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Are there any surveys on mutual zugzwang positions and the longest checkmates (split into categories of DTM, DTC, and DTZ) in the endgame KRPP vs. KRP (King+Rook+2 Pawns vs. King+Rook+Pawn)? In particular, I would be interested in the full-point-mutual-zugzwangs in this endgame.
Unfortunately, the 7 men tablebases are not available for free online, and I do not know how I can download the required files (including all needed additional files due to the possibility of (under)promotions).
I have been able to find information for everything asked of. However, I have not found any large surveys; just mere snippets.
This page on http://ruszchessstudies.blogspot.com/ provides several examples of half-point mutual zugzwangs along with some general information. Here is one of them.
[FEN "3K4/P7/P7/8/8/8/R5rp/3k4 w - - 0 1"]
As for full point mutual zugzwangs, one such position was given by @mbourzut in this a Rybka forum. This forum contains numerous drawing and winning positions; a small survey.
[FEN "8/8/2P5/2r1p3/RK1kP3/8/8/8 w - - 0 1"]
The record for the longest DTC sequence is 79 moves, according to page 24 of this arves.org PDF. It contains further information KRPP-KRP endgames.
[FEN "8/r7/2K3p1/k7/8/8/P4P2/1R6 w - - 0 1"]
1. Rb7 Ra6+ 2. Kc5 Ka4 3. Rd7 Ra5+ 4. Kd4 Rf5 5. Ke3 Kb4 6. Rd6 Re5+ 7. Kd4 Rf5 8. Rb6+ Ka3 9. Ra6+ Kb4 10. Ke3 Re5+ 11. Kf3 Rg5 12. Re6 Ka3 13. Re2 Kb4 14. Kf4 Rg2 15. Ke3 Rg1 16. Rc2 Re1+ 17. Kf4 Rg1 18. f3 g5+ 19. Ke3 Re1+ 20. Re2 Rc1 21. Rg2 Rc5 22. Rb2+ Ka3 23. Rd2 Rf5 24. Rc2 Kb4 25. Rc7 Kb5 26. Rc8 Re5+ 27. Kf2 Kb6 28. a4 Rd5 29. Rb8+ Kc6 30. Kg3 Rf5 31. Re8 Kd7 32. Re4 Rd5 33. Kg4 Kd6 34. Re8 Rc5 35. Kh5 Rf5 36. Re3 Ra5 37. Ra3 Kd7 38. Kg6 Ke7 39. Ra2 Ke8 40. Kf6 Kf8 41. Ra3 Ke8 42. Re3+ Kf8 43. Re4 Kg8 44. Ke7 Kg7 45. Kd6 Kf6 46. Kc6 Ra8 47. Kb5 Rb8+ 48. Kc4 Rc8+ 49. Kb4 Rb8+ 50. Ka3 Rh8 51. Re3 Rh3 52. Rb3 Ke7 53. a5 Kd8 54. Ka4 Rh4+ 55. Rb4 Kc8 56. a6 Rh6 57. Ka5 Rh7 58. Rb6 Rg7 59. Rb7 Rg8 60. Rb5 Rg7 61. Rb6 Rf7 62. Kb4 Rf4+ 63. Kb5 Rf5+ 64. Kc4 Rf4+ 65. Kd5 Kc7 66. a7 Ra4 67. Rf6 Kb7 68. Rf7+ Ka8 69. Ke5 Ra2 70. Rg7 Rg2 71. Ke4 Rg3 72. Ke3 Rg2 73. Kd3 Rf2 74. Ke4 Re2+ 75. Kf5 Re3 76. Kg4 Re4+ 77. Kg3 Rg4+ 78. Kf2 Rc4 79. Rxg5
The record for the longest DTM sequence is 218 moves. It can be found on page 105 of this PDF, created by Guy Haworth, about tablebase length records.
[FEN "8/k1P5/8/8/1R5P/7p/r7/1K6 b - - 0 1"]
1... h2 2. Kxa2 h1=Q 3. c8=R Qd5+ 4. Kb1 Qa5 5. Rcc4 Qe5 6. Ra4+ Kb6 7. Rc2 Kb5 8. Rac4 Qg7 9. Rc5+ Kb4 10. R2c4+ Kb3 11. Rc3+ Kb4 12. R5c4+ Kb5 13. Rc7 Qg1+ 14. Ka2 Qg2+ 15. Ka3 Qg1 16. Rb7+ Ka6 17. Rb2 Qa1+ 18. Kb3 Qe1 19. Rc6+ Ka7 20. Rc4 Qe6 21. Rbc2 Ka6 22. Ka4 Qd7+ 23. Rc6+ Ka7 24. Kb3 Qd5+ 25. Kb4 Qh1 26. Rc7+ Ka8 27. R7c4 Qh3 28. Ka4 Ka7 29. Rb4 Qd7+ 30. Ka3 Qd3+ 31. Kb2 Qd5 32. Rbc4 Qh1 33. Ka2 Qd5 34. Ka3 Qd6+ 35. Kb2 Qf6+ 36. Kb1 Qb6+ 37. Ka1 Qg1+ 38. Ka2 Qg8 39. Kb2 Qd8 40. Ra4+ Kb6 41. Rb4+ Ka5 42. Rbc4 Qh8+ 43. Kb3 Qg8 44. Ka3 Qf8+ 45. Rc5+ Ka6 46. h5 Ka7 47. Kb4 Kb6 48. Kb3 Qf3+ 49. Ka2 Qf7+ 50. Kb2 Qf6+ 51. R2c3 Qf2+ 52. Ka3 Qf8 53. Ka4 Qf1 54. Rc6+ Kb7 55. h6 Qa1+ 56. Kb4 Qb2+ 57. Rb3 Qd2+ 58. Kc5+ Ka7 59. Ra3+ Kb7 60. Rb6+ Kc8 61. Ra8+ Kc7 62. Ra7+ Kc8 63. Rc6+ Kb8 64. Ra4 Kb7 65. Rb4+ Ka7 66. Rc4 Qe3+ 67. Kd5 Qd2+ 68. Ke5 Qe3+ 69. Kf5 Qd3+ 70. Ke6 Ka8 71. Rc8+ Ka7 72. R8c7+ Ka6 73. h7 Qh3+ 74. Kf6 Qh6+ 75. Kf5 Qh3+ 76. Kf4 Kb5 77. Rc3 Qh1 78. Rb3+ Ka6 79. Rd7 Qh4+ 80. Ke5 Qg5+ 81. Kd4 Qf6+ 82. Kd3 Qg6+ 83. Kc3 Qg3+ 84. Kc2 Qg2+ 85. Kb1 Qf1+ 86. Ka2 Qe2+ 87. Ka3 Qe5 88. Rbd3 Qa1+ 89. Kb3 Qb1+ 90. Kc4 Qc1+ 91. Kd5 Qg5+ 92. Ke4 Qg4+ 93. Ke3 Qg5+ 94. Kf2 Qh4+ 95. Ke2 Qe4+ 96. Kd1 Qg4+ 97. Kc1 Qc4+ 98. Kd2 Qf4+ 99. Re3 Qf2+ 100. Kd3 Qf5+ 101. Kc3 Qc5+ 102. Kd2 Qa5+ 103. Rc3 Qa2+ 104. Ke3 Qe6+ 105. Kf2 Qb6+ 106. Re3 Qf6+ 107. Rf3 Qb6+ 108. Kg2 Qg6+ 109. Kf1 Qb1+ 110. Ke2 Qb5+ 111. Ke3 Qe5+ 112. Kd2 Kb5 113. Rdf7 Qd5+ 114. Ke2 Qe5+ 115. Kf1 Qh2 116. R3f4 Ka5 117. Ke1 Kb5 118. Kd1 Qh5+ 119. Kd2 Qd5+ 120. Ke2 Qe6+ 121. Kf2 Qh3 122. R4f5+ Ka4 123. Ra7+ Kb4 124. Rb7+ Kc4 125. Rc7+ Kb4 126. Rf4+ Kb5 127. Rfc4 Qh2+ 128. Ke3 Qh1 129. Kd2 Kb6 130. Kc2 Qa1 131. R4c6+ Kb5 132. Rc3 Qa2+ 133. Kc1 Qa1+ 134. Kd2 Qb2+ 135. Ke3 Qh2 136. Kd3 Kb6 137. R3c6+ Ka5 138. Rc5+ Kb4 139. Rc4+ Ka5 140. Kc3 Kb6 141. Kb3 Qh1 142. R4c6+ Kb5 143. Rc2 Qf3+ 144. Kb2 Qh1 145. Rf2 Qh4 146. Rf3 Qh2+ 147. Kb3 Qh1 148. Rf5+ Kb6 149. Rcf7 Kc6 150. R7f6+ Kd7 151. Kb2 Qh2+ 152. Kc3 Ke7 153. Rc6 Qg3+ 154. Kc2 Qg2+ 155. Kb3 Qg3+ 156. Rc3 Qb8+ 157. Kc4 Qc7+ 158. Kb4 Qb6+ 159. Rb5 Qd4+ 160. Kb3 Qd1+ 161. Ka3 Qa1+ 162. Kb4 Qb2+ 163. Kc4 Qh2 164. Kb3 Kd6 165. Rb7 Qh1 166. Rbc7 Ke5 167. R3c5+ Kd4 168. Kb2 Qh6 169. Rb5 Qf8 170. Rbb7 Ke4 171. Rc4+ Ke5 172. Rc3 Qf2+ 173. Kb3 Qh2 174. Re7+ Kd6 175. Rec7 Qh1 176. R3c5 Ke6 177. Kb4 Kf6 178. Rd7 Ke6 179. Rcd5 Qe1+ 180. Kb5 Qb1+ 181. Ka6 Qa1+ 182. Kb6 Qb2+ 183. Rb5 Qh8 184. Rb7 Kd6 185. Rf5 Ke6 186. Rh5 Qd4+ 187. Ka6 Qa4+ 188. Ra5 Qe8 189. Re7+ Qxe7 190. h8=Q Qd6+ 191. Kb5 Qd5+ 192. Kb4 Qd6+ 193. Rc5 Qb6+ 194. Rb5 Qd6+ 195. Kb3 Qd1+ 196. Ka3 Qd6+ 197. Rb4 Qd3+ 198. Ka4 Qc2+ 199. Rb3 Qc4+ 200. Ka5 Qc5+ 201. Ka6 Qc4+ 202. Rb5 Kd7 203. Qh5 Kd6 204. Qf5 Kc7 205. Qc5+ Qxc5 206. Rxc5+ Kd7 207. Kb6 Kd6 208. Rh5 Ke6 209. Kc6 Kf6 210. Kd6 Kg6 211. Rd5 Kf6 212. Kd7 Kf7 213. Rd6 Kf8 214. Ke6 Kg7 215. Ke7 Kg8 216. Kf6 Kh8 217. Kg6 Kg8 218. Rd8#
The DTZ length records can be found in the Syzygy endgame tablebases. Here are the record positions without the moves.
[Title "Longest Winning DTZ, Without The 50-Move Rule-136 ply"]
[FEN "6k1/8/3pP1R1/3P4/8/1K6/8/3r4 b - - 0 1"]
[Title "Longest Winning DTZ, With The 50-Move Rule-100 ply"]
[FEN "2r5/8/8/2pP3K/2P5/3R2k1/8/8 b - - 0 1"]
[Title "Longest Losing DTZ, Without The 50-Move Rule-124 ply"]
[FEN "1k6/4K3/5R2/8/5P2/1p6/3P4/4r3 w - - 0 1"]
[Title "Longest Losing DTZ, With The 50-Move Rule-63"]
[FEN "8/8/8/K7/P5R1/1k6/P1p5/r7 b - - 0 1"]
