Another example of an ending that could have potentially reached R+f+h vs. R is my game against Billy Colias from 1983 at the Chicago Chess Center. After 40. Rxc6
Without the f5-pawn, he certainly would have found the right move, but instead 40... Rh2? 40... Rg2+! 41. Kxf5 (41. Kh5 Rg4 and White canít make progress) 41... Rh2 is a drawn ending since 42. Rc7+ is met by 42...Kh6! Now, the Black king gets driven to the back rank, which we have seen is usually fatal for the defender in this type of ending. 41. Rc7+! Kg8 42. Kg6 42. Kxf5? Rxh4 is a straight-forward draw 42... Kf8 42... Rg2+ 43. Kxf5 is also winning for White by the methods described in the notes to Bereolos-Durham, but I think that offers better practical chances to draw. Now White is able to drive the Black king away from the pawns. 43. Rc8+ Ke7 44. Rh8 Ke6 Again, 44... Rg2+ 45. Kxf5 is winning for White, since the Black king is too far afield, but now White doesnít even need the h-pawn to win. 45. Re8+ Kd7 46. Re1 Rxh4 47. Kxf5 Rh2 48. Kg6 Rg2+ 49. Kf6 Rh2 50. f5 Rf2 51. Kg6 Rg2+ 52. Kf7 Rd2 53. f6 Rd3 54. Kg7 Rd2 55. f7 Rg2+ 56. Kf8 Ra2 57. Rg1 Rf2 58. Kg7 [1:0]
One of the most notoriously difficult rook endings is R+BP+RP vs. R. Iíve only had to defend this ending once, in a 1985 game against Dan Durham in Las Vegas. Euwe and Hopper give the basic rules of thumb for the defender: N2 is the best place for the king; the king should move forward or to the side if checked, since being driven to the back rank is usually fatal; and the rook should keep in position to be able to check from either the side or the back. I didnít really show this technique and it nearly cost me a half point. We entered this ending after he captured my last pawn with 59...gxf5
This position is drawn. Both the White King and Rook are in near ideal positions 60. Kg3 Rg4+ 61. Kf3 Rg6 62. Ra7+ Kf6 63. Kf4 Rg4+ 64. Kf3 Kg5 65. Rg7+ Kf6 66. Rh7 66. Ra7 repeating the position is a better practical choice 66... Kg6 67. Rh8 Rb4 68. Rg8+ A rather pointless check. While this move doesnít throw away the draw, but this is a continuation of minor inaccuracies that show White isnít really well acquainted with the drawing principles for this ending, better is 68. Kg3 68... Kf6 69. Rh8 Kg5 70. Rg8+ Kh4 71. Rf8 Rb1 72. Kf2 not 72. Rxf5? Rf1+ 73. Ke4 Rxf5 74. Kxf5 Kg3 -+; but 72. Kg2 getting to the best defensive square is better 72... Kg4 73. Rg8+! Kf4 74. Rh8? At this point it was necessary to play 74. Kg2! Rb2+ 75. Kh3! = now the White king gets cut off on the back rank 74... Rb2+! 75. Kg1 h4 76. Rg8
76... h3? This premature advance of the pawn allows White to draw by methods similar to those employed if Black had only an f-pawn. Winning was 76... Kf3 when the utility of the h-pawn is shown by looking at the two methods White would hold the draw in the absence of the h-pawn: 1. Defending a la Philidor with 77. Ra8 f4 78. Ra3+ Kg4 79. Rc3 h3 80. Ra3 f3 81. Ra8 Rg2+ 82. Kh1 (The Philidor move 82. Kf1 fails since the h-pawn rolls through after 82... h2) 82... Kg3 83. Rg8+ Kf2 84. Ra8 Rg1+ 85. Kh2 Re1 86. Ra2+ Kf1 -+] 2. Defending by latching on to the f-pawn also fails 77. Rf8 f4 78. Rf7 Rb1+ 79. Kh2 Ke3 80. Kg2 Rb4 81. Rf8 Re4 82. Rf7 Ke2 83. Rf8 f3+ and the h4 pawn prevents the two drawing moves that would exist if it wasn't there: 84. Kg3 is illegal and 84. Rxf3 drops the rook to 84... Rg4+ 77. Rh8 Kg3 78. Rg8+! Kf3 79. Rh8! Rg2+ 80. Kh1! 80. Kf1? Kg3 81. Rg8+ Kh2 82. Rf8 Ra2 83. Rg8 (83. Rxf5 Kg3! 84. Rg5+ Kf3 85. Rf5+ Kg4 and the h-pawn rolls through) 83... f4 84. Rg7 f3 85. Rg8 Rg2 86. Rf8 Kg3! and again the h-pawn cannot be stopped 80... Rg3 81. Ra8 f4 82. Kh2 82. Rf8 also holds the draw, but it is safer to get the king out of the corner where it would find itself in trouble after indifferent moves like 82. Ra3+? -+ or 82. Ra7? -+ 82... Rg5 83. Ra3+ Kf2 83... Kg4 84. Rxh3= 84. Ra2+ 84. Kxh3? Rg3+ is straightforward, capturing with the rook also loses 84. Rxh3? f3 85. Rh8 Rg2+ 86. Kh1 (86. Kh3 Kg1) 86... Kf1 87. Ra8 Re2! 88. Ra1+ Re1! 89. Ra2 f2 90. Kh2 Re8 -+ 84... Ke1 85. Ra1+ The simplest, but here and on the next several moves, 85. Kxh3= is also possible since Black doesnít have the resource ...Rg3+ that he had if White captures on move 84 85... Kd2 86. Ra2+ Ke3 87. Ra3+ Ke4 88. Ra4+ Kf5 89. Ra5+ Kg4 90. Rxg5+ Kxg5! 91. Kxh3! Kf5 92. Kg2! Ke4 93. Kf2! f3 94. Kf1! [Ĺ:Ĺ]
As I mentioned in the previous post, Iíve started looking at my games and analyses compared to the new 6-piece endgame tablebases. Here is the first half point Iíve found, against Lawrence Lipking in the 1983 US Class Championships. We entered a R+2P vs. R ending after 64...Kxh5
The win for Black shouldn't be too difficult. The idea is to head the king over to the queenside to support the b-pawn, while the White king is kept busy taking time to capture the g-pawn. 65. Rb2 Rb8! Rooks belong behind passed pawns. After the awkward 65... Ra7? White has no problems as his rook can roam the b-file without fear of the Black b-pawn being pushed. 66. Rb6 g5 67. Kg2 Kh4 better is 67... Kg4 heading towards the queenside 68. Rb4+ 68. Kf3 holds out for more moves, but is easier for Black since he doesn't have to sacrifice his g-pawn 68... Rf8+! 69. Kg2 Rf7 70. Rb4+ g4 71. Rb5 Rg7 and the Black king will cross to the queenside (Black can play ...g3 if necessary) 68... g4? Now it was necessary to repeat the position with 68... Kh5! 69. Rb6 Kg4 -+ 69. Rb6 other moves along the b-file also draw, but this is the most consistent, preventing immediate advance of the b-pawn 69... Kg5 70. Kg3 Kf5 71. Rb5+? bumping the Black king off of defense of the g-pawn, but allowing decisive penetration to the queenside. White holds the draw with 71. Rb4! b5 (White also has to be precise after 71... Ke5 72. Kxg4! (not 72. Rxg4? Kd5 73. Kf3 Re8! and the White king is cut off) 72...Kd5 73. Kf3 Kc5 74. Rb1! b5 75. Ke3! Kc4 76. Kd2! and the White king will get in front of the pawn)72. Rxg4 b4 (72... Ke5 73. Kf3 and Black is not able to cut the king off with Re8 as above) 73. Kf3 b3 74. Rg1 and the rook is in time to stop the pawn while the White king holds off the Black king. This position is somewhat reminiscent of the 9th game of the Kasparov-Short PCA Championship match played 10 years after this game where Kasparov blundered in a R+2P vs. R ending and Short failed to find this drawing method. 71... Ke4! retreating to the sixth rank allows White to draw since the Black king will be cut off 72. Kxg4 b6 73. Rb4+ Kd3 74. Kf4 Kc3 75. Rb5 Kc4 76. Rb1 b5 77. Ke3 Kc3 78. Rc1+ Kb2 With the Black king safely in front of the pawn and the White king on the long side, Black easily achieves a Lucena-like position. 79. Rc7 b4 80. Rd7 Rc8 81. Kd2 b3 82. Rd6 Kb1 83. Rb6 b2 84. Rb7 Rd8+ 85. Ke2 Ra8 86. Kd2 Ka2 [0:1]
Recently, some new 6-piece endgame tablebases have been generated. These new tablebases include pawns, which makes them very important from the perspective of endgame theory since now the truth about difficult endings like R+f+h vs. R can be known. This data will also help in the analysis of 7-piece endings, since the result of any capture will be absolutely known.
It doesn't look like any of the web interfaces have added these yet, but the raw data files are available in the Nalimov format (which works with most chess engines) at the Crafty ftp site. Of course these files are much bigger than the 5-piece tablebases, but for example all of the files for KRPP vs. KR take only 4.35 GB, which isn't a whole lot by the standards of today's hard drives.
Hopefully, the upcoming endgame manuals by Dvoretsky and Benko will have been checked with this new data (although I believe the former is a translation of his German book). It would be ironic if Benko's update of BCE has evaluations overturned, since discoveries by 4 and 5-piece tablebases is how many of the incorrect evaluations in the original BCE were found.
I've started looking through some of my games using these tablebases, and have already found a few half point changes. I'll start posting some of these soon.