Answers.Body: <p>The positions are not unique if they are in some way symmetrical.</p>
  <p>The five positions where KN wins vs. KR are:</p>
  <ol>
  <li>White to play:  White Kc1 Nd2, Black Ka1 Ra2</li>
  <li>White to play:  White Kc1 Nd4, Black Ka1 Ra2</li>
  <li>White to play:  White Kc1 Nc5, Black Ka1 Ra2</li>
  <li>White to play:  White Kc1 Na5, Black Ka1 Ra2</li>
  <li>Finished game:  White Kc1 Nb3, Black Ka1 Ra2</li>
  </ol>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-10-20T02:30:31.393Z
Answers.Text: Didn't know that. But why are symmetrical positions not unique? The pieces are in different squares, right...?
Answers.UserDisplayName: Yash Jain
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Answers.CreationDate: 2020-10-20T08:49:51.617Z
Answers.Text: @edit_profile : When using databases to "solve" chess, saving as much memory space and processing time is essential. There would be no point in stocking symmetrical pawnless positions and multiply eightfold the space devoted to them.
Answers.UserDisplayName: Evargalo
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-10-21T01:02:51.620Z
Answers.Text: The symmetry doesn't just apply left to right, but also down to up? What's stored in tablebases if pawns were involved on the previous move?
Answers.UserDisplayName: Inertial Ignorance
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-10-21T09:15:48.173Z
Answers.Text: @InertialIgnorance if there are pawns involved a position and its top-down flipped image are not considered to be symetrical
Answers.UserDisplayName: David
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Answers.CreationDate: 2020-10-21T09:30:02.453Z
Answers.Text: @David I know, but if there were a pawn and it was captured, the subsequent position on the next move in the database would involve all the pieces in the above mate shifted to their appropriate positions in the left-hand corner (assuming they weren't in that corner already, and that the left-corner is the only version stored). Although now I realize this isn't that big of a deal, since tablebases aren't actively calculating the number of moves to mate. They already have the numbers stored for each position when the users are employing them.
Answers.UserDisplayName: Inertial Ignorance
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Answers.CreationDate: 2020-10-20T02:03:16.620Z
Answers.LastActivityDate: 2020-10-20T02:03:16.620Z
Answers.UserDisplayName: Andrew Chin
Body: <p>I can come up with 8 positions where the knight would deliver checkmate to a rook and king. However, on endgame tablebases, there are only 5 positions where a King knight wins against King rook. Why?</p>
  
Tags: <endgame><tablebases>
Title: What is the fifth position in the KN vs. KR endgame with the knight mating?
ThreadText: # What is the fifth position in the KN vs. KR endgame with the knight mating?
  
  (Asked by: username_0 on 2020-10-20)
  
  I can come up with 8 positions where the knight would deliver checkmate to a rook and king. However, on endgame tablebases, there are only 5 positions where a King knight wins against King rook. Why?
  
  **Tags:** endgame, tablebases
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-10-20. Score: 2 | Accepted answer
  
  The positions are not unique if they are in some way symmetrical.
  
  The five positions where KN wins vs. KR are:
  
  1. White to play: White Kc1 Nd2, Black Ka1 Ra2
  2. White to play: White Kc1 Nd4, Black Ka1 Ra2
  3. White to play: White Kc1 Nc5, Black Ka1 Ra2
  4. White to play: White Kc1 Na5, Black Ka1 Ra2
  5. Finished game: White Kc1 Nb3, Black Ka1 Ra2
  
  > **Comments:**
  > **username_0**: Didn't know that. But why are symmetrical positions not unique? The pieces are in different squares, right...?  
  > **username_2**: @edit_profile : When using databases to "solve" chess, saving as much memory space and processing time is essential. There would be no point in stocking symmetrical pawnless positions and multiply eightfold the space devoted to them.  
  > **username_3**: The symmetry doesn't just apply left to right, but also down to up? What's stored in tablebases if pawns were involved on the previous move?  
  > **username_4**: @username_3 if there are pawns involved a position and its top-down flipped image are not considered to be symetrical  
  > **username_3**: @username_4 I know, but if there were a pawn and it was captured, the subsequent position on the next move in the database would involve all the pieces in the above mate shifted to their appropriate positions in the left-hand corner (assuming they weren't in that corner already, and that the left-corner is the only version stored). Although now I realize this isn't that big of a deal, since tablebases aren't actively calculating the number of moves to mate. They already have the numbers stored for each position when the users are employing them.  
  
  ---
  
  