Fortresses

Maybe the last stand in standardchess in which we can beat the computer is to recognize and build fortresses. There exist a lot of definitions for fortresses but in this article I stick to endgames (maximum 4 pieces besides pawns and kings) in which material is sacrificed to defend successfully. Some trivial endgames like rook-pawn + bishop of the wrong colour are evaluated correctly by our current engines but a fortress like in the high-class game Shakhriyar Mamedyarov - Fabiano Caruana created a lot of confusion.

[Event "Tata Steel"] [Site "Wijk aan Zee NED"] [Date "2016.01.29"] [Round "11"] [White "Shakhriyar Mamedyarov"] [Black "Fabiano Caruana"] [Result "1/2-1/2"] [ECO "B22"] [WhiteElo "2747"] [BlackElo "2787"] [SetUp "1"] [FEN "5k2/1P3p1p/4p1p1/8/1K6/5P1P/3r4/8 w - - 0 46"] [PlyCount "9"] [EventDate "2016.01.15"] 46. b8=Q Kg7 47. Qe5 {(Maybe Carlsen would still try here Kc5.)} (47. Kc5 Rd3 {(Black should not take up the defense lightly.)} (47... Rd5 48. Kc6 h5 49. f4 Rd3 50. Qb1 Rd8 51. Qb4 Rd1 52. Qb3 Rd8 53. Kc7 Rd5 54. f5 gxf5 55. Qg3 Kf8 56. Qf4 Ke8 57. Kc6 Rd3 58. Qh4 f4 59. Qxh5 Rc3 60. Kb6 Rb3 61. Ka5 f3 62. Qh8 Ke7 63. Qh4 Kf8 64. Qd8 Kg7 65. Qd4 $18 {(Stockfish already shows more than 9 so that should be sufficient for the win.)}) 48. Kc6 (48. f4 Kf6 49. Qf8 {(Otherwise black plays Ke7 after which he should not fear anymore an infiltration of the white king.)} Rxh3 50. Qd8 Kf5 51. Qd4 Rh4 52. Qe5 Kg4 53. Kd4 f5 54. Qxe6 Kh3 55. Qb3 Kg2 56. Qc2 Kg1 57. Qd1 Kh2 58. Qd2 Kh3 59. Qe3 Kg2 60. Qe2 Kh3 61. Qf1 Kh2 62. Qf2 Kh3 63. Qg1 Rxf4 $11) 48... Rxf3 49. Kd6 Rf5 50. Ke7 h6 51. Qb2 Kg8 52. Qc3 g5 53. Qb2 Rf4 54. Qb8 Kg7 55. Qe5 Kg8 56. Qe3 Rf1 57. Qe2 Rf4 58. Ke8 Kg7 59. Qe1 Kg8 60. Qc3 Rf2 61. h4 Rf5 62. Qd3 Kg7 63. Qg3 Kg8 64. Qg2 Kg7 65. Qg4 Kf6 66. Kf8 Rf4 67. Qh5 Ke5 68. Kg7 Rxh4 69. Qe2 Kf4 70. Kxf7 Kg3 71. Kxe6 $11) 47... Kg8 48. Qb8 Kg7 49. Qe5 Kg8 50. Qb8 1/2-1/2

Commentators initially thought that Fabiano blundered and even after the game some players weren't convinced about the fortress, see chessbomb or the blog of James Stripes. Today we are so dependent and addicted to evaluations of our engines that we don't question them anymore. Personally I only believe a score of +5 or a tablebase-hit that a win is 99,99% certain as I described earlier in my article to analyze with engines. Setting +5 is really not too high as some time ago the scores went up high while analyzing an endgame with Stockfish and Komodo while eventually they didn't manage to find the killer.

[Event "Analyse vesting"] [Date "2015"] [White "Bratuszewski, J."] [Black "Brabo"] [Result "*"] [ECO "A90"] [WhiteElo "1940"] [BlackElo "2271"] [SetUp "1"] [FEN "2Q5/6p1/1p3rkp/p4p2/P2Pn2P/1P2P2K/8/8 b - - 0 40"] [PlyCount "54"] {(I played with only 1 second remaining on my clock the weak Rd6 but my opponent was satisfied a couple of moves later anyway with a draw. Theoretically Kh5 gives the best surviving-chances.)} 40... Kh5 $1 41. d5 Nf2 42. Kh2 Ne4 43. Qh8 Kxh4 44. Qxg7 Rd6 45. Qe5 $5 Kg5 46. Kh3 Rf6 $1 47. Qf4 Kg6 48. Qb8 $5 Rd6 $1 49. Kg2 Kf7 $1 50. Kf3 Rxd5 51. Qxb6 h5 52. b4 h4 53. bxa5 h3 54. Kf4 h2 55. Qh6 Rxa5 56. Qxh2 Ke7 57. Qh4 Kd7 58. Qe1 Ra6 59. Qb4 Nd6 60. Ke5 Rb6 61. Qc5 Ra6 62. Kd5 Ne8 63. a5 Nd6 64. Qb4 Ne8 65. Qb5 Ke7 66. Kd4 Nc7 67. Qxf5 {(Stockfish shows 4,2 and Komodo 2,8. Nevertheless the Lomonosov tablebases tell us it is draw as black defends a zone. It is evident that I will not claim this line is forced as therefore it is way too long.)} *

The finalgentool can't judge the final position but with the help of HK5000 I got to know that it is indeed a draw after he checked the lomonosov 7 men tablebases. Yes indeed scores of +4,2 for Stockfish and +2,8 for Komodo don't mean there is a win. You don't expect that immediately of the current leaders which are considered generally invincible. I also expect that these are no records even if we don't take special positions into account from the world of compositions. Komodo even showed a personal higher score of +3,2 in the fortress which I met in my analysis of move 42 in my game against Stone, see my article bricks. Do you know fortresses from practice which are evaluated even worse then write it down in a reaction below this article !

On the other hand above analysis of both fortresses also show that engines can still discover a lot of interesting lines. Not seldom a strong engine can crack a fortress by using some very complicated constructions. I had a look to the so-called fortress which appeared in the marathon-game of 122 moves in the last world-championship. Neither Carlsen nor the commentators found a win in the 7th game but thanks to Lets Check I still found a weak spot.

[Event "Carlsen-Anand World Championship"] [Site "Sochi RUS"] [Date "2014.11.17"] [Round "7"] [White "Magnus Carlsen"] [Black "Viswanathan Anand"] [Result "1/2-1/2"] [ECO "C67"] [PlyCount "243"] [EventDate "2014.11.07"] 1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. O-O Nxe4 5. d4 Nd6 6. Bxc6 dxc6 7. dxe5 Nf5 8. Qxd8 Kxd8 9. h3 Ke8 10. Nc3 h5 11. Bf4 Be7 12. Rad1 Be6 13. Ng5 Rh6 14. g3 Bxg5 15. Bxg5 Rg6 16. h4 f6 17. exf6 gxf6 18. Bf4 Nxh4 19. f3 Rd8 20. Kf2 Rxd1 21. Nxd1 Nf5 22. Rh1 Bxa2 23. Rxh5 Be6 24. g4 Nd6 25. Rh7 Nf7 26. Ne3 Kd8 27. Nf5 c5 28. Ng3 Ne5 29. Rh8 Rg8 30. Bxe5 fxe5 31. Rh5 Bxg4 {(Played intuitively but it is unclear if the fortress can hold.)} 32. fxg4 Rxg4 33. Rxe5 b6 34. Ne4 Rh4 35. Ke2 Rh6 36. b3 Kd7 37. Kd2 Kc6 38. Nc3 a6 39. Re4 Rh2 40. Kc1 Rh1 41. Kb2 Rh6 42. Nd1 Rg6 43. Ne3 Rh6 44. Re7 Rh2 45. Re6 Kb7 46. Kc3 Rh4 47. Kb2 Rh2 48. Nd5 Rd2 49. Nf6 Rf2 50. Kc3 Rf4 51. Ne4 Rh4 52. Nf2 { (Thanks to Lets Check I got to know that Re7 is very strong. I could not find a defense anymore for black.)} (52. Re7 $1 a5 (52... Rh6 53. Ng5 Rh8 54. Ne6 Rc8 55. Rf7 Kc6 56. Rf8 Rxf8 57. Nxf8 Kb5 58. Ne6 Kc6 59. Kd3 Kd6 60. Ng5 Kc6 61. c4 b5 62. Ne6 Kd6 $18) (52... Rh3 53. Kb2 Kc6 54. Nf6 Kd6 55. Rh7 Re3 56. Rd7 Ke6 57. Re7 {(I expect this key-move was missed.)} Kxe7 58. Nd5 Kd6 59. Nxe3 c4 60. Nxc4 Kd5 61. Kc3 Ke4 62. Nb2 Kd5 63. Kd3 Kc5 64. Ke4 Kb4 $18) 53. Nd6 Kc6 54. Ne8 b5 55. Rxc7 Kb6 56. Kb2 a4 57. Rg7 Kc6 58. bxa4 Rxa4 59. Rg6 Kd7 60. Nf6 Ke6 61. Rh6 Rb4 62. Kc1 Rd4 63. Ng4 Kd5 64. Ne3 Ke4 65. Re6 Kf4 66. Nd1 b4 67. Nb2 c4 68. Rc6 Kf5 69. Rxc4 Rd5 70. Rh4 Rd8 71. Rxb4 $18) 52... Rh2 53. Rf6 Rh7 54. Nd3 Rh3 55. Kd2 Rh2 56. Rf2 Rh4 57. c4 Rh3 58. Kc2 Rh7 59. Nb2 Rh5 60. Re2 Rg5 61. Nd1 b5 62. Nc3 c6 63. Ne4 Rh5 64. Nf6 Rg5 65. Re7 Kb6 66. Nd7 Ka5 67. Re4 Rg2 68. Kc1 Rg1 69. Kd2 Rg2 70. Ke1 bxc4 71. Rxc4 Rg3 72. Nxc5 Kb5 73. Rc2 a5 74. Kf2 Rh3 75. Rc1 Kb4 76. Ke2 Rc3 77. Nd3 Kxb3 78. Ra1 Kc4 79. Nf2 Kb5 80. Rb1 Kc4 81. Ne4 Ra3 82. Nd2 Kd5 83. Rh1 a4 84. Rh5 Kd4 85. Rh4 Kc5 86. Kd1 Kb5 87. Kc2 Rg3 88. Ne4 Rg2 89. Kd3 a3 90. Nc3 Kb6 91. Ra4 a2 92. Nxa2 Rg3 93. Kc2 Rg2 94. Kb3 Rg3 95. Nc3 Rh3 96. Rb4 Kc7 97. Rg4 Rh7 98. Kc4 Rf7 99. Rg5 Kb6 100. Na4 Kc7 101. Kc5 Kd7 102. Kb6 Rf1 103. Nc5 Ke7 104. Kxc6 Rd1 105. Rg6 Kf7 106. Rh6 Rg1 107. Kd5 Rg5 108. Kd4 Rg6 109. Rh1 Rg2 110. Ne4 Ra2 111. Rf1 Ke7 112. Nc3 Rh2 113. Nd5 Kd6 114. Rf6 Kd7 115. Nf4 Rh1 116. Rg6 Rd1 117. Nd3 Ke7 118. Ra6 Kd7 119. Ke4 Ke7 120. Rc6 Kd7 121. Rc1 Rxc1 122. Nxc1 1/2-1/2

I looked on the web for serious analysis of this endgame but I didn't find much. The only exception was the remarkable study of the Russian grandmaster Pavel Maletin on the site of the Russian chessfederation but it is not very readable and he admits that improvements are possible. I am curious if some other analysis exists but who wants to stick out their neck? I expect that even Kasparov would need a lot of time to make a decent analysis as published in his world-championship books.

While preparing this article, I also reviewed some analysis of fortresses popping up in my older games. No surprise here too as I also found some holes in the analysis. I mentioned in my article the Spanish with d5 that a fortress exists in the analysis of move 50 of my game against Fabien Libiszewski. Stockfish must move heaven and earth but in the end manages to breakthrough.

[Event "Analyse vesting"] [Date "2004"] [White "Libisewski, F."] [Black "Brabo"] [Result "*"] [ECO "C97"] [WhiteElo "2457"] [BlackElo "2308"] [SetUp "1"] [FEN "8/8/5Bp1/1p1q2P1/1P4k1/5R2/5K2/8 w - - 0 66"] [PlyCount "68"] {(In my analysis of 2004 I wrote that it is a draw but today I am not sure anymore.)} 66. Rg3 Kh4 $1 {(The black king pushes the white king out of the corner.)} 67. Re3 Qf5 68. Ke1 Qb1 69. Kd2 Qxb4 70. Kc2 Kg4 71. Rb3 Qe1 72. Rb1 Qe2 73. Kb3 Qd3 74. Kb2 Kf5 75. Ra1 Qd2 76. Ka3 Ke6 77. Rb1 Qe3 78. Kb2 Qe4 79. Ka2 b4 80. Rb2 Qc4 81. Kb1 b3 82. Rd2 Qb4 83. Re2 Kf5 84. Kb2 Qa5 85. Kc1 Qa3 86. Kd1 Qb4 87. Rd2 Ke4 88. Kc1 Ke3 89. Rh2 Qa3 90. Kb1 Kd3 91. Rh3 Kc4 92. Rh2 Qd6 93. Rg2 Qf4 94. Kb2 Kd3 95. Bg7 Qf3 96. Rh2 Qg3 97. Rh8 Qf2 98. Kxb3 Qf7 99. Ka3 Qxg7 {(We obtained a tablebase which black wins.)} *

Later I did find an improvement for white just before the start-position by playing immediately 64.Rxf3+. That avoids the black king running to h4 and chasing away the white king out of the corner. If white positions the rook on g2 and the king on g1/h2 then it is although a fortress but that doesn't matter in this story. Fortresses are often too abstract for our engines but that is not the same as engines are useless to analyze fortresses. There is continuous progress made but fortunately still some mystery remains for a while.

Brabo