Answers.Body: <p>In all the chess books I've read, &quot;trébuchet&quot; is actually one particular case of a full-point double-zugzwang: the most minimalist one you can get, with only one pawn for each player:</p>
  <pre><code>8/8/8/3pK3/2kP4/8/8/8 w - - 0 1
  </code></pre>
  <p>This pattern can be translated to 30 different positions, with the black pawn on any square in the b7-g7-g3-b3 rectangle. Whoever is on move will lose.</p>
  
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Answers.Text: That's a cool position, unfortunately it doesn't have mirror symmetry
Answers.UserDisplayName: klm123
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Answers.Text: @klm123 No mirror symetry, but a point symmetry.
Answers.UserDisplayName: Evargalo
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Answers.Text: A geometrical evoking operation on the board might benefit from also mentioning the center of the reflection or rotation it is pointing at.  Thanks for this last dialog.  Mirror symmetry might be meaning a specific mirror slicing through the horizontal center line of the board, is usual chess parlance.  I was not sure.  line symmetry, point symmetry, and rotation around the center of the board.  Always a referential object. Did not mean to interrupt though (:).
Answers.UserDisplayName: dbdb
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Answers.Text: @dbdb The center of rotation is the middle of the edge shared by the squares d4 and d5. We can forgive you for interrupting a conversation that was stalled for 30 months.
Answers.UserDisplayName: Evargalo
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Answers.UserDisplayName: Evargalo
Answers.Body: <p>You can easily construct many such positions. For instance:</p>
  
  <pre><code>4k3/8/3P1P/8/8/3p1p2/8/4K3 w - - 0 1
  </code></pre>
  
  <p>First to move loses - either by moving a king and allowing the opponent to promote or by losing one (and subsequently next) pawn.</p>
  
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Answers.CreationDate: 2016-12-02T00:05:38.427Z
Answers.Text: What about: Kd1 f2 Ke1 f1=Q Kxf1 d2 Ke1........
Answers.UserDisplayName: AAM111
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Answers.Text: @OldBunny2800: Your king uses an invisibility cloak at Ke1 so the pawn at f2 can't see it?
Answers.UserDisplayName: user21820
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Answers.Text: @user21820 ????
Answers.UserDisplayName: AAM111
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Answers.Text: @OldBunny2800: Your suggestion in your comment is invalid because you moved the king into check.
Answers.UserDisplayName: user21820
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Answers.Text: @user21820 ohhhh, my bad.
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Body: <p>Although very unlikely, the starting position <em>could</em> be a forced win for Black. This would mean it is a position of mutual zugzwang, in the strong sense that whoever moves first loses. <a href="https://en.wikipedia.org/wiki/Zugzwang#Tr.C3.A9buchet" rel="noreferrer">Wikipedia</a> refers to one such position as <em>trébuchet</em>. Such positions are rare, and it would be a big surprise if the starting position was one of them.</p>
  <p>The starting position has another property in that it is symmetric. White and Black have exactly the same possible moves (when written in descriptive notation). Are there any symmetric positions that are known to be a mutual zugzwang?</p>
  
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Comments.CreationDate: 2017-10-11T15:28:35.120Z
Comments.Text: Great question, thank you! Nit: I think the trebuchet is a specific example of full point Zugzwang (KPvKP) rather than a synonym for full point Zugzwang.
Comments.UserDisplayName: Laska
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Comments.Text: The trebuchet is symmetrical if you are playing on a 7x8 board! :D
Comments.UserDisplayName: Laska
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Comments.CreationDate: 2017-10-11T19:49:59.113Z
Comments.Text: @Laska I think maybe the wiki article has been updated and expanded since I asked this question.
Comments.UserDisplayName: Dag Oskar Madsen
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Comments.CreationDate: 2023-11-16T01:04:34.027Z
Comments.Text: Should we always keep the definition scope to its original example. I also found it noticeable that "trebuchet" was propose as being generalizable.  I think while not calling everything trébuchet, it is appropriate to mention it, as particular case already containing the elements of the abstraction.  As chess is still being explored, and chess theory would evolve, there is some question of naming and increasing the number of names for essentially logically the same mathematical (or not yet) abstractions. This is a question.
Comments.UserDisplayName: dbdb
Tags: <zugzwang>
Title: Are there any symmetric zugzwang positions?
ThreadText: # Are there any symmetric zugzwang positions?
  
  (Asked by: username_0 on 2016-12-01)
  
  Although very unlikely, the starting position *could* be a forced win for Black. This would mean it is a position of mutual zugzwang, in the strong sense that whoever moves first loses. [Wikipedia](https://en.wikipedia.org/wiki/Zugzwang#Tr.C3.A9buchet) refers to one such position as *trébuchet*. Such positions are rare, and it would be a big surprise if the starting position was one of them.
  
  The starting position has another property in that it is symmetric. White and Black have exactly the same possible moves (when written in descriptive notation). Are there any symmetric positions that are known to be a mutual zugzwang?
  
  **Tags:** zugzwang
  
  > **Comments:**
  > **username_1**: Great question, thank you! Nit: I think the trebuchet is a specific example of full point Zugzwang (KPvKP) rather than a synonym for full point Zugzwang.  
  > **username_1**: The trebuchet is symmetrical if you are playing on a 7x8 board! :D  
  > **username_0**: @username_1 I think maybe the wiki article has been updated and expanded since I asked this question.  
  > **username_2**: Should we always keep the definition scope to its original example. I also found it noticeable that "trebuchet" was propose as being generalizable.  I think while not calling everything trébuchet, it is appropriate to mention it, as particular case already containing the elements of the abstraction.  As chess is still being explored, and chess theory would evolve, there is some question of naming and increasing the number of names for essentially logically the same mathematical (or not yet) abstractions. This is a question.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_5 on 2016-12-01. Score: 24 | Accepted answer
  
  You can easily construct many such positions. For instance:
  4k3/8/3P1P/8/8/3p1p2/8/4K3 w - - 0 1
  
  First to move loses - either by moving a king and allowing the opponent to promote or by losing one (and subsequently next) pawn.
  
  > **Comments:**
  > **username_6**: What about: Kd1 f2 Ke1 f1=Q Kxf1 d2 Ke1........  
  > **username_7**: @OldBunny2800: Your king uses an invisibility cloak at Ke1 so the pawn at f2 can't see it?  
  > **username_6**: @username_7 ????  
  > **username_7**: @OldBunny2800: Your suggestion in your comment is invalid because you moved the king into check.  
  > **username_6**: @username_7 ohhhh, my bad.  
  
  ---
  
  ### Answer by username_3 on 2017-10-12. Score: 7
  
  In all the chess books I've read, "trébuchet" is actually one particular case of a full-point double-zugzwang: the most minimalist one you can get, with only one pawn for each player:
  8/8/8/3pK3/2kP4/8/8/8 w - - 0 1
  
  This pattern can be translated to 30 different positions, with the black pawn on any square in the b7-g7-g3-b3 rectangle. Whoever is on move will lose.
  
  > **Comments:**
  > **username_4**: That's a cool position, unfortunately it doesn't have mirror symmetry  
  > **username_3**: @username_4 No mirror symetry, but a point symmetry.  
  > **username_2**: A geometrical evoking operation on the board might benefit from also mentioning the center of the reflection or rotation it is pointing at.  Thanks for this last dialog.  Mirror symmetry might be meaning a specific mirror slicing through the horizontal center line of the board, is usual chess parlance.  I was not sure.  line symmetry, point symmetry, and rotation around the center of the board.  Always a referential object. Did not mean to interrupt though (:).  
  > **username_3**: @username_2 The center of rotation is the middle of the edge shared by the squares d4 and d5. We can forgive you for interrupting a conversation that was stalled for 30 months.  
  
  ---
  
  