What is the longest proven forced win (including 50 & 75 move rules)? What is the longest (currently discovered) number of moves for a forced mate position where players will use both the 50-move draw rule and the 3-fold repetition rule if it will help them avoid losing?
By this, I mean an a game where the losing player attempts to make the game last as long as possible (or if possible, draw) and the winning player attempts to checkmate as fast as possible. Both players playing perfectly.
For those interested this question covers
&quot;What is the longest forced win with 3 to 6 pieces (ignoring 50 &amp; 75 move rules)?&quot;
Otto Blathy is famous for his long mate problems. There are different records depending on whether you allow an illegal starting position, or promoted pieces, or minor duals in the solution, so your answer might be anywhere between 257 and 292 moves.
This answer on Puzzling.SE shows a construction in 271 moves that is not Blathy, but by Nenad Petrovic.
[Title &quot;Nenad Petrovic, Zagreb 1969, Mate In 271&quot;]
[FEN &quot;8/Bk3p1p/1P3p2/KP2n2p/1P1p4/1Pp2p2/B1P5/7B w - - 0 1&quot;]

1. Bb1 h4 2. Ka4 Ka8 3. Ka3 Kb7 4. Ka2 Ka8 5. Ka1 Kb7 6. Ba2 Ka8 7. Kb1 Kb7 8. Kc1 Ka8 9. Kd1 Kb710. Ke1 Ka8 11. Bb1 Kb7 12. Kf1 Ka8 13. Kf2 Kb7 14. Ke1 Ka8 15. Kd1 Kb7 16. Kc1 Ka8 17. Ba2 Kb7 18. Kb1 Ka8 19. Ka1 Kb7 20. Bb1 Ka8 21. Ka2 Kb7 22. Ka3 Ka8 23. Ka4 Kb7 24. Ka5 f5 25. Ka4 Ka8 26. Ka3 Kb7 27. Ka2 Ka8 28. Ka1 Kb7 29. Ba2 Ka8 30. Kb1 Kb7 31. Kc1 Ka8 32. Kd1 Kb7 33. Ke1 Ka8 34. Bb1 Kb7 35. Kf1 Ka8 36. Kf2 Kb7 37. Ke1 Ka8 38. Kd1 Kb7 39. Kc1 Ka8 40. Ba2 Kb7 41. Kb1 Ka8 42. Ka1 Kb7 43. Bb1 Ka8 44. Ka2 Kb7 45. Ka3 Ka8 46. Ka4 Kb7 47. Ka5 f4 48. Ka4 Ka8 49. Ka3 Kb7 50. Ka2 Ka8 51. Ka1 Kb7 52. Ba2 Ka8 53. Kb1 Kb7 54. Kc1 Ka8 55. Kd1 Kb7 56. Bb1 Ka8 57. Ke1 Kb7 58. Kf1 Ka8 59. Kf2 Kb7 60. Ke1 Ka8 61. Kd1 Kb7 62. Kc1 Ka8 63. Ba2 Kb7 64. Kb1 Ka8 65. Ka1 Kb7 66. Bb1 Ka8 67. Ka2 Kb7 68. Ka3 Ka8 69. Ka4 Kb7 70. Ka5 f6 71. Ka4 Ka8 72. Ka3 Kb7 73. Ka2 Ka8 74. Ka1 Kb7 75. Ba2 Ka8 76. Kb1 Kb7 77. Kc1 Ka8 78. Kd1 Kb7 79. Ke1 Ka8 80. Bb1 Kb7 81. Kf1 Ka8 82. Kf2 Kb7 83. Ke1 Ka8 84. Kd1 Kb7 85. Kc1 Ka8 86. Ba2 Kb7 87. Kb1 Ka8 88. Ka1 Kb7 89. Bb1 Ka8 90. Ka2 Kb7 91. Ka3 Ka8 92. Ka4 Kb7 93. Ka5 f5 94. Ka4 Ka8 95. Ka3 Kb7 96. Ka2 Ka8 97. Ka1 Kb7 98. Ba2 Ka8 99. Kb1 Kb7 100. Kc1 Ka8 101. Kd1 Kb7 102. Ke1 Ka8 103. Bb1 Kb7 104. Kf1 Ka8 105. Kf2 Kb7 106. Ke1 Ka8 107. Kd1 Kb7 108. Kc1 Ka8 109. Ba2 Kb7 110. Kb1 Ka8 111. Ka1 Kb7 112. Bb1 Ka8 113. Ka2 Kb7 114. Ka3 Ka8 115. Ka4 Kb7. 116. Ka5 h3 117. Ka4 Ka8 118. Ka3 Kb7 119. Ka2 Ka8 120. Ka1 Kb7 121. Ba2 Ka8 122. Kb1 Kb7 123. Kc1 Ka8 124. Kd1 Kb7 125. Ke1 Ka8 126. Bb1 Kb7 127. Kf1 Ka8 128. Kf2 Kb7 129. Ke1 Ka8 130. Kd1 Kb7 131. Kc1 Ka8 132. Ba2 Kb7 133. Kb1 Ka8 134. Ka1 Kb7 135. Bb1 Ka8 136. Ka2 Kb7 137. Ka3 Ka8 138. Ka4 Kb7 139. Ka5 h2 140. Ka4 Ka8 141. Ka3 Kb7 142. Ka2 Ka8 143. Ka1 Kb7 144. Ba2 Ka8 145. Kb1 Kb7 146. Kc1 Ka8 147. Kd1 Kb7 148. Ke1 Ka8 149. Bb1 Kb7 150. Kf1 Ka8 151. Kf2 Kb7 152. Ke1 Ka8 153. Kd1 Kb7 154. Kc1 Ka8 155. Ba2 Kb7 156. Kb1 Ka8 157. Ka1 Kb7 158. Bb1 Ka8 159. Ka2 Kb7 160. Ka3 Ka8 161. Ka4 Kb7 162. Ka5 h6 163. Ka4 Ka8 164. Ka3 Kb7 165. Ka2 Ka8 166. Ka1 Kb7 167. Ba2 Ka8 168. Kb1 Kb7 169. Kc1 Ka8 170. Kd1 Kb7 171. Ke1 Ka8 172. Bb1 Kb7 173. Kf1 Ka8 174. Kf2 Kb7 175. Ke1 Ka8 176. Kd1 Kb7 177. Kc1 Ka8 178. Ba2 Kb7 179. Kb1 Ka8 180. Ka1 Kb7 181. Bb1 Ka8 182. Ka2 Kb7 183. Ka3 Ka8 184. Ka4 Kb7 185. Ka5 h5 186. Ka4 Ka8 187. Ka3 Kb7 188. Ka2 Ka8 189. Ka1 Kb7 190. Ba2 Ka8 191. Kb1 Kb7 192. Kc1 Ka8 193. Kd1 Kb7 194. Ke1 Ka8 195. Bb1 Kb7 196. Kf1 Ka8 197. Kf2 Kb7 198. Ke1 Ka8 199. Kd1 Kb7 200. Kc1 Ka8 201. Ba2 Kb7 202. Kb1 Ka8 203. Ka1 Kb7 204. Bb1 Ka8 205. Ka2 Kb7 206. Ka3 Ka8 207. Ka4 Kb7 208. Ka5 h4 209. Ka4 Ka8 210. Ka3 Kb7 211. Ka2 Ka8 212. Ka1 Kb7 213. Ba2 Ka8 214. Kb1 Kb7 215. Kc1 Ka8 216. Kd1 Kb7 217. Ke1 Ka8 218. Bb1 Kb7 219. Kf1 Ka8 220. Kf2 Kb7 221. Ke1 Ka8 222. Kd1 Kb7 223. Kc1 Ka8 224. Ba2 Kb7 225. Kb1 Ka8 226. Ka1 Kb7 227. Bb1 Ka8 228. Ka2 Kb7 229. Ka3 Ka8 230. Ka4 Kb7 231. Ka5 h3 232. Ka4 Ka8 233. Ka3 Kb7 234. Ka2 Ka8 235. Ka1 Kb7 236. Ba2 Ka8 237. Kb1 Kb7 238. Kc1 Ka8 239. Kd1 Kb7 240. Ke1 Ka8 241. Bb1 Kb7 242. Kf1 Ka8 243. Kf2 Kb7 244. Ke1 Ka8 245. Kd1 Kb7 246. Kc1 Ka8 247. Ba2 Kb7 248. Kb1 Ka8 249. Ka1 Kb7 250. Bb1 Ka8 251. Ka2 Kb7 252. Ka3 Ka8 253. Ka4 Kb7 254. Ka5 Kc8 255. Ka6 Kd8 256. b7 Nd7 257. Bxf3 h1=Q 258. Bxh1 d3 259. cxd3 f3 260. Bxf3 Ke7 261. b8=Q Nxb8+ 262. Bxb8 c2 263. Bxc2 Ke6 264. b6 Kf6 265. b7 Ke6 266. d4 h2 267. Bxh2 f4 268. b8=Q Kf7 269. Bxf4  Kg7 270. Bh5 Kf6 271. Qe5#

(legal position, with promoted piece, with minor duals in the solution)
Those problems involve regular pawn moves, so the fifty-moves rule doesn't change their validity. On the other hand, all long (500+ moves) tablebase mates (as the first diagram in the answer linked above) show series of more than 50 moves without capture nor pawn moves.
Finally a beautiful problem exploiting the 50-moves rule was composed by Noam Elkies, who comes sometimes on Chess.SE. I will refrain from giving the solution here for people who want to search (but I have already given away the main indication and lazy people can just follow the link).
     [Title &quot;Noam Elkies, 1991 - White to play and draw&quot;]
 [FEN &quot;8/1p6/1p6/kPp2P1K/2P5/N1Pp4/q2P4/1N6 w - - 0 1&quot;]