Answers.Body: <p>As <strong>Glorfindel</strong> notes,
  the Lomonosov tables are great but might not have the answer you want.
  In RPP/RP, according to the list in
  <a href="http://centaur.reading.ac.uk/34268/2/chessendrecann.pdf" rel="nofollow noreferrer">this
  article</a> by Guy Haworth, we find that the maximal distance to mate
  is 200+ moves, from the following position -- which happens not to have
  the White pawns connected, but worse for your purpose,
  it looks like most of the play is post-conversion:</p>
  
  <pre><code>[Title "Black to move; White eventually wins"]
  [Fen "8/k1P5/8/8/1R5P/7p/r7/1K6 b - - 0 1"]
  [StartFlipped "0"]
  
  1...h2 2.Kxa2 h1=Q 3.c8=R!
  </code></pre>
  
  <p>after Kxa2 we're in 6-man territory, and the k4it.de site says
  "Win in 216" starting Qd5+ 4 Kb1 Qa5(d6) -- that's right, not Qd1(h1)+,
  which lets White win in only 200, nor Qd3+, which hastens the end
  by another move (199).</p>
  
  <p>Possibly Guy Haworth has enough access to 7-man tables
  to get the answer to your query.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-01-17T02:57:38.470Z
Answers.LastActivityDate: 2017-01-17T15:50:09.923Z
Answers.LastEditDate: 2017-01-17T15:50:09.923Z
Answers.UserDisplayName: Noam D. Elkies
Answers.Body: <p>Just this week the 7-piece Syzygy table for this endgame was published and is now available online, together with some basic statistics about this endgame. It <a href="https://syzygy-tables.info/?fen=6k1/8/3pP1R1/3P4/8/1K6/8/3r4_b_-_-_0_1" rel="nofollow noreferrer">gives</a> a maximum DTZ of 136 (in a position that happens to match your criteria).</p>
  
  <p>So in any case 136 is a lower bound for the maximum DTC.</p>
  
  <p>To get from DTZ to DTC for paths leading through this position we just need to check: (1) It is indeed a conversion (by capturing the black pawn), instead of just a pawn push. (2) The phase was not entered by a non-capturing pawn push.</p>
  
  <p>For (1) see the DTZ-mainline:</p>
  
  <pre><code>[FEN "6k1/8/3pP1R1/3P4/8/1K6/8/3r4 b - - 0 1"]
  
  1... Kf8 2. Rf6+ Ke8 3. Kc4 Rc1+ 4. Kd3 Rd1+ 5. Ke4
  Re1+ 6. Kf4 Rf1+ 7. Kg5 Rg1+ 8. Kh6 Rh1+ 9. Kg7
  Rg1+ 10. Rg6 Rd1 11. Rg5 Ke7 12. Rf5 Rg1+ 13. Kh6
  Rd1 14. Kg5 Rg1+ 15. Kf4 Rf1+ 16. Ke4 Re1+ 17. Kd3
  Rd1+ 18. Ke3 Ke8 19. Ke4 Re1+ 20. Kf4 Rg1 21. Rh5
  Rd1 22. Ke4 Re1+ 23. Kf5 Rf1+ 24. Kg5 Rg1+ 25. Kf6
  Rf1+ 26. Rf5 Rd1 27. Rf2 Rd4 28. Ra2 Rf4+ 29. Kg5
  Rd4 30. Ra1 Rd2 31. Kf5 Rd4 32. Ra7 Rd1 33. Ra4
  Ke7 34. Ke4 Re1+ 35. Kd3 Rd1+ 36. Kc4 Rc1+ 37. Kb4
  Rb1+ 38. Kc3 Rc1+ 39. Kd2 Rc5 40. Rd4 Ra5 41. Ke3
  Ra3+ 42. Rd3 Ra1 43. Rb3 Re1+ 44. Kd2 Re5 45. Rb5
  Rg5 46. Kc3 Kf6 47. Kb4 Rg1 48. Ka5 Ra1+ 49. Kb6
  Ke7 50. Ra5 Rb1+ 51. Kc6 Rc1+ 52. Kb5 Rb1+ 53. Kc4
  Rc1+ 54. Kd3 Rd1+ 55. Kc3 Rc1+ 56. Kd2 Rc8 57. Kd3
  Rc7 58. Ra1 Rb7 59. Rh1 Rb5 60. Rh7+ Kf6 61. Rf7+
  Kg6 62. Kc4 Rc5+ 63. Kd4 Ra5 64. Rc7 Ra1 65. Rc6
  Rd1+ 66. Kc4 Rc1+ 67. Kb3 Rb1+ 68. Kc2 Ra1 69. Rxd6
  </code></pre>
  
  <p>For (2) it helps that white is giving check, so the last move was:</p>
  
  <ul>
  <li>A capture on g6. But that would have started the phase.</li>
  <li>Rf6-g6+. But e7 would have been better.</li>
  <li>Rh6-g6+. But Rf6 would have been better.</li>
  </ul>
  
  <p>Admittedly it might still be possible that there are entirely different positions, stringed together by pawn pushes, that achieve a higher DTC (total DTZ).</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2018-08-12T01:02:37.163Z
Answers.LastActivityDate: 2018-08-12T01:36:36.537Z
Answers.LastEditDate: 2018-08-12T01:36:36.537Z
Answers.UserDisplayName: Niklas
Answers.Body: <p>Download the <a href="https://play.google.com/store/apps/details?id=com.convekta.android.lomonosovtb" rel="nofollow noreferrer">Lomonosov endgame Android application</a>, it is what you are looking for. This probably solves your issue if you toy around for a while.</p>
  
  <p><a href="https://i.sstatic.net/ZOXjEl.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ZOXjEl.jpg" alt="enter image description here"></a></p>
  
  <p>In the Play Store, it looks like this.</p>
  
  <p><a href="https://i.sstatic.net/bGKmtl.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bGKmtl.jpg" alt="enter image description here"></a></p>
  
  <p>Hope this helps!</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-12-17T14:37:19.367Z
Answers.Text: While this is a valuable tool, it won't help you find the longest Distance-To-Conversion for a certain endgame.
Answers.UserDisplayName: Glorfindel
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2016-05-07T17:03:57.287Z
Answers.LastActivityDate: 2016-12-17T14:36:31.397Z
Answers.LastEditDate: 2016-12-17T14:36:31.397Z
Answers.UserDisplayName: InfiniteFlash
Body: <p>I am trying to learn single rook endgames with two pawns against one, with added stipulation that the two pawns of the attacking side are on neighboring files with the pawn of the defending side also on one of those files. It could for instance be <code>e</code>+<code>f</code> pawns vs <code>f</code> pawn or <code>g</code>+<code>h</code> pawns vs <code>g</code> pawn.</p>
  
  <p>What is the most complicated such position that is still won for the attacking side? To make the question precise, I am asking for the position with the maximum <a href="https://en.wikipedia.org/wiki/Endgame_tablebase#Metrics:_Depth_to_conversion_and_depth_to_mate" rel="noreferrer">depth to conversion</a>.</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2016-12-17T20:43:55.083Z
Comments.Text: How does this information about maximum depth to  conversion help you for studying rook endgames? There are tablebases which will show you perfect play for both sides and will give you the information you ask for, but IMO they are only of limited use for studying as they won't tell you typical strategies/patterns.... etc
Comments.UserDisplayName: user1583209
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-01-16T16:08:57.657Z
Comments.Text: @user1583209 Some positions will be obviously winning and some will be obviously drawn. What I am interested in are positions that winning, but close to the border between a win and a draw. A slightly artificial way to find such positions is to ask for maximum depth to conversion.
Comments.UserDisplayName: Dag Oskar Madsen
Tags: <endgame><tablebases><rook-endgame>
Title: KRPP vs KRP - maximum depth to conversion?
ThreadText: # KRPP vs KRP - maximum depth to conversion?
  
  (Asked by: username_0 on 2016-05-03)
  
  I am trying to learn single rook endgames with two pawns against one, with added stipulation that the two pawns of the attacking side are on neighboring files with the pawn of the defending side also on one of those files. It could for instance be `e`+`f` pawns vs `f` pawn or `g`+`h` pawns vs `g` pawn.
  
  What is the most complicated such position that is still won for the attacking side? To make the question precise, I am asking for the position with the maximum [depth to conversion](https://en.wikipedia.org/wiki/Endgame_tablebase#Metrics:_Depth_to_conversion_and_depth_to_mate).
  
  **Tags:** endgame, tablebases, rook-endgame
  
  > **Comments:**
  > **username_1**: How does this information about maximum depth to  conversion help you for studying rook endgames? There are tablebases which will show you perfect play for both sides and will give you the information you ask for, but IMO they are only of limited use for studying as they won't tell you typical strategies/patterns.... etc  
  > **username_0**: @username_1 Some positions will be obviously winning and some will be obviously drawn. What I am interested in are positions that winning, but close to the border between a win and a draw. A slightly artificial way to find such positions is to ask for maximum depth to conversion.  
  
  ---
  
  ## 3 answers
  
  ### Answer by username_2 on 2017-01-17. Score: 4
  
  As **username_5** notes,
  the Lomonosov tables are great but might not have the answer you want.
  In RPP/RP, according to the list in
  [this
  article](http://centaur.reading.ac.uk/34268/2/chessendrecann.pdf) by Guy Haworth, we find that the maximal distance to mate
  is 200+ moves, from the following position -- which happens not to have
  the White pawns connected, but worse for your purpose,
  it looks like most of the play is post-conversion:
  
  ```
  [Title "Black to move; White eventually wins"]
  [Fen "8/k1P5/8/8/1R5P/7p/r7/1K6 b - - 0 1"]
  [StartFlipped "0"]
  
  1...h2 2.Kxa2 h1=Q 3.c8=R!
  
  ```
  
  after Kxa2 we're in 6-man territory, and the k4it.de site says
  "Win in 216" starting Qd5+ 4 Kb1 Qa5(d6) -- that's right, not Qd1(h1)+,
  which lets White win in only 200, nor Qd3+, which hastens the end
  by another move (199).
  
  Possibly Guy Haworth has enough access to 7-man tables
  to get the answer to your query.
  
  
  ---
  
  ### Answer by username_3 on 2018-08-12. Score: 2
  
  Just this week the 7-piece Syzygy table for this endgame was published and is now available online, together with some basic statistics about this endgame. It [gives](https://syzygy-tables.info/?fen=6k1/8/3pP1R1/3P4/8/1K6/8/3r4_b_-_-_0_1) a maximum DTZ of 136 (in a position that happens to match your criteria).
  
  So in any case 136 is a lower bound for the maximum DTC.
  
  To get from DTZ to DTC for paths leading through this position we just need to check: (1) It is indeed a conversion (by capturing the black pawn), instead of just a pawn push. (2) The phase was not entered by a non-capturing pawn push.
  
  For (1) see the DTZ-mainline:
  
  ```
  [FEN "6k1/8/3pP1R1/3P4/8/1K6/8/3r4 b - - 0 1"]
  
  1... Kf8 2. Rf6+ Ke8 3. Kc4 Rc1+ 4. Kd3 Rd1+ 5. Ke4
  Re1+ 6. Kf4 Rf1+ 7. Kg5 Rg1+ 8. Kh6 Rh1+ 9. Kg7
  Rg1+ 10. Rg6 Rd1 11. Rg5 Ke7 12. Rf5 Rg1+ 13. Kh6
  Rd1 14. Kg5 Rg1+ 15. Kf4 Rf1+ 16. Ke4 Re1+ 17. Kd3
  Rd1+ 18. Ke3 Ke8 19. Ke4 Re1+ 20. Kf4 Rg1 21. Rh5
  Rd1 22. Ke4 Re1+ 23. Kf5 Rf1+ 24. Kg5 Rg1+ 25. Kf6
  Rf1+ 26. Rf5 Rd1 27. Rf2 Rd4 28. Ra2 Rf4+ 29. Kg5
  Rd4 30. Ra1 Rd2 31. Kf5 Rd4 32. Ra7 Rd1 33. Ra4
  Ke7 34. Ke4 Re1+ 35. Kd3 Rd1+ 36. Kc4 Rc1+ 37. Kb4
  Rb1+ 38. Kc3 Rc1+ 39. Kd2 Rc5 40. Rd4 Ra5 41. Ke3
  Ra3+ 42. Rd3 Ra1 43. Rb3 Re1+ 44. Kd2 Re5 45. Rb5
  Rg5 46. Kc3 Kf6 47. Kb4 Rg1 48. Ka5 Ra1+ 49. Kb6
  Ke7 50. Ra5 Rb1+ 51. Kc6 Rc1+ 52. Kb5 Rb1+ 53. Kc4
  Rc1+ 54. Kd3 Rd1+ 55. Kc3 Rc1+ 56. Kd2 Rc8 57. Kd3
  Rc7 58. Ra1 Rb7 59. Rh1 Rb5 60. Rh7+ Kf6 61. Rf7+
  Kg6 62. Kc4 Rc5+ 63. Kd4 Ra5 64. Rc7 Ra1 65. Rc6
  Rd1+ 66. Kc4 Rc1+ 67. Kb3 Rb1+ 68. Kc2 Ra1 69. Rxd6
  
  ```
  
  For (2) it helps that white is giving check, so the last move was:
  
  * A capture on g6. But that would have started the phase.
  * Rf6-g6+. But e7 would have been better.
  * Rh6-g6+. But Rf6 would have been better.
  
  Admittedly it might still be possible that there are entirely different positions, stringed together by pawn pushes, that achieve a higher DTC (total DTZ).
  
  
  ---
  
  ### Answer by username_4 on 2016-05-07. Score: 1
  
  Download the [Lomonosov endgame Android application](https://play.google.com/store/apps/details?id=com.convekta.android.lomonosovtb), it is what you are looking for. This probably solves your issue if you toy around for a while.
  
  [![enter image description here](https://i.sstatic.net/ZOXjEl.jpg)](https://i.sstatic.net/ZOXjEl.jpg)
  
  In the Play Store, it looks like this.
  
  [![enter image description here](https://i.sstatic.net/bGKmtl.jpg)](https://i.sstatic.net/bGKmtl.jpg)
  
  Hope this helps!
  
  > **Comments:**
  > **username_5**: While this is a valuable tool, it won't help you find the longest Distance-To-Conversion for a certain endgame.  
  
  ---
  
  