Author: Duncan Roberts
Date: 07:45:38 08/29/05
Go up one level in this thread
On August 29, 2005 at 03:29:12, Marc Bourzutschky wrote: >During the past 6 months Yakov Konoval and I have collaborated on efficient >algorithms to exactly solve 7-man endgames. Yakov has come up with a program >that contains every trick in the book, and then some. Many of the ideas are >refinements of those used by Johan de Koning in his path breaking FEG program. > >Our hardware is extremely basic, about US $3,000 worth of equipment: a single >3.6 GHZ PIV, with 4 GB RAM, two 250 GB IDE hard disks, running Windows XP. > >To put Yakov's programming skills in perspective, his program solves the >infamous 6-man krnknn endgame in just over one hour on that hardware. Great achievement. well done. how long would a dtm program have taken to solve the 6-man krnknn endgame on your machine. ? have you ever tested the elo increase in strength for a complete 6 man endgame ? how many computer months roughly do you reckon it would take all the pawnless 7 man database to complete as well as the whole 7 man database. and how many positions are there ? is there any computer knowledge you can extract from these tests that could be put in an evaluate for those particular positions. thank you duncan > >So far we have focused on pawnless endgames. While those may have little >practical relevance, they are an important first step. Pawnless endgames will >also, in the words of Tim Krabbe, show many examples of the eerie beauty of >perfect but incomprehensible chess. Perhaps there will be endings that break >the record of 243 moves without mate or capture in krnknn. > >The largest database we have generated so far is krbnkrb. This endgame is of >some interest to endgame study composers, particularly the question how the >outcome depends on whether the bishops have the same or opposite colors. This >ending also arises occasionally in practice. For example, it occurred during >the 11th Postal World Championship, in the game Buj vs. Thiele. It was >adjudicated a draw. Pablo Buj was not happy and showed analysis claiming he >was winning. The database indeed confirms the win, and a relatively >straightforward one at that, with only 18 moves to conversion. > >The krbnkrb database has almost a trillion entries (462*64^5 for both White >and Black.) Almost half of these entries represent legal positions, making it >the largest chess endgame solved by far. Generation time was about 17.5 days, >and the final size is about 168 GB. Verification took another 5 days. > >All the endgames are created using the DTZ metric, which for pawnless endings >is the shortest distance to either checkmate or capture to a won subgame. >DTZ is faster to generate than distance to mate (DTM), and also compresses >better. The improvement of DTZ over DTM is roughly a factor of two in speed >and size for 6-man endgames, and probably more for 7-man endgames. > >Generation times scale roughly with the permutation symmetries of the ending. >Ball park figures are half a day for endings of the form kxxxxky, a day for >kxxxkyy, two days for kxxxkyz or kxyyykz, etc. Verification usually takes >between 1/2 and 3/4 of the generation time. > >Now some examples. I show play all the way to mate, even if there is a capture >before the end. Exclamation marks are attached to moves if any other move >would throw away the win. > >KQQQKQQ > >Not a terribly interesting ending in itself, but a useful reference point, >perhaps for a future KQPPKQP where only queen promotions are considered. The >longest winning distance is 76 moves. As expected, there are often cannonades >of successive checks, 73 in the maximal position below: > >[D] 4Qq2/5Q2/8/8/8/2q5/Q7/2K4k w - - 0 1 > >[Event "?"] >[White "QQQ"] >[Black "QQ"] >[Result "1-0"] >[SetUp "1"] >[FEN "4Qq2/5Q2/8/8/8/2q5/Q7/2K4k w - - 0 1"] >[PlyCount "167"] > >1. Kd1! Qd4+ 2. Ke2! Qg4+ 3. Kd3! Qd1+ 4. Qd2 Qa3+ 5. Ke4! Qg4+ 6. Ke5! Qag3+ >7. Qff4! Qg5+ 8. Ke4! Qg6+ 9. Kd5! Qb3+ 10. Kd4! Qg7+ 11. Kc5 Qa7+ 12. Kd6! >Qaa3+ 13. Ke5 Qc5+ 14. Kf6! Qbb6+ 15. Qe6! Qf8+ 16. Ke5! Qg7+ 17. Qef6 Qg5+ >18. Ke4! Qb1+ 19. Kd4! Qa1+ 20. Kc4 Qa4+ 21. Kd3! Qb3+ 22. Qfc3 Qb1+ 23. Kd4! >Qb6+ 24. Ke4 Qbg6+ 25. Ke3 Qg1+ 26. Ke2! Q6g2+ 27. Kd3! Qb1+ 28. Kd4! Qb6+ 29. >Qc5 Qf2+ 30. Qde3! Qfb2+ 31. Kd5! Qa2+ 32. Qfc4! Qd2+ 33. Qcd3 Qa2+ 34. Kd4 >Qf6+ 35. Qee5! Qff2+ 36. Qde3 Qfb2+ 37. Qec3! Qf2+ 38. Qee3 Qf6+ 39. Kd3 Qb1+ >40. Kc4! Qa6+ 41. Kd5 Qf5+ 42. Qee5! Qf7+ 43. Ke4 Qe2+ 44. Kd4! Qef2+ 45. Qee3 >Q2f6+ 46. Kd3 Qf1+ 47. Ke4 Qe6+ 48. Q5e5! Qg4+ 49. Q3f4! Qfg2+ 50. Kd4 Qd7+ >51. Qd6! Qf2+ 52. Kc4! Qa2+ 53. Kd3 Qb5+ 54. Kd4! Qa7+ 55. Ke4! Qe2+ 56. Qfe3 >Qa4+ 57. Kd5 Qeb5+ 58. Qec5 Qa2+ 59. Kd4! Qf2+ 60. Qe3! Qbb2+ 61. Ke4 Qg2+ 62. >Kf5! Qb1+ 63. Kf4 Qbf1+ 64. Ke5! Qg7+ 65. Kd5! Qfg2+ 66. Kc4 Qa2+ 67. Qb3 Qg4+ >68. Qcd4! Qc8+ 69. Kb4 Qb7+ 70. Q6b6 Qe7+ 71. Kc4 Qae2+ 72. Kc3 Qf3+ 73. Kb2 >Qee2+ 74. Qc2 Qef2 75. Qh8+ Kg1 76. Qcxf2+ Qxf2+ 77. Qxf2+! Kxf2 78. Qg8 Ke3 >79. Qg4 Kf2 80. Kc1 Kf1 81. Kd1 Kf2 82. Kd2 Kf1 83. Ke3 Ke1 84. Qg1# 1-0 > >KBBBBKQ > >This is the companion to knnnnkq I had written about earlier this year, which >appeared in EG: http://www.gadycosteff.com/eg/eg156.pdf >Yakov's program is a good 6 times faster and more memory efficient than my >early effort. kbbbbkq with a pair of opposite colored bishops is a general win >for the bishops. The longest win takes 101 moves. One is reminded of fox and >geese where the plodding bishops finally prevail over the wily queen: > >[D] 8/3B2k1/8/6B1/7B/q6B/8/K7 w - - 0 1 > >[Event "?"] >[White "BBBB"] >[Black "Q"] >[Result "1-0"] >[SetUp "1"] >[FEN "8/3B2k1/8/6B1/7B/q6B/8/K7 w - - 0 1"] >[PlyCount "201"] > >1. Kb1 Qb3+ 2. Kc1 Qc3+ 3. Kd1 Qd3+ 4. Ke1 Qe4+ 5. Kf2 Qd4+ 6. Kf3 Qd5+ 7. Ke3 >Qe5+ 8. Kd2 Qd4+ 9. Kc2 Qe4+ 10. Kc1 Qc4+ 11. Kb2 Qb4+ 12. Ka2 Qc4+ 13. Ka3 >Qd3+ 14. Kb4 Qe4+ 15. Kc5! Qe5+ 16. Kb6! Qb8+ 17. Kc6 Qa8+ 18. Kc7 Qa5+ 19. >Kb8 Qb6+ 20. Kc8 Qa6+ 21. Kd8 Qa8+ 22. Bc8 Qd5+ 23. Bhd7 Kf7 24. Kc7! Qc5+ 25. >Kb7 Qb4+ 26. Kc6 Qc4+ 27. Kb6 Qd4+ 28. Kb5 Qd5+ 29. Kb4 Qd4+ 30. Kb3 Qd3+ 31. >Kb2 Qd4+ 32. Kc2 Qc4+ 33. Kd2 Qd4+ 34. Ke2 Qe4+ 35. Kf2 Kg6 36. Be7! Qd4+ 37. >Ke2 Qe4+ 38. Kd2 Qd4+ 39. Kc2 Qc4+ 40. Kb2 Qe2+ 41. Kc3 Qe5+ 42. Kc4 Qe4+ 43. >Kc5 Kf7 44. Bd8 Qe5+ 45. Kc4 Qe4+ 46. Kc3 Qe3+ 47. Kc2 Qe2+ 48. Kc1 Qe3+ 49. >Kd1 Qf3+ 50. Ke1 Qe4+ 51. Kf1 Qh1+ 52. Kf2 Qh2+ 53. Kf3 Qh1+ 54. Ke3 Qc1+ 55. >Kf2 Qc2+ 56. Kg1 Qd1+ 57. Kg2 Qd5+ 58. Kh2 Qa2+ 59. Kh3 Qb1 60. Bf5 Qh1+ 61. >Kg3 Qg1+ 62. Kf3 Qf1+ 63. Ke3 Qc1+ 64. Kf2 Qc5+ 65. Kg2 Qc6+ 66. Kh2 Qd6+ 67. >Kh3 Qc6 68. Kg4 Qa4+ 69. Kg5 Qc6 70. Bg3 Qc1+ 71. Bf4 Qc6 72. Bcd7 Qg2+ 73. >Kh4 Qf2+ 74. Bg3 Qd4+ 75. Kh3 Qd5 76. Kg4 Qd1+ 77. Kg5 Qd2+ 78. Kh5 Qe2+ 79. >Kh4 Qe3 80. Bg5 Qe2 81. Bc6 Qc4+ 82. Bfe4 Ke6 83. Be3 Qb3 84. Bef4 Qc4 85. Kg5 >Qd4 86. Bf5+ Kf7 87. Be5 Qd2+ 88. Bgf4 Qd8+ 89. Kg4 Qd1+ 90. Bf3 Qf1 91. Bd5+ >Ke7 92. Bfe4 Qd1+ 93. Kg5 Qg1+ 94. Kh6 Qb6+ 95. Kg7 Qa7 96. Bg5+ Kd7 97. Kf8 >Qa3+ 98. Kf7 Qh3 99. Bc6+ Kc8 100. Bb7+ Kd7 101. Bec6# 1-0 > >For those who love the bizarre, here is the unique mutual zugzwang (out of 303) >which is perfectly symmetric about the a1-h8 diagonal. All the bishops have >the same color. White to move loses, but black to move only achieves a draw: > >[D] 6B1/1B4qB/5k2/8/3K4/8/6B1/8 b - - 0 1 > > >KBNNNKQ > >This endings has about 4 times as many positions as knnnnkq or kbbbbkq. The >uneasy collaboration between bishop and knight, making even kbnk a non-trivial >endeavor, seems to be multiplied here to make this a very difficult win. The >longest win takes 224 moves. There are over 140 checks by the queen, who >buzzes about like an angry insect before Black finally succumbs: > >[D] 5N2/5k1N/7q/8/8/3B4/8/2K2N2 w - - 0 1 > >[Event "?"] >[Date "????.??.??"] >[White "BNNN"] >[Black "Q"] >[Result "1-0"] >[SetUp "1"] >[FEN "5N2/5k1N/7q/8/8/3B4/8/2K2N2 w - - 0 1"] >[PlyCount "447"] > >1. Kd1! Qh5+ 2. Ke1! Qe5+ 3. Kf2! Qd4+ 4. Ke2! Qg4+ 5. Kd2 Qb4+ 6. Ke3 Qe1+ 7. >Kf4 Qf2+ 8. Ke4! Qg2+ 9. Kd4 Qb2+ 10. Ke3 Qg2 11. Nd2 Qg1+ 12. Ke2! Qh2+ 13. >Kd1 Qd6 14. Kc2 Qc6+ 15. Nc4 Kg7 16. Kd2! Qg2+ 17. Kc3! Qd5 18. Bc2 Qc6 19. >Kd4! Qa6 20. Ne3! Qb6+ 21. Ke4 Qc6+ 22. Kf4 Qh6+ 23. Kf3 Qh3+ 24. Ke4 Kh8 25. >Bd1 Qh1+ 26. Bf3 Qb1+ 27. Kf4 Qb8+ 28. Kg4 Qb4+ 29. Kg3 Qb8+ 30. Kf2 Qb2+ 31. >Be2 Qb8 32. Bc4 Qh2+ 33. Kf3 Qh1+ 34. Kf4 Qh4+ 35. Ke5 Qe7+ 36. Kd4 Qh4+ 37. >Kd3 Qg3 38. Bd5 Qe1 39. Ng2 Qg3+ 40. Ke2 Kg7 41. Ne3 Qh2+ 42. Kf3 Qh5+ 43. Kg3 >Qe5+ 44. Kf2 Qh2+ 45. Bg2 Qh4+ 46. Kf3 Qh5+ 47. Kf4 Qh6+ 48. Ke4 Qh4+ 49. Kd3 >Qh5 50. Bc6 Qa5 51. Bd5 Qb5+ 52. Ke4 Qe2 53. Be6 Qe1 54. Kd3 Qb4 55. Bf5 Qb5+ >56. Ke4 Qc6+ 57. Kf4 Qh6+ 58. Kf3 Qh5+ 59. Kg3 Qe2 60. Ng4 Qe1+ 61. Kg2! Qd2+ >62. Nf2! Qd5+ 63. Be4! Qc4 64. Kg3 Qc7+ 65. Kg4 Qc4 66. Kh4 Qe2 67. Kg3! Qc4 >68. Kg2 Kg8 69. Kf3 Qf7+ 70. Kg3 Qc7+ 71. Kh3 Qc3+ 72. Nd3 Qd4 73. Bf5! Qe3+ >74. Kg4 Qg1+ 75. Kf4 Qh2+ 76. Ke4 Qg2+ 77. Ke5 Qg7+ 78. Kd6 Qd4+ 79. Kc6 Qa4+ >80. Kd5 Qb3+ 81. Ke5 Qb8+ 82. Kd4 Qa7+ 83. Nc5 Kh8 84. Be4 Qa1+ 85. Kd5 Qa5 >86. Kc6 Qa3 87. Bd3 Qa2 88. N5e6 Qa3 89. Bb5 Qa8+ 90. Kc5 Qa3+ 91. Kb6 Qe3+ 92. >Kb7 Qb3 93. Nc7 Qb4 94. Kc8 Qc5 95. Bd7 Qd6 96. Bf5 Qc5 97. Be4 Qb4 98. Bb7 >Qa3 99. Ba8 Qb4 100. Nce6 Qc3+ 101. Kd7 Qd3+ 102. Ke8 Qb5+ 103. Ke7! Qa5 104. >Bc6 Qa3+ 105. Ke8 Qa6 106. Bf3 Qb5+ 107. Ke7! Qb4+ 108. Kd7 Qb5+ 109. Kd6 Qd3+ >110. Bd5! Qa6+ 111. Ke5 Qa1+ 112. Kf5 Qf1+ 113. Nf4 Kg7 114. Be4 Qf2 115. Kg4 >Qg1+ 116. Kf3 Qf1+ 117. Ke3 Kh6 118. Nd5! Qg1+ 119. Ke2 Qh2+ 120. Kd3 Qb8 121. >Ndf6 Qb3+ 122. Ke2 Qc4+ 123. Kf2 Qd4+ 124. Kf3 Qd1+ 125. Kf4 Qd2+ 126. Kg4 Qe3 >127. Bf3 Qg1+ 128. Kf5 Qg3 129. Ke4 Qh4+ 130. Ke3 Qe1+ 131. Kf4 Qc1+ 132. Kf5 >Qc5+ 133. Ke4 Qb4+ 134. Kd3 Qd6+ 135. Ke3 Qc5+ 136. Ke2 Qb5+ 137. Kf2 Qb2+ >138. Kg3 Qe5+ 139. Kg2 Qb2+ 140. Kh3 Qc3 141. Kg4 Qc4+ 142. Ne4 Kg7 143. Kg3 >Qc7+ 144. Kh3 Qc8+ 145. Bg4 Qa6 146. Ng3 Kg8 147. Bf5 Qh6+ 148. Kg4 Qg7+ 149. >Kh4 Qe7+ 150. Kh3 Qe5 151. Be4 Qd4 152. Bf3 Qd3 153. Bg2 Qd2 154. Ne4 Qe3+ >155. Kg4 Qg1 156. Kf3 Qd1+ 157. Kf2 Qc2+ 158. Kg3 Qc7+ 159. Kf3 Qb7 160. Kg4 >Qc8+ 161. Kh5 Qc2 162. Bf3 Kg7 163. Neg5 Qh2+ 164. Kg4! Qg1+ 165. Kh3 Qf1+ 166. >Bg2 Qd3+ 167. Kh4 Qd2 168. Nfe6+ Kh6 169. Kg3 Qe3+ 170. Kg4 Qe2+ 171. Bf3 Qc4+ >172. Kg3 Qc3 173. Nf4 Qd4 174. Nd5 Qc4 175. Ndf6 Qc1 176. Be4 Qg1+ 177. Kh4 >Qf2+ 178. Kg4 Qg1+ 179. Kf5 Qf2+ 180. Nf3 Qc5+ 181. Ne5 Qf2+ 182. Ke6 Qb6+ >183. Bc6 Qc5 184. Bd5 Qc8+ 185. Ned7 Kg6 186. Be4+ Kh6 187. Ng4+ Kh5 188. Ne5 >Kh4 189. Nf6 Kg5 190. Bc6 Kf4 191. Nd5+ Kg5 192. Ne7 Qa6 193. Nf6 Qa2+ 194. >Ned5 Qg2 195. Bb5 Qh3+ 196. Ke7 Qf5 197. Kd6 Qb1 198. Nf3+ Kh6 199. Bd7 Qa2 >200. Ne5 Qe2 201. Nf4 Qd2+ 202. Nfd3 Qe2 203. Bc6 Qa2 204. Ne4 Qg8 205. Ke7 Kg7 >206. Ndc5 Qf8+ 207. Kd7 Qb8 208. Ne6+ Kh8 209. Nd6 Kg8 210. Ndf7 Qa7+ 211. Ke8 >Qb8+ 212. Ke7 Qb4+ 213. Kf6 Qh4+ 214. Neg5 Qf2+ 215. Bf3 Qb6+ 216. Nc6 Qb2+ >217. Nfe5 Qf2 218. Ne7+ Kf8 219. Nf5 Qb6+ 220. Bc6 Qd8+ 221. Kg6! Qa5 222. Nef7 >Qb6 223. Nh7+ Kg8 224. Ne7# 1-0 > > >kbnnnkq contains 3 full-point mutual zugzwangs, where whoever is to move loses. >Such zugzwangs are extremely rare in endings without pawns. Here is one of the >3 cases: > >[D] 8/8/5N2/8/6N1/2kq1N2/8/2KB4 w - - 0 1 > >White to move loses: > >[Event "?"] >[Date "????.??.??"] >[White "BNNN"] >[Black "Q"] >[Result "0-1"] >[SetUp "1"] >[FEN "8/8/5N2/8/6N1/2kq1N2/8/2KB4 w - - 0 1"] >[PlyCount "8"] > >1. Nh6 Qe3+! 2. Kb1 Qb6+ 3. Bb3 Qxb3+ 4. Kc1 Qc2# 0-1 > > >Black to move from the same position also loses: > >[Event "?"] >[Date "????.??.??"] >[White "BNNN"] >[Black "Q"] >[Result "1-0"] >[SetUp "1"] >[FEN "8/8/5N2/8/6N1/2kq1N2/8/2KB4 b - - 0 1"] >[PlyCount "134"] > >1... Qc4 2. Ne3 Qc6 3. Ne1 Kd4+ 4. N1c2+ Ke5 5. Nfd5 Qg6 6. Be2 Qh7 7. Bf3 Qd3 >8. Kb2 Kd6 9. Ndb4 Qg6 10. Kc3 Qg1 11. Nc4+ Ke6 12. Nd4+ Kf7 13. Nd6+ Kg6 14. >Ne4 Qa1+ 15. Kc4 Qa4 16. Bg4 Kg7 17. Bf5 Kh6 18. Nc5 Qa8 19. Be4 Qa7 20. Nde6 >Kh5 21. Nc2 Qa2+ 22. Kc3 Qb1 23. Ncd4 Qa2 24. Bf5 Qf2 25. Ne4 Qe3+ 26. Kc4 Qa3 >27. Kd5 Qa5+ 28. Kd6 Qb4+ 29. Ke5 Qb8+ 30. Kf6 Qh8+ 31. Kf7 Qa8 32. N4g5 Qh8 >33. Ndf3 Qc3 34. Nfd4 Qa5 35. Bh3 Kh4 36. Nf5+ Kh5 37. Ne4 Qc7+ 38. Ne7 Qb7 >39. Bf5 Kh4 40. Nf8 Kh5 41. Nd7 Kh4 42. Kg8 Qa8+ 43. Kh7 Qa7 44. Be6 Qb7 45. >Ng6+ Kh5 46. Nd6 Qc7 47. Nf7 Qc3 48. Nde5 Qc4 49. Bd5 Qe4 50. Bc6 Qf5 51. Bf3+ >Qg4 52. Nh4 Qxf3 53. Nexf3! Kg4 54. N7g5 Kf4 55. Ng6+ Kg4 56. Kg7 Kg3 57. Kf6 >Kg2 58. Nf4+ Kf2 59. Kg6 Kg3 60. Nd3 Kg4 61. Nd2 Kh4 62. Nde4 Kg4 63. Kf6 Kh5 >64. Ndf2 Kh6 65. Kf7 Kh5 66. Kg7 Kh4 67. Nf3+ Kh5 68. Nf6# 1-0 > >(KBBNNKQ and KBBBNKQ have not been generated yet.) > > >KRRRKQB > >This turns out to be another marathon, with the win taking up to 200 moves. >In the line below it is entertaining to watch what happens after move 200. >Play can only be understood by realizing that the algorithm prefers a capture >in one move to a mate in 2 moves, so the bizarre moves are fully correct from >a game theoretic point of view. Of course, play before move 200 may well be >beyond human understanding, with the rooks finally prevailing after a stately >progression like in a Japanese tea ceremony: > >[D] 8/4R3/8/1R5b/5R2/8/7k/K6q w - - 0 1 > >[Event "?"] >[Date "????.??.??"] >[White "RRR"] >[Black "QB"] >[Result "1-0"] >[SetUp "1"] >[FEN "8/4R3/8/1R5b/5R2/8/7k/K6q w - - 0 1"] >[PlyCount "437"] > >1. Ka2! Qa8+ 2. Kb3! Qd8 3. Rfe4! Qd3+ 4. Kb4! Qd6+ 5. Rc5 Qb6+ 6. Kc4 Qa6+ 7. >Kc3 Qa3+ 8. Kd4 Qb4+ 9. Rc4! Qd6+ 10. Kc3 Bg6 11. Re2+! Kg1 12. R7e6! Qa3+ 13. >Kd4! Qd3+ 14. Kc5! Qa3+ 15. Kc6 Qa6+ 16. Kd5 Qa8+ 17. Kd4 Qa1+ 18. Ke3 Bh5 19. >Rd2! Qe1+ 20. Kd3! Qf1+ 21. Kc3! Qc1+ 22. Rc2 Qa3+ 23. Kd4! Qa7+ 24. Rc5 Qd7+ >25. Ke5! Bg4 26. Rc1+! Kg2 27. R5c2+ Kg3 28. Rc3+! Kh4 29. Rec6! Qg7+ 30. Kd5 >Qf7+ 31. Kd4 Qd7+ 32. Kc5 Qe7+ 33. Kb6 Qb4+ 34. Ka7 Qa4+ 35. Ra6 Qd4+ 36. Rc5 >Be2 37. Rc6! Qa4+ 38. Kb7! Qb3+ 39. Rb6! Qf3+ 40. Rcc6 Qf7+ 41. Rc7 Qd5+ 42. >Kb8! Qg8+ 43. Rc8 Qg3+ 44. Kb7 Qa3 45. Rh1+ Kg5 46. Kb8! Qg3+ 47. Rc7! Qe5 48. >Rg1+! Kh5 49. Rc1 Qe8+ 50. Rc8 Qe5+ 51. Kb7 Qd5+ 52. R8c6 Qf7+ 53. Rc7 Qd5+ >54. Kb8 Qg8+ 55. Rc8 Qg3+ 56. Kb7 Qf3+ 57. R1c6 Qe4 58. Rc7! Bf3 59. Rb5+! Kh4 >60. Kb6! Qd4+ 61. Rcc5! Qf6+ 62. Ka7 Qd4 63. Ra5 Be4 64. Ra3! Bd3 65. Rc3 Qa4+ >66. Kb8! Qb4+ 67. Rb7 Qf4+ 68. Rcc7 Qf8+ 69. Ka7! Qf2+ 70. R7c5 Qa2+ 71. Kb8 >Qg8+ 72. Rc8 Qg3+ 73. Ka7 Qf2+ 74. Ka8 Qa2+ 75. Kb8! Qh2+ 76. R8c7 Qd6 77. >Rbb3! Be2 78. Rc6 Qf4 79. Rc2 Qd4 80. R2c5 Kg4 81. Rcc3 Qd6 82. Rc6 Qd8+ 83. >Rc8 Qd5 84. Rb4+ Kg3 85. Rg6+ Kf2 86. Rf6+! Bf3 87. Rbb6 Qe5+ 88. Rbd6 Kg3 89. >Re6 Qb2+ 90. Rb6! Qd4 91. Rce8 Bh5 92. Rb3+ Kf2 93. Rf8+ Kg2 94. Rg8+ Kf2 95. >Rbb6 Qf4+ 96. Red6 Bf3 97. Re8 Kg3 98. Kc7 Qc1+ 99. Kd7 Qc4 100. Kd8 Qh4+ 101. >Rf6 Qg5 102. Kc7 Qc5+ 103. Kb8 Qd4 104. Rg6+ Bg4 105. Rgd6 Qf4 106. Kc7 Qf7+ >107. Kd8! Qf5 108. Rbc6 Qg5+ 109. Re7 Kh3 110. Rh6+ Bh5 111. Rhf6 Kh2 112. Rd7 >Bf3 113. Ra6! Qg8+ 114. Kc7 Qc4+ 115. Kb6 Qb4+ 116. Ka7 Qc5+ 117. Rab6 Be4 >118. Rg7 Qa3+ 119. Ra6! Qc5+ 120. Kb8 Qe5+ 121. Rad6! Bf5 122. Rh6+ Bh3 123. >Rgh7 Qb5+ 124. Rb6 Qe5+ 125. Kb7 Qd5+ 126. Kc7 Qc5+ 127. Rhc6 Qe5+ 128. Kb7 >Qd5 129. Rb4 Kg3 130. Rg7+ Kf2 131. Kb6! Bf5 132. Rgc7 Bd3 133. Rc8 Qa2 134. >Re8 Kg2 135. Rd6 Qa6+ 136. Kc7! Qa7+ 137. Rb7 Qc5+ 138. Rc6! Qd5 139. Rbb6 Kg3 >140. Rd6 Qc5+ 141. Kd8 Qg5+ 142. Re7 Qg8+ 143. Kc7 Bf5 144. Rbc6 Qh8 145. Rd5 >Qf8 146. Rc3+! Kf4 147. Rd4+ Kg5 148. Rce3! Qc8+ 149. Kb6! Qb8+ 150. Rb7 Qh8 >151. Rg3+ Kh5 152. Rd5 Qb2+ 153. Kc6 Qf6+ 154. Kc5! Qf8+ 155. Kb5 Qe8+ 156. >Kb4! Qe4+ 157. Kc5! Qc2+ 158. Kd6 Kh4 159. Re3 Qc8 160. Rbb3 Qf8+ 161. Kc7 >Qc8+ 162. Kb6 Qb8+ 163. Kc5 Qf8+ 164. Kc4 Qc8+ 165. Kb4 Qf8+ 166. Kc3 Qc8+ >167. Kb2 Qc2+ 168. Ka3! Qc1+ 169. Kb4! Qc8 170. Ree5 Bg4 171. Rbd3 Qb7+ 172. >Rb5 Qe4+ 173. Kc3! Qc6+ 174. Rec5 Qh1 175. Rcd5 Qc1+ 176. Kb4 Qe1+ 177. Rd2 >Bf3 178. Rd6 Kg3 179. Rc5 Qb1+ 180. Ka4 Qa1+ 181. Kb3 Qb1+ 182. Rb2 Qh7 183. >Rd4 Qb7+ 184. Kc3 Qe7 185. Rcc4 Qe1+ 186. Kb3 Bd1+ 187. Ka2! Qa5+ 188. Kb1! >Qf5+ 189. Re4 Qf3 190. Ka2 Qf7 191. Re3+ Bf3 192. Rc2 Qa7+ 193. Ra3! Qf7 194. >Rc1 Qe6 195. Rb3 Qd5 196. R4c3 Qa8+ 197. Ra3 Qd5+ 198. Ka1 Qe5 199. Rf1 Qf6 >200. Rxf3+ Kh4 201. Rxf6 Kh5 202. Ra4 Kg5 203. Rh3 Kxf6 204. Rh6+ Kg7 205. Rf4 >Kg8 206. Rf7 Kxf7 207. Ra6 Ke8 208. Ra7 Kd8 209. Kb2 Kc8 210. Rh7 Kd8 211. Kc3 >Ke8 212. Kd4 Kf8 213. Ke5 Ke8 214. Kf6 Kd8 215. Ke6 Kc8 216. Kd6 Kb8 217. Kc6 >Ka8 218. Kb6 Kb8 219. Rh8# 1-0 > > >KRBNKRB > >Now finally the largest ending of the lot. To make it more manageable, we >broke it into two independent components, one with the bishops having the same >color (sc), the other with the bishops having opposite colors (oc). sc has the >longer winning line of 226 vs. 191 for oc. However, the sc ending is "simpler" >in the sense that it compresses better (75 GB for sc, 92 GB for oc). What >this means exactly is not clear to us yet. > >Below a 226 move winning line. Particularly striking is the retreat by the >white king to h1 on move 28, where he remains for over a hundred moves until >finally reemerging on move 134. It is almost as if the white monarch lets >his minions play cat and mouse with his black counterpart, who gets chased all >around the board in the meantime: > >[D] 8/8/1b6/8/4N2r/1k6/7B/R1K5 w - - 0 1 > >[Event "?"] >[Date "????.??.??"] >[White "RBN"] >[Black "RB"] >[Result "1-0"] >[SetUp "1"] >[FEN "8/8/1b6/8/4N2r/1k6/7B/R1K5 w - - 0 1"] >[PlyCount "499"] > >1. Rb1+! Kc4 2. Nd2+! Kd3 3. Nf3! Rh6 4. Kd1! Ba5 5. Rb3+! Bc3 6. Ne5+! Ke4 7. >Ng4! Rg6 8. Nf2+! Kd4 9. Rb8! Re6 10. Rd8+! Kc4 11. Rc8+! Kd4 12. Ng4 Re1+ 13. >Kc2 Re2+ 14. Kb3! Rb2+ 15. Ka3! Rc2 16. Bg1+ Kd3 17. Rd8+! Ke4 18. Nf2+ Kf5 >19. Rd3! Rc1 20. Rf3+! Ke6 21. Nh3! Be5 22. Kb3! Rb1+ 23. Kc2 Rb2+ 24. Kd1! >Rb1+ 25. Ke2 Rb2+ 26. Kf1 Rb1+ 27. Kg2 Rb2+ 28. Kh1 Rb4 29. Ng5+! Kd5 30. >Rd3+! Kc4 31. Rd1! Rb3 32. Re1! Kd5 33. Rf1 Ra3 34. Rf2! Rb3 35. Rf5 Rb4 36. >Nf3 Ke4 37. Rf7! Rb2 38. Ng5+! Kd5 39. Ra7 Bd6 40. Ra5+! Kc4 41. Ne4! Bb8 42. >Ra8 Bc7 43. Nf6 Kb5 44. Rg8! Kc6 45. Rg6! Kd6 46. Ng4+! Kd5 47. Ne3+! Ke4 48. >Re6+! Kf3 49. Nd5 Ba5 50. Re3+! Kg4 51. Re4+! Kg3 52. Re8 Kf3 53. Rf8+ Kg3 54. >Rf1 Bb4 55. Rf7! Bd6 56. Rd7 Bb8 57. Rd8 Be5 58. Re8! Bd6 59. Re6 Bb8 60. Re3+ >Kg4 61. Ra3 Kf5 62. Ra4! Rd2 63. Ne3+! Ke6 64. Nc4 Rc2 65. Ra6+ Kd7 66. Ne3! >Rc6 67. Ra4! Bc7 68. Ng4! Rc2 69. Re4 Bd6 70. Nf6+! Kc7 71. Re6! Bc5 72. Bh2+! >Kb7 73. Ne4 Bb6 74. Be5 Bc5 75. Rh6 Bb6 76. Nc3 Ba5 77. Nd5 Rc5 78. Rh7+! Ka6 >79. Rd7! Kb5 80. Bg3! Kc6 81. Nf6! Rg5 82. Rd6+! Kb5 83. Rd3! Rg6 84. Ne4 Kc6 >85. Rd1! Re6 86. Ng5 Rg6 87. Bf4 Rf6 88. Nh3 Rg6 89. Rc1+ Kd7 90. Nf2 Ke6 91. >Rb1! Kf5 92. Bh2! Rb6 93. Rc1! Rb5 94. Rc8! Bb6 95. Rf8+! Ke6 96. Nd3! Rb3 97. >Nf4+! Ke7 98. Rh8 Rb2 99. Nd3! Rd2 100. Ne5! Bc5 101. Bf4 Re2 102. Nd3 Be3 >103. Bg3 Rd2 104. Bh4+ Kd6 105. Be1! Rc2 106. Rh7 Ra2 107. Bg3+ Ke6 108. Rh5! >Bd4 109. Be1 Ba7 110. Rg5 Bd4 111. Nf4+ Kf7 112. Rf5+ Ke8 113. Nd3 Ra3 114. >Rf3! Ra2 115. Rf4 Ba7 116. Nc1 Rb2 117. Rf5 Kd8 118. Nd3 Ra2 119. Bg3 Kd7 120. >Rh5 Be3 121. Rd5+ Kc8 122. Rf5 Rd2 123. Rf8+ Kb7 124. Rd8 Ka7 125. Be1 Rc2 >126. Re8 Bb6 127. Nb4 Rc4 128. Re6 Kb7 129. Nd5! Ba5 130. Bg3 Rc5 131. Re7+ >Kc6 132. Nf6 Rf5 133. Re6+ Kc5 134. Kg2 Bc3 135. Ne8 Kd5 136. Nc7+! Kc4 137. >Re7 Rf6 138. Ne6 Bd2 139. Ng7 Bh6 140. Ne8 Rf8 141. Nd6+ Kd5 142. Re4 Bd2 143. >Rg4 Be3 144. Rh4 Kc5 145. Ne4+ Kc6 146. Nc3 Kc5 147. Re4 Bd4 148. Ne2 Bg7 149. >Nf4 Rf7 150. Bf2+ Kc6 151. Rc4+ Kb5 152. Rc5+ Ka4 153. Ne6 Re7 154. Nc7 Rd7 >155. Bg3 Kb4 156. Rc6 Rd3 157. Bd6+ Kb3 158. Ne6 Bd4 159. Bf4 Be3 160. Be5 Ba7 >161. Nf4 Rd2+ 162. Kf3 Bd4 163. Bb8 Bg1 164. Ne2 Rd3+ 165. Kg4 Rd2 166. Re6 >Bc5 167. Bf4 Rd7 168. Kf3 Kc4 169. Re4+ Kd5 170. Nc3+ Kc6 171. Re6+ Kb7 172. >Ne4 Rd3+ 173. Kg4 Rd5 174. Rh6 Ba3 175. Rh3 Ra5 176. Rc3 Bf8 177. Rc7+ Ka6 >178. Be3 Re5 179. Kf3 Bb4 180. Bd4 Re6 181. Rc5 Ba5 182. Rd5 Bb6 183. Ba1 Re8 >184. Rd1 Rd8 185. Nc5+! Kb5 186. Nd7 Bc7 187. Rb1+ Kc6 188. Nf6! Bd6 189. Ke4 >Bc5 190. Rc1 Kb6 191. Be5 Kc6 192. Nh5 Kb5 193. Ng7 Rd2 194. Ne6 Re2+ 195. Kf5 >Bf2 196. Nc7+ Kb4 197. Nd5+ Kb3 198. Rb1+ Kc4 199. Ke6 Rc2 200. Rb4+ Kd3 201. >Ra4 Rd2 202. Kf5 Bc5 203. Bg7 Rc2 204. Bf6 Rd2 205. Nf4+ Ke3 206. Rc4 Bd6 207. >Rc3+ Kf2 208. Ne6 Re2 209. Ng5 Kg2 210. Bd4 Rd2 211. Rc4 Bg3 212. Ne4 Ra2 213. >Rc1 Bb8 214. Kg4 Ba7 215. Nc3 Ra5 216. Rc2+ Kf1 217. Bf6 Bb8 218. Bh4 Ba7 219. >Bg3 Ra1 220. Kf3 Bd4 221. Bh4 Be5 222. Be7 Re1 223. Bc5 Ra1 224. Rf2+ Kg1 225. >Re2+ Bd4 226. Bxd4+ Kf1 227. Rf2+ Kg1 228. Ra2+ Kh1 229. Rxa1+ Kh2 230. Rh1+ >Kxh1 231. Ne4 Kh2 232. Ng3 Kh3 233. Bg1 Kh4 234. Ne4 Kh5 235. Bd4 Kg6 236. Nd6 >Kg5 237. Kg3 Kh5 238. Bf6 Kg6 239. Be7 Kh5 240. Bd8 Kg6 241. Kh4 Kh6 242. Be7 >Kg6 243. Bg5 Kh7 244. Kh5 Kg7 245. Be7 Kh8 246. Kh6 Kg8 247. Kg6 Kh8 248. Nf7+ >Kg8 249. Nh6+ Kh8 250. Bf6# 1-0 > > >The longest line for the opposite color case seems to strongly suggest that the >ending is a general win, since white starts with his pieces rather awkwardly >placed and still wins. The poor steed in particular is marooned in the >h1 corner all of the first 142 moves, before finally entering the fray to >great effect: > > >[D] 8/b2r4/1R4B1/8/8/4k3/8/2K4N w - - 0 1 > > >[Event "?"] >[Date "????.??.??"] >[White "RBN"] >[Black "RB"] >[Result "1-0"] >[SetUp "1"] >[FEN "8/b2r4/1R4B1/8/8/4k3/8/2K4N w - - 0 1"] >[PlyCount "383"] > >1. Rb3+! Kf4 2. Rb4+! Ke5 3. Rb5+! Rd5 4. Rb3! Kf4 5. Rb4+! Rd4 6. Rb7! Ra4 7. >Kc2! Ra2+ 8. Kb3! Rg2 9. Rf7+! Ke3 10. Re7+! Kf4 11. Bc2 Bb8 12. Bd1 Rd2 13. >Rf7+! Ke3 14. Rf3+ Kd4 15. Bc2 Rg2 16. Rd3+! Kc5 17. Rd1 Rh2 18. Bf5! Re2 19. >Bd3! Rh2 20. Rf1 Kd4 21. Bf5! Ke3 22. Bd7! Ke2 23. Bb5+ Ke3 24. Bc6 Ke2 25. >Rc1 Kd3 26. Rc5 Ke3 27. Rc4 Kd3 28. Rg4 Rd2 29. Rg5 Kd4 30. Rd5+ Ke3 31. Rf5! >Rh2 32. Kc3 Rh6 33. Ba8 Ra6 34. Rf3+! Ke2 35. Rf2+! Ke3 36. Bg2 Ra4 37. Rf3+! >Ke2 38. Rf7 Bd6 39. Bd5! Rh4 40. Rf2+! Ke1 41. Ra2 Be5+ 42. Kb3! Rd4 43. Be6! >Rd2 44. Ra5! Bf6 45. Bf5 Bh4 46. Ra4 Rd5 47. Bc2! Rh5 48. Ra2! Kf1 49. Bd3+! >Kg1 50. Be4! Re5 51. Ba8! Rc5 52. Ra4 Be1 53. Re4! Kf1 54. Re3 Bh4 55. Kb4 Rc1 >56. Re6 Rc7 57. Re4! Be1+ 58. Kb5! Rd7 59. Bc6 Rd3 60. Re6 Rc3 61. Bd5 Bh4 62. >Re4 Rh3 63. Kc6 Rh2 64. Re5 Rb2 65. Kc5 Rh2 66. Kb5 Bf2 67. Kb4 Bh4 68. Re3 >Rd2 69. Kc4 Be1 70. Re6 Rc2+ 71. Kd4 Rd2+ 72. Kc5 Bh4 73. Kc4 Re2 74. Rg6 Rd2 >75. Bf3 Rd8 76. Rh6 Be1 77. Re6 Rd2 78. Bb7 Bh4 79. Re4 Be1 80. Ba6 Rd6 81. >Bb5 Rd1 82. Re6 Rb1 83. Bc6 Rb4+ 84. Kc5 Rb1 85. Kd4 Rb4+ 86. Ke3 Rb3+ 87. Kf4 >Rb4+ 88. Kf5 Rd4 89. Re8 Rh4 90. Bf3 Ra4 91. Re3 Ra7 92. Rd3 Ra4 93. Rb3 Ra7 >94. Rb2 Ra5+ 95. Kf4 Ra4+ 96. Be4 Bh4 97. Rc2 Be1 98. Ke5 Rb4 99. Kf5 Rb5+ >100. Kf4 Rb4 101. Ra2 Bh4 102. Ke3 Rb3+ 103. Kd4 Ke1 104. Kd5 Re3 105. Bf5 Kf1 >106. Kd4 Re1 107. Be4 Kg1 108. Bc6 Rc1 109. Rg2+ Kf1 110. Be4 Rd1+ 111. Ke5 >Be1 112. Ra2 Rd2 113. Ra1 Ke2 114. Bf5! Bf2 115. Ra3 Kd1 116. Ra4 Kc1 117. >Rb4! Re2+ 118. Kf4! Bh4 119. Kf3 Re5 120. Be4! Kd2 121. Rc4! Ra5 122. Rc2+! >Kd1 123. Rh2 Ra3+ 124. Kg4! Ra4 125. Kf4 Be1 126. Ke3! Ra5 127. Rg2 Rg5 128. >Bf3+ Kc1 129. Re2 Bh4 130. Kf4 Rc5 131. Re4 Rc2 132. Kg4! Bf2 133. Kh3 Kb2 >134. Bd1 Rd2 135. Be2! Be1 136. Bh5 Bf2 137. Kg2 Bc5+ 138. Be2 Rd5 139. Rg4 >Rf5 140. Bf3 Be7 141. Re4 Rg5+ 142. Bg4 Bd6 143. Nf2 Bc5 144. Nh3 Rd5 145. Re6 >Rd6 146. Re5 Rd2+ 147. Be2 Rc2 148. Re8 Kb3 149. Re4 Kc3 150. Nf4 Kd2 151. Nd5 >Rb2 152. Bc4 Kd1+ 153. Kg3 Rd2 154. Nc3+ Kc2 155. Nb5 Kc1 156. Re1+ Kb2 157. >Kf3 Rc2 158. Bd5 Rh2 159. Be6 Rc2 160. Rh1 Be7 161. Bf7 Rc5 162. Rh2+ Rc2 163. >Rh6 Rc1 164. Ke4 Bc5 165. Rh2+ Rc2 166. Rh8 Rf2 167. Be6 Re2+ 168. Kd5 Be7 >169. Rb8 Kc1 170. Nc3 Rb2 171. Rg8 Rb6 172. Ne4 Kc2 173. Bf7 Kb3 174. Nc5+ Kb4 >175. Rg4+ Ka3 176. Nd3 Kb3 177. Rc4 Rf6 178. Be6 Rh6 179. Rc7 Bf8 180. Ke5+ >Ka4 181. Rb7 Rh5+ 182. Ke4 Rh6 183. Bc4 Rh4+ 184. Kd5 Rh5+ 185. Kd4 Rg5 186. >Ra7+ Ra5 187. Nb2+ Kb4 188. Rb7+ Ka3 189. Rb3+ Ka2 190. Rb5+ Ka3 191. Rxa5+ >Kb4 192. Ra4# 1-0 > > >Here a list of the other endings generated, with the longest winning lengths >shown in parentheses: krrrkqn (131), knnnknn (93), krrkbbb (50), krrknnn (49), >kqqkrrr (40), kbbbknn (36), krrrkrr (34), kbbbkbb (32), knnnkbb (30). > >Some of the remaining endings we are considering are kbbbnkq, kbbnnkq, krrbkrr, >kbnnknn, kbnnkbn, krnnkbb. > >-Marc
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