10 Oct 20161. e3 b6 is now solved as a win for White. As usual, the bulk of time was wasted on false leads. Probably already a year ago I could have solved the remaining line 1. e3 b6 2. a4 e6 3. Ra3 Bxa3 4. Nxa3 Qh4 but did not search 5. a5 bxa5 6. Qh5! into queen races far enough. Once I did this, it was actually quite easy (only taking a few hours). The history of my attempts is here The biggest subtree in this line is with 4... b5, which was solved some time ago. Here is a solution file for 1. e3 b6: e3b6.proof.bz2 (740MB) d19df1d18518c7a216b44a1e878550cd (warning, this takes around 4 or 5GB of RAM to load in WinningGUI) Tree data (from ./verify): Tree size is 491933802 [3753mb] trans 43338390 terminal 28307121 internal 420288291 forced 206484729 5+6 50122697+56144321 tb4 14896555 nomoves 13410566 nopieces 5998652 patt 7411914 FICS 7411914 MAXREV 118 [this will be reduced in the future, not sure where it's from?] OK Some people have asked me: "Why 2. a4, is there a threat or...?" One answer: White would like to play 2. Ba6 Nxa6 3. b4 Nxb4 4. Q-move, but when Black has Nxa2 (instead of Nxc2) this is not so potent. ======================================================================== Breaking into parts (probably necessary for Windows, and also useful with faster counting of nodes in subtrees): A. This file proves that 1. e3 b6 2. a4 wins against everything but e6: e3b6.no2e6.proof.bz2 (214MB) dfc00a6cfe7453d32f3f8e7fb4411b15 B. This (very big) file handles 1. e3 b6 2. a4 e6 3. Ra3 Bxa3 4. Nxa3 b5 BIG.4b5.proof.bz2 (483MB) 1dc400748ee5b793299c774316dc9821 Here it is split into four parts (again to fit in 32-bit Windows): B1. Everything but 5. Bxb5 Qg5 6. Bxd7 Qxg2 7. Bxe6 Bxe6 8. h3 Bxh3 9. Rxh3 Qxf2 10. Kxf2 h5 11. Rxh5 Rxh5 12. Qxh5 Ne7 13. Qxf7 Kxf7 14. d4 Ng8 and 8... Bxh3 9. Rxh3 Qxh3 10. Nxh3 Nd7 11. c4 Nf8 12. c5 Rd8 (includes 8... Qxf2 and 8... Qxh3 by transposition) WORKING.4b5.win.bz2 (258MB) fb76d0d36d9a41a10b10ec7c296bd6a0 B1a. Reduction in Qxf2 line: everything but 14. d4 Ng8 15. e4 Nd7 15. Nh6 Nxh6 17. e5 Nxe5 18. dxe5 Rd8 MORE_REDUCED.win.bz2 (55MB) 96f2b29b15f2153ad27a4047e2153e46 B1a1. Solves the 18. dxe5 Rd8 line: (could combine with previous) SOLVED.18Rd8.proof.bz2 (122MB) 1d517c862455ee3477f91397db5f78b9 B1b. Solves the Qxh3 line: 12. c5 Rd8 13. Qg4 Rxd2 14. Qxg7 REDUCTION.8Qxh3.win.bz2 (54MB) 3117a5467be29fd734983c1ed881006d C. This file solves other 4th moves, including Qh4: DONE.mv4.proof.bz2 (42MB) 9b84c3db0c5ee1995726495128578ff5 ======================================================================== The next goal will likely be to reduce the size of some parts of the proof (all 20 responses to e3). In particular, the MAXREV indicator (reversible move count) from the verify programme is often shown as maximimizing at 95, which is unnecessarily large I am sure. Searching alternate lines may also prove to be productive (as Klaas Steenhuis has shown in other lines). Some effort may also be made (by me or others) to make the solution browseable on the web. ======================================================================== For aficionados, here is a complete proof that 1. e3 wins all in one file. 1e3.wins.proof.bz2 (1.3GB) 781bfb6168eb009ba3eb2106c6688cca (warning, this takes around 8 or 10GB of RAM to load in WinningGUI) And its ./verify data: Tree size is 929489715 [7091mb] trans 66187848 terminal 58752229 internal 804549638 forced 403561005 tb4 23448460 5+6 79840511+90352974 nomoves 35303769 nopieces 18117361 patt 17186408 FICS 17186408 MAXREV 118 OK Note that tree size is internal plus terminal plus trans, while terminal is itself tb4 plus nomoves, and nomoves is nopieces plus patt (and all are FICS). The 5+6 are for informational purposes, as back in 2012 I decided to make the baseline be 4 piece TBs. Ben Nye built 5 piece TBs a long time ago, and Ronald de Man has more recently made 6 piece, both under FICS, I think. Noam Elkies inquired what the longest path in the proof is (with caveats about trees versus graphs vis-a-vis transpositions). Just to display that the solver need not use much intelligence, it is this monstrosity of shuffling until a reversible-move rule kicks in. 1. e3 b6 2. a4 e6 3. Ra3 Bxa3 4. Nxa3 b5 5. Bxb5 Qe7 6. Bxd7 Qxa3 7. bxa3 Kxd7 8. e4 Kc6 9. a5 Ne7 10. Qf3 Ba6 11. Qxf7 Bb5 12. Qxg7 Be2 13. Nxe2 Rg8 14. Qxh7 Rxg2 15. Qxe7 Rxf2 16. Kxf2 a6 17. Qxc7 Kxc7 18. Nc3 Kb6 19. axb6 a5 20. e5 Na6 21. Nd5 exd5 22. Rg1 Rg8 23. Rxg8 Nb8 24. Rxb8 a4 25. d3 d4 26. c4 dxc3 27. Be3 c2 28. Bd4 c1=K 29. Bb2 Kxb2 30. Rc8 Kxa3 31. b7 Ka2 32. Kf3 Ka1 33. h4 a3 34. h5 Ka2 35. h6 Ka1 36. b8=B Ka2 37. Rc4 Ka1 38. Ke2 Ka2 39. h7 Ka1 40. Rc6 Ka2 41. h8=Q Ka1 42. Rc4 Ka2 43. Ba7 Ka1 44. Rc6 Ka2 45. Qh4 Ka1 46. Rc8 Ka2 47. Bb6 Ka1 48. e6 Ka2 49. e7 Ka1 50. Rc6 Ka2 51. e8=Q Ka1 52. Rc7 Ka2 53. Bg1 Ka1 54. Rc5 Ka2 55. Bh2 Ka1 56. Rc6 Ka2 57. Bc7 Ka1 58. Rc5 Ka2 59. Qg6 Ka1 60. Rc4 Ka2 61. Qf5 Ka1 62. Rc6 Ka2 63. Ke3 Ka1 64. Rc4 Ka2 65. Bb8 Ka1 66. Rc6 Ka2 67. Ke2 Ka1 68. Rc8 Ka2 69. Ba7 Ka1 70. Rc7 Ka2 71. Rc6 Ka1 72. Bb8 Ka2 73. Ke3 Ka1 74. Bc7 Ka2 75. Ke2 Ka1 76. Rc4 Ka2 77. Qd5 Ka1 78. Ke3 Ka2 79. Bb8 Ka1 80. Qf5 Ka2 81. Qd8 Ka1 82. Rc6 Ka2 83. Bg3 Ka1 84. Rc4 Ka2 85. Ke2 Ka1 86. Rc6 Ka2 87. Bh2 Ka1 88. Rc4 Ka2 89. Qe8 Ka1 90. Rc7 Ka2 91. Bg1 Ka1 92. Rc4 Ka2 93. Bb6 Ka1 94. Rc7 Ka2 95. Bf2 Ka1 96. Qg4 Ka2 97. d4 Ka1 98. Qgd7 Ka2 99. Rc5 Ka1 100. Rc6 Ka2 101. Qe5 Ka1 102. Rc8 Ka2 103. Bh4 Ka1 104. Rc6 Ka2 105. Qg4 Ka1 106. Rc7 Ka2 107. Qg2 Ka1 108. Rc8 Ka2 109. Qgg7 Ka1 110. Qd7 Ka2 111. Kd3 Ka1 112. Qg4 Ka2 113. Be1 Ka1 114. Rc6 Ka2 115. Ba5 Ka1 116. Rc8 Ka2 117. Qf3 Ka1 118. Rc6 Ka2 119. Rc7 Ka1 120. Rc8 Ka2 121. Rc6 Ka1 122. Bd8 Ka2 123. Rc4 Ka1 124. Rc7 Ka2 125. Qe8 Ka1 126. Rc5 Ka2 127. Bh4 Ka1 128. Rc7 Ka2 129. Qf5 Ka1 130. Rc6 Ka2 131. Rc4 Ka1 132. Rc7 Ka2 133. Bg3 Ka1 134. Rc6 Ka2 135. Rc4 Ka1 136. Rc7 Ka2 137. Bh2 Ka1 138. Rc6 Ka2 139. Rc4 Ka1 140. Rc7 Ka2 141. Qf3 Ka1 142. Rc5 Ka2 143. Rc4 Ka1 144. d5 Ka2 145. d6 Ka1 146. Rc5 Ka2 147. Qg4 Ka1 148. Rc7 Ka2 149. Bg1 Ka1 150. Rc5 Ka2 151. Bf2 Ka1 152. Rc7 Ka2 153. Bb6 Ka1 154. Bg1 Ka2 155. Bf2 Ka1 156. Rh7 Ka2 157. Bb6 Ka1 158. Rc7 Ka2 159. Rf7 Ka1 160. Rh7 Ka2 161. Qg5 Ka1 162. d7 Ka2 163. d8=Q Ka1 164. Kc4 a2 165. Bg1 Kb1 166. Qc1 Kxc1 167. Qd1 Kxd1 168. Qe2 Kxe2 169. Be3 Kxe3 *