 Bb6 67. Rb2 Bc5 68. Rc2 Be3 69. Ke4 Bh6 70.
Rh2 Bg7 71. Kf4 Bf8 72. Kf3 Ba3 73. Ra2 Be7 74. Re2 {Figure 4d} Bf6 (74... Bxh4
{is met by} 75. Rh2 Kg5 76. Rh1 $18 {Figure 4e, very beautiful!}) 75. Kf4 Bd8
76. Rc2 $1 Be7 77. Rd2 Bb4 78. Rd8 Bc3 79. Kg3 $18)) (54. h3 Ba1 55. g4 hxg4
56. hxg4 Bb2 57. g5 Ba1 58. Rf7 Bb2 59. Rf6 {Figure 5a, is just met by the calm
} Kg7 $1 $11) 54... Ba1 55. Rg2 Kg7 56. g4 hxg4 57. Rxg4 Bc3 58. Rc4 Ba1 59.
Rf4 Bb2 60. Rf1 Bd4 61. Rf7+ Kg8 62. Rf4 Bc3 63. Rg4 Kg7 $1 (63... Kh7 $2 64.
Kf7 $18) 64. Rg2 Bf6 65. Rc2 Ba1 66. Rc7+ Kg8 67. h4 Bb2 68. Rc2 $5 {Figure 5b}
Bd4 $1 {Now this is the only move. Black must indeed by very careful, when
defending this fortress.} 69. Rd2 (69. Rg2 Kh7 70. Kf7 Kh6 71. Rxg6+ Kh5 72.
Rc6 Bf2 73. Kf6 Kxh4 $1 $11) ({After} 69. Rc4 {
Figure 5c, the only move is the amazing} Be3 $3 {with the point} 70. Kf6 Kh7
71. Rg4 Kh6 72. Rxg6+ Kh5 73. Rg3 Bb6 74. Rh3 Kg4 75. Rh1 Bd8+ $11) 69... Bc3
70. Rd3 {Figure 5d} Be1 $1 {Again Ivanchuk is up to the task and finds the
only defense. The bishop must leave the long diagonal now as} (70... Bb2 $2 {
runs into} 71. Rg3 Kh7 72. Kf7 Kh6 73. Rxg6+ Kh5 74. Rg2 {
and wins as seen in the line 54.h4 Bd4?.}) 71. Kf6 (71. Rd4 Kg7 72. Rg4 Kh6 73.
Kf6 Kh5 74. Rxg6 Kxh4 75. Kf5 Bd2 $11) 71... Bxh4+ 72. Kxg6 Kf8 73. Rh3 Bd8 74.
Rh7 Ke8 75. Kf5 Kf8 76. Ke6 Bg5 77. Rf7+ Kg8 78. Rd7 Kf8 79. Rd5 Bc1 80. Rd1
Bb2 81. Rf1+ Kg7 82. Rf7+ Kg6 83. Rf2 Bc1 84. Rg2+ Kh5 85. Kf5 Kh4 $1 86. Rc2
Be3 $1 87. Ke4 Ba7 88. Ra2 Bb6 89. Kf4 Bc7+ {Figure 5e} 1/2-1/2



[Event "Frunze op"]
[Site "Frunze"]
[Date "1989.??.??"]
[Round "?"]
[White "01.05 Tiviakov, S."]
[Black "Korsunsky, R."]
[Result "1-0"]
[ECO "B22"]
[WhiteElo "2480"]
[BlackElo "2390"]
[Annotator "Karsten Müller"]
[SetUp "1"]
[FEN "8/1k6/p7/1pb2K1R/8/P7/1P6/8 w - - 0 45"]
[PlyCount "69"]
[EventDate "1989.??.??"]
[EventType "swiss"]
[EventCountry "KGZ"]

{Now finally comes a real revolution. Human theory had thought that the
following position, Figure 6a, is a fortress, which also I had claimed many
times, e.g. in Endgame Corner 70. But White can win which was first pointed
out by Jonathan Hawkins in his excellent book Amateur to IM - Proven Ideas and
Training Methods, Mongoose Press 2012 on page 105. Either by invading with his
king to c6 (this winning aim was known to human theory) or and this is really
amazing by exchanging pawns with a3-a4 at the right time:} 45. Ke4 Bf2 46. Rf5
Bg1 47. Rf1 Bc5 48. Kd5 Be3 49. Rf7+ Kb6 50. Rf3 Bg1 51. Rf1 (51. Rf6+ Kb7 52.
Rf4 Kb6 {
Figure 6b, is more direct. Now, remarkably, White should exchange pawns with}
53. a4 $3 bxa4 54. Rxa4 {Figure 6c, dtc/m/z = -50/-73/-41m. White's rook now
wins a long domination duel as in, e.g., this initially DTC/M--minimaxing line
from  AR/HvdH/YK} Bf2 55. Rf4 Bg1 56. Rf6+ Kb7 {Figure 6d} 57. Rf1 $1 Be3 58.
Rf3 $1 Bg1 59. Kd6 $1 Bh2+ 60. Ke6 $1 Kc6 61. Rf1 $1 Bg3 62. Kf5 $1 {Figure 7a.
This is really amazing! White's king has moved to f5 to win the domination
fight. Chess really is a rich game!} Bd6 63. Rc1+ Kb6 64. Ke4 $1 Bc5 65. Kd3 $1
Kb5 66. Ra1 $1 Kb6 67. Kc4 $1 Be3 68. Re1 Bf2 69. Rf1 $1 Be3 70. Rf3 $1 Bg1 71.
Kb4 $1 Bd4 72. Rb3 $1 Be5 73. Ka4+ $1 Ka7 74. Ka5 $1 Bf6 75. Kb4 $1 Kb6 76.
Ka4+ $1 Ka7 77. Rb4 $1 {SC-/SC+} Bd8 ({SM-C-/SM+C+} 77... Be5 78. Kb3 Bd6 79.
Rg4 Be5 80. Re4 Bg3 81. Kb4 Kb6 82. Rg4 Bb8 83. Kc4 Kc6 84. Rg6+ Kb7 85. Kd5
Bf4 86. Rg4 Bb8 87. Kc5 Ba7+ 88. Kd6 Bb8+ 89. Kd7 a5 90. Rc4 Kb6 91. Ke6 Kb5
92. Kd5 a4 93. Rc5+ Kb6 94. Kc4 Bf4 95. Rb5+ Ka6 96. Kc5 Be3+ 97. Kc6 Bc1 98.
Rb8 Ka5 99. Kc5 Be3+ 100. Kc4 Bd2 101. Ra8+ Kb6 102. Rxa4) 78. Kb3 $1 Ba5 79.
Rg4 $1 Kb7 80. Kc4 $1 Bb6 81. Kd5 $1 Bf2 82. Kd6 $1 Be1 83. Rg8 $1 Bb4+ 84. Kd5
$1 Be1 85. Rf8 $1 Kb6 86. Rf6+ $1 Kb5 87. Rf4 $1 Bd2 88. Rf8 $1 Kb6 89. Rb8+ $1
Kc7 90. Re8 $1 Bc1 91. Re2 $1 Kb6 92. Kc4 $1 Bf4 93. Re6+ $1 Kb7 94. Kc5 $1 Bg5
95. Rb6+ $1 Ka7 96. Kc6 $1 Be3 97. Rb7+ Ka8 98. b4 Bd4 99. Rd7 $1 Bf2 100. Rd2
$1 Be1 101. Rd1 $1 Bf2 102. Ra1 $1 Ka7 103. b5 $1 a5 104. Rxa5+) 51... Be3 52.
Ke4 Bg5 53. Rf5 Bc1 54. Rf2 Bg5 55. Kd4 Bc1 56. Re2 Ka5 (56... Bg5 57. Re6+ Kb7
58. Kc5 Bd8 59. b4 Bh4 60. Rb6+ Ka7 61. Kc6 $18) 57. Kc3 Kb6 58. Kd4 Ka5 59.
Rc2 Bh6 60. Rg2 Bc1 61. Rc2 Bh6 {Figure 7b} 62. Rc7 $6 {
Allows Black to get back in his house.} (62. Rg2 {wins quicker, e.g.} Bc1 (
62... Bf8 63. Kc3 Kb6 64. Rg6+ Kb7 65. b4 $18) (62... Ka4 63. Rg6 Bc1 64. Kc3
$18) 63. Re2 Kb6 (63... Bh6 64. Kc3 Bg7+ 65. Kb3 Bf6 66. Re6 Bd4 67. Ka2 b4 68.
axb4+ Kb5 69. Kb3 $18) 64. Kd5 Bg5 (64... a5 65. Kd4 a4 66. Kd5 b4 67. Rc2 Be3
68. axb4 Kb5 69. Rc8 $18) 65. Re6+ Kb7 66. Kc5 {
Figure 7c, and White's king invades to c6.} Bd8 67. b3 Bg5 68. Rb6+ Ka7 69. Kc6
$18) 62... Kb6 63. Re7 Bc1 (63... Bg5 64. Re6+ Kb7 65. Kc5 Bd8 66. b3 Bh4 67.
Rb6+ Ka7 68. Kc6 $18) 64. Re6+ Kb7 65. Re2 {Figure 7d} ({Even} 65. Kc5 {
is playable:} Bxb2 66. Re7+ Kb8 67. Re3 (67. Kb6 $2 Bd4+ 68. Kxa6 Bc5 $11)
67... Kc7 68. Rf3 Kb7 69. Rh3 Kc7 70. Rh7+ Kb8 71. Kb6 $18) 65... Kb6 $6 {
Figure 8a. Now the bishop is dominated.} (65... Bg5 $5 66. Kc5 Bh4 {
Figure 8b, was more tenacious, e.g.} 67. a4 bxa4 68. Kb4 Bg3 69. Kxa4 {
dtc/m/z = -53/-76/-44m, and as in, e.g., this DTC/Z-minimaxing line from AR/
HvdH/YK} Bc7 70. Re6 Bd8 71. Kb4 Bb6 72. Kc4 Bg1 73. Rf6 Be3 74. Kd5 Bg1 {
Figure 6d once again}) (65... Bf4 $6 66. Re7+ Kb6 67. Re6+ Kb7 68. Kc5 Bg5 69.
Rb6+ Ka7 70. Kc6 $18) 66. Kd5 Bg5 (66... a5 67. Kd4 a4 68. Kd5 b4 69. Rc2 Be3 (
69... bxa3 70. Rxc1 axb2 71. Rb1 a3 72. Kc4 $18) 70. axb4 Kb5 71. Rc8 $18) (
66... Ka5 67. Rc2 Be3 (67... Bf4 68. Rc6 $18) 68. Rc6 b4 69. axb4+ Kb5 70. Rc8
Bf4 71. Rc5+ Kb6 72. Kc4 $18) 67. Re6+ Kb7 68. Kc5 Bd8 (68... Bh4 69. Rb6+ Ka7
70. Kc6 $18) 69. b3 Bh4 70. Rb6+ Ka7 71. Kc6 {
Figure 8c. White's king has reached the key square c6 and it is over:} Bf2 72.
Rb7+ Ka8 73. Rf7 Bg1 74. Rf4 Ka7 75. a4 bxa4 76. Rxa4 {dtc/m = -7-12m} Bf2 77.
b4 Be3 78. b5 Kb8 79. Rxa6 {Figure 8d} 1-0

[Event "Tata Steel (Group C)"]
[Site "Wijk aan Zee NED"]
[Date "2012.01.25"]
[EventDate "2012.01.14"]
[Round "10"]
[Result "1-0"]
[White "Tania Sachdev"]
[Black "Lisa Schut"]
[ECO "D85"]
[WhiteElo "2411"]
[BlackElo "2290"]
[PlyCount "117"]

1. d4 Nf6 2. c4 g6 3. Nc3 d5 4. cxd5 Nxd5 5. Bd2 Nb6 6. Bf4
Bg7 7. e3 c5 8. dxc5 Bxc3+ 9. bxc3 Qxd1+ 10. Rxd1 N6d7 11. Bb5
a6 12. Ba4 Nc6 13. Bc7 O-O 14. Bb6 Nce5 15. Rd4 Nxb6 16. cxb6
Be6 17. Nf3 Nxf3+ 18. gxf3 Bxa2 19. Rd7 Rfc8 20. Rxb7 Rab8
21. Bc6 Rxb7 22. Bxb7 Rb8 23. Bxa6 Rxb6 24. Bd3 Rb2 25. O-O
Rd2 26. Bb1 Bc4 27. Rc1 Kg7 28. f4 f5 29. Bc2 Kf6 30. Ba4 e5
31. Rb1 exf4 32. exf4 Rd3 33. Rb6+ Kg7 34. Rc6 Rxc3 35. h3
Rc1+ 36. Kh2 Rc3 37. Bb5 Rxh3+ 38. Kxh3 Bxb5 39. Rb6 Bc4
40. Rb7+ Bf7 41. Kg3 Kf6 42. Rb6+ Be6 43. Kf3 h6 44. Ke3 g5
45. fxg5+ hxg5 46. f4 gxf4+ 47. Kxf4 Kf7 48. Ke5 Bc4 49. Kxf5
Kg7 50. Rb7+ Kh8 51. Kg6 Bd3+ 52. Kh6 Bc4 53. Rh7+ Kg8
54. Rg7+ Kh8 55. Rh7+ Kg8 56. Rc7 Be6 57. Kg6 Kh8 58. Rh7+ Kg8
59. Re7 1-0


[Event "Rio De Janeiro"]
[Site "Rio De Janeiro"]
[Date "1979.??.??"]
[EventDate "?"]
[Round "?"]
[Result "1-0"]
[White "Jan Timman"]
[Black "Dragoljub Velimirovic"]
[ECO "D30"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "205"]

1.d4 d5 2.c4 e6 3.Nf3 c5 4.cxd5 exd5 5.g3 Nc6 6.Bg2 cxd4
7.Nxd4 Bc5 8.Nxc6 bxc6 9.Qc2 Qe7 10.O-O Bd7 11.Nc3 Nf6 12.Bg5
O-O 13.Bxf6 gxf6 14.Rac1 Bb6 15.e3 h5 16.h4 Kh8 17.Ne2 Bg4
18.Nf4 Rg8 19.Bh3 Bxh3 20.Nxh3 Qe5 21.Nf4 Rac8 22.Qe2 Rxg3+
23.fxg3 Bxe3+ 24.Kg2 Bxf4 25.Qxe5 Bxe5 26.b3 Kg7 27.Rfd1 Rc7
28.Rc2 Bd6 29.b4 Bxb4 30.Rxd5 Kg6 31.Rd4 a5 32.g4 c5 33.gxh5+
Kxh5 34.Rd5+ Kh6 35.Rc4 a4 36.Kf3 a3 37.Rd6 Re7 38.Rxf6+ Kg7
39.Rf5 Rd7 40.Rg5+ Kf8 41.Rg2 Rd5 42.Ke4 Rh5 43.Kf3 Ke7 44.Kg4
Rh7 45.Rf2 Rg7+ 46.Kf5 Rh7 47.Rf3 Kf8 48.Rh3 Rh5+ 49.Ke4 Ke7
50.Kf4 Kf6 51.Kg4 Kg6 52.Rf4 f5 53.Kf3 Kf7 54.Ke2 Ke6 55.Rc4
Kd5 56.Rf4 Ke5 57.Rc4 Kd5 58.Kd3 Ba5 59.Rh1 Bd8 60.Rf1 Be7
61.Rcf4 Bxh4 62.Rxf5+ Rxf5 63.Rxf5+ Ke6 64.Rxc5 Bf6 65.Rc6+
Ke7 66.Ke4 Bb2 67.Kd5 Kf7 68.Re6 Kf8 69.Ke4 Kf7 70.Kf5 Kf8
71.Kg6 Ba1 72.Ra6 Bb2 73.Ra7 Ke8 74.Kf5 Kf8 75.Ke6 Kg8 76.Rf7
Bc3 77.Rf3 Bb2 78.Ke7 Kh7 79.Rg3 Kh6 80.Kd6 Kh5 81.Kc5 Kh4
82.Rg8 Be5 83.Kd5 Bb2 84.Kc4 Bf6 85.Rg6 Bg5 86.Kd5 Bc1 87.Ke4
Bb2 88.Kf5 Kh5 89.Rd6 Kh4 90.Rd3 Bc1 91.Rc3 Bb2 92.Re3 Bc1
93.Re1 Bd2 94.Rh1+ Kg3 95.Rd1 Bb4 96.Rd3+ Kf2 97.Ke4 Ke2
98.Kd4 Bc5+ 99.Kc4 Be7 100.Rh3 Bd6 101.Kb3 Bf8 102.Rh8 Bd6
103.Ra8 1-0


[Event "20th Amber Tournament (Blindfold)"]
[Site "Monaco MNC"]
[Date "2011.03.20"]
[EventDate "2011.03.12"]
[Round "8"]
[Result "1/2-1/2"]
[White "Boris Gelfand"]
[Black "Vassily Ivanchuk"]
[ECO "D34"]
[WhiteElo "2733"]
[BlackElo "2779"]
[PlyCount "178"]

1. Nf3 d5 2. d4 Nf6 3. c4 e6 4. g3 c5 5. cxd5 exd5 6. Bg2 Be7
7. O-O O-O 8. Nc3 Nc6 9. Bg5 cxd4 10. Nxd4 Re8 11. e3 Be6
12. Rc1 h6 13. Bxf6 Bxf6 14. Nxc6 bxc6 15. Na4 Qa5 16. Rxc6
Rad8 17. a3 d4 18. b4 Qb5 19. Rc5 Qb8 20. e4 d3 21. Qd2 Bb3
22. Nc3 Bd4 23. Rc6 Qb7 24. b5 Bc2 25. a4 Bb6 26. Nd5 Bxa4
27. e5 Qb8 28. e6 Rxe6 29. Rxe6 fxe6 30. Ne7+ Kh8 31. Nc6 Qd6
32. Nxd8 Qxd8 33. Bc6 Qd4 34. Kg2 Bc2 35. Re1 Qxf2+ 36. Qxf2
Bxf2 37. Rxe6 d2 38. Bf3 Bb6 39. Rd6 Ba4 40. Rxd2 Bxb5 41. Be4
Kg8 42. Rd5 Bc6 43. Re5 Bxe4+ 44. Rxe4 h5 45. Kf3 g6 46. Kf4
Kg7 47. Ke5 Bd8 48. Ke6 Bf6 49. Ra4 Bb2 50. Rxa7+ Kg8 51. Ra2
Bc3 52. Rc2 Ba1 53. Rc7 Bb2 54. Rc2 Ba1 55. Rg2 Kg7 56. g4
hxg4 57. Rxg4 Bc3 58. Rc4 Ba1 59. Rf4 Bb2 60. Rf1 Bd4 61. Rf7+
Kg8 62. Rf4 Bc3 63. Rg4 Kg7 64. Rg2 Bf6 65. Rc2 Ba1 66. Rc7+
Kg8 67. h4 Bb2 68. Rc2 Bd4 69. Rd2 Bc3 70. Rd3 Be1 71. Kf6
Bxh4+ 72. Kxg6 Kf8 73. Rh3 Bd8 74. Rh7 Ke8 75. Kf5 Kf8 76. Ke6
Bg5 77. Rf7+ Kg8 78. Rd7 Kf8 79. Rd5 Bc1 80. Rd1 Bb2 81. Rf1+
Kg7 82. Rf7+ Kg6 83. Rf2 Bc1 84. Rg2+ Kh5 85. Kf5 Kh4 86. Rc2
Be3 87. Ke4 Ba7 88. Ra2 Bb6 89. Kf4 Bc7+ 1/2-1/2


[Event "Frunze op"]
[Site "Frunze"]
[Date "1989.??.??"]
[Round "?"]
[White "Tiviakov, Sergei"]
[Black "Korsunsky, Rostislav R"]
[Result "1-0"]
[WhiteElo "2480"]
[BlackElo "2390"]
[ECO "B22"]

1.e4 c5 2.Nf3 Nc6 3.c3 Nf6 4.e5 Nd5 5.d4 cxd4 6.cxd4 d6 7.Bc4 Nb6 8.Bb5 dxe5
9.Nxe5 Bd7 10.Nc3 Nxe5 11.dxe5 Bxb5 12.Nxb5 Qxd1+ 13.Kxd1 Nd5 14.Ke2 a6 15.Rd1 O-O-O
16.Nd4 e6 17.Bd2 b6 18.Rac1+ Kb7 19.Rc4 Bc5 20.Nf3 Rd7 21.Ng5 Rhd8 22.Rdc1 h6
23.Ne4 Be7 24.g3 Bf8 25.a3 f5 26.exf6 gxf6 27.R1c2 h5 28.Rc6 Re8 29.Be3 f5
30.Ng5 Bc5 31.Rxe6 Rde7 32.Rxe7+ Rxe7 33.Kf3 Nxe3 34.fxe3 Bxe3 35.h4 Bd4
36.Kf4 Be5+ 37.Kxf5 Bxg3 38.Ne6 Bxh4 39.Nd8+ Ka8 40.Rc8+ Ka7 41.Nc6+ Kb7
42.Nxe7 Bxe7 43.Rh8 Bc5 44.Rxh5 b5 45.Ke4 Bf2 46.Rf5 Bg1 47.Rf1 Bc5 48.Kd5 Be3
49.Rf7+ Kb6 50.Rf3 Bg1 51.Rf1 Be3 52.Ke4 Bg5 53.Rf5 Bc1 54.Rf2 Bg5 55.Kd4 Bc1
56.Re2 Ka5 57.Kc3 Kb6 58.Kd4 Ka5 59.Rc2 Bh6 60.Rg2 Bc1 61.Rc2 Bh6 62.Rc7 Kb6
63.Re7 Bc1 64.Re6+ Kb7 65.Re2 Kb6 66.Kd5 Bg5 67.Re6+ Kb7 68.Kc5 Bd8 69.b3 Bh4
70.Rb6+ Ka7 71.Kc6 Bf2 72.Rb7+ Ka8 73.Rf7 Bg1 74.Rf4 Ka7 75.a4 bxa4 76.Rxa4 Bf2
77.b4 Be3 78.b5 Kb8 79.Rxa6 1-0



{DTx-minimaxing lines in the appendix)

[White "KRP"]
[Black "KBP"]
[Result "1-0"]
[Date "2014.03.14"]
[Event "6m, 3-3m, KRP(a2)KBP(a3), GBR 0130.11, maxDTC KRP(a2)KBP(a3) w&l: SV+C-/SV+C+"]
[Annotator "Haworth,Guy"]
[SetUp "1"]
[FEN "1K6/8/1k6/6R1/8/p3b3/P7/8 w - - 0 1"]
[PlyCount "109"]

{Figure 2e, the unique maxDTC KRP(a2)KRP(a3) position, dtc/m = 55/82m: SC-M-/
SC+M+:} 1. Rd5 Bc1 2. Rd8 Bb2 3. Rc8 Be5+ 4. Ka8 Bc7 5. Re8 Bf4 6. Re4 Bc1 7.
Rc4 Bb2 8. Kb8 Kb5 9. Rc2 Kb4 10. Rc6 Bd4 11. Kc7 Bc5 12. Ra6 {
and here, SM+ diverges} Kc3 13. Kc6 Kc4 14. Ra4+ Bb4 15. Kb6 Kc3 16. Kb5 Bf8
17. Ra8 Bd6 18. Re8 Kb2 19. Re2+ Kc3 20. Ka4 Bc5 21. Re5 Bd6 22. Rb5 Be7 23.
Rb1 Bd6 24. Rb3+ Kc4 25. Rb6 Be7 26. Rc6+ Bc5 27. Rc7 Kd4 28. Kb3 Kd5 29. Rf7
Bd6 30. Rf5+ Kd4 31. Rf1 Kd5 32. Rd1+ Ke6 33. Rd3 Ke5 34. Kc4 Bf8 35. Rf3 Bd6
36. Rf2 Ke6 37. Re2+ Kf6 38. Kd5 Bb4 39. Re3 Kf5 40. Rf3+ Kg4 41. Rb3 Bf8 42.
Rb7 Bh6 43. Rc7 Kh5 44. Ke6 Kg6 45. Rc3 Bf8 46. Rg3+ Kh5 47. Kf6 Kh4 48. Rc3
Kh5 49. Rc4 Bh6 50. Kf5 Bf8 51. Rc8 Bg7 52. Rc1 Kh4 53. Rh1+ Kg3 54. Rg1+ Kf3
55. Rxg7 {KRPKP: dtc/m/z = -2/-9/-2m  YK DTC EGT (Konoval, 2014), FREEZER DTC
EGT (Rusz, 2014)} 1-0


[White "KRP"]
[Black "KBP"]
[Result "*"]
[Date "2014.04.08"]
[Event "6m, 3-3m, KRPKBP, GBR 0130.11, maxDTC KRPKBP l&w: SV+C-/SV+C+"]
[Annotator "Haworth, Guy"]
[SetUp "1"]
[FEN "8/6p1/8/8/1b6/2k5/6P1/3K2R1 b - - 0 1"]
[PlyCount "198"]

1... Kd3 {the maxDTC KRPKBP wtm win} 2. Rh1 Bd6 3. Re1 Kd4 4. Ke2 Ke4 5. Kf2+ Kf4 
6. Rc1 Be7 7. Rc4+ Kg5 8. Rc6 Kf4 9. Kg1 Bf6 10. Kh2 Kg4 11. Rc5 {zugzwang} Be7 
12. Rc4+ Kf5 13. Rc6 Bh4 14. Kh3 Be1 15. Rc1 Bd2 16. Rc2 Be3 17. Kh4 Bg5+ 18. Kg3 Bh6 
19. Rc6 Kg5 20. Rd6 g6 21. Rc6 Bg7 22. Kf3 Kf5 23. Ke3 Bh8 24. Kd3 Bg7 25. Kc4 Bh8 
26. Kb5 Be5 27. Kc5 Bf4 28. Kd5 Bh6 29. Rc3 Kf6 30. Kd6 Bf4+ 31. Kd7 Be5 32. Re3 Bd4 
33. Re7 Bc5 34. Rh7 Be3 35. Ke8 Bf4 36. Rd7 Kf5 37. Rd5+ Kg4 38. Rd3 g5 39. Rf3 Be5 
40. Kf7 Bh8 41. Ke6 Bd4 42. Kd5 Bg7 43. Ke4 Bh8 44. Ke3 Bg7 45. Ke2 Bh8 46. Rd3 Kf4 
47. Kf2 g4 48. Rd7 Bc3 49. Rf7+ Kg5 50. Re7 Kf4 51. Rd7 Be5 52. Rf7+ Kg5 53. Rb7 Bd6 
54. Rb5+ Kh4 55. Rb3 Bc7 56. Ke2 Bd8 57. Kd2 Be7 58. Rd3 Bb4+ 59. Kc2 Bc5 60. Kc3 Bf2 
61. Kc4 Kg5 62. Kd5 Kf5 63. Rc3 Bh4 64. Rc4 Bg5 65. Re4 Bh4 66. Kd4 Bg3 67. Ke3 Bf2+ 
68. Kd3 Bh4 69. Rc4 Bf2 70. Ke2 Bh4 71. Rd4 Bf6 72. Rd7 Ke4 73. Rc7 Bh4 74. Rf7 Bg3 
75. Kd2 Be5 76. Kc2 Kd4 77. Kb3 Kd5 78. Rf1 Bc7 79. Kb4 Bb8 80. Re1 Be5 81. Kb5 Bd6 
82. Rd1+ Ke5 83. Kc6 Bb8 84. Rd8 Ba7 85. Rf8 Be3 86. Rf1 g3 87. Re1 Kf4 88. Kd5 Bb6 
89. Re4+ Kg5 90. Re5+ Kg4 91. Ke6 Bc7 92. Rf5 Bd8 93. Rb5 Bg5 94. Rb4+ Kh5 95. Re4 Bh6 
96. Kf5 Bd2 97. Re7 Bg5 98. Rg7 Kh4 99. Rh7+ Bh6? 
100. Rxh6# {YK DTC EGT (Konoval, 2014), FREEZER DTC EGT (Rusz, 2014)} 1-0.


[White "KRP"]
[Black "KBP"]
[Result "1-0"]
[Date "2014.03.14"]
[Event "6m, 3-3m, KRPKBP, GBR 0130.11, maxDTM w: SV+M-/SV+M+"]
[Annotator "Haworth,Guy"]
[SetUp "1"]
[FEN "8/3R2P1/7k/8/8/8/5p2/K5b1 w - - 0 1"]
[PlyCount "331"]

{dtc/m/z = 1/166/1m} 1. g8=N+ {KRNKBP: dtc/m/z = -5/-165/-5m: SV+M-/SV+M+} Kg6 2. Rd1 Kf5 
3. Kb2 Ke4 4. Kc2 Ke3 5. Nf6 Ke2 6. Ne4 f1=N {KRNKBN: dtm = 159m} 7. Nc3+ Kf2 8. Rc1 Ng3 
9. Kd3 Kg2 10. Nd5 Ba7 11. Rc7 Bb8 12. Rf7 Kh3 13. Rf8 Be5 14. Re8 Bd6 
15. Re6 Bc5 16. Rc6 Ba7 17. Rc4 Nh5 18. Rc7 Bf2 19. Rc8 Kg4 20. Rg8+
Kf3 21. Rf8+ Kg2 22. Rf5 Ng3 23. Rf6 Nh5 24. Rf8 Bg1 25. Rg8+ Ng3 26. Nf4+ Kf3
27. Ne6 Ba7 28. Ra8 Bb6 29. Rb8 Ba7 30. Rb7 Bg1 31. Rf7+ Kg4 32. Rg7+ Kh4 33.
Rg8 Bf2 34. Nf8 Bg1 35. Nd7 Kh3 36. Rg6 Bf2 37. Rf6 Bg1 38. Rf4 Nh5 39. Ra4 Bf2
40. Ne5 Bg3 41. Ng6 Bf2 42. Rc4 Kg2 43. Ne5 Bg3 44. Nf7 Bb8 45. Rc8 Ba7 46. Rh8
Nf4+ 47. Ke4 Ne2 48. Ng5 Bb6 49. Rf8 Ng3+ 50. Kd3 Nh5 51. Rf5 Ng3 52. Rb5 Bf2
53. Rb7 Nf5 54. Rb2 Ng3 55. Rc2 Nh1 56. Ne6 Ng3 57. Nd4 Nh1 58. Ke4 Kh3 59. Nc6
Kg3 60. Ne5 Bg1 61. Rc7 Nf2+ 62. Kd5 Nh1 63. Rf7 Bb6 64. Rh7 Kg2 65. Nc4 Bg1
66. Rf7 Ng3 67. Ke5 Nf1 68. Kf4 Bh2+ 69. Kg4 Bg3 70. Rb7 Nh2+ 71. Kf5 Nf1 72.
Ke4 Bh4 73. Rg7+ Kf2 74. Kd3 Kf3 75. Ne5+ Kf4 76. Ng6+ Kg4 77. Nf8+ Kf3 78. Ne6
Ng3 79. Rf7+ Kg2 80. Ke3 Nf1+ 81. Ke4 Ng3+ 82. Kf4 Nf1 83. Ke5 Nd2 84. Rd7 Bg3+
85. Kd4 Nf1 86. Rg7 Kf2 87. Kd3 Be5 88. Rg5 Bd6 89. Rd5 Bh2 90. Rb5 Kf3 91. Rb4
Be5 92. Re4 Bb2 93. Rf4+ Kg2 94. Ra4 Bh8 95. Ra6 Be5 96. Ke4 Bg3 97. Ra7 Nd2+
98. Kd3 Nf3 99. Rg7 Kh3 100. Ke3 Nh2 101. Ke4 Nf1 102. Rg8 Nd2+ 103. Kd3 Nf1
104. Ke2 Nh2 105. Nd4 Bf4 106. Nf5 Be5 107. Ke3 Bc7 108. Rc8 Be5 109. Rc4 Kg2
110. Ke2 Bf6 111. Rc6 Be5 112. Rg6+ Kh3 113. Kf2 Bc7 114. Rg7 Bf4 115. Rg8 Be5
116. Rg5 Bf4 117. Rg7 Be5 118. Rb7 Kg4 119. Ne3+ Kg5 120. Rb5 Kf4 121. Rb4+ Kg5
122. Kg2 Kg6 123. Rc4 Kf7 124. Ra4 Kg6 125. Ra6+ Kf7 126. Ra5 Kf6 127. Rd5 Bb8
128. Rd8 Be5 129. Rf8+ Ke7 130. Rf2 Kd7 131. Rd2+ Ke6 132. Re2 Kf6 133. Rf2+
Kg6 134. Kh3 Bd4 135. Rg2+ Kh5 136. Nd5 Be5 137. Rf2 Kg5 138. Rf8 Bd6 139. Rf7
Be5 140. Ne7 Bb8 141. Rf8 Bc7 142. Rf5+ Kh6 143. Rf2 Kg5 144. Rf8 Kh6 145. Nd5
Be5 146. Re8 Bd6 147. Re6+ Kg5 148. Rxd6 {KRNKN: dtc/m/z = -12/-18/-12m} Nf3 
149. Kg3 Nd2 150. Nf6 Nc4 151. Rd4 Ne3 152. Kf3 Nf5 153. Rf4 Ne7 154. Ke4 Ng6 
155. Rf1 Ne7 156. Nd5 Nc6 157. Rg1+ Kh5 158. Rg2 Kh4 159. Rg6 Nd8 160. Nf4 Nc6 
161. Rxc6 {KRNK: dtc/m/z = -4/-5/-4m} Kg5 162. Kf3 Kf5 163. Ng6
Kg5 164. Nh4 Kh5 165. Kf4 Kxh4 {KRK: dtx = 1m} 166. Rh6# {Nalimov DTM EGTs} *