Are there any symmetric zugzwang positions?

Question

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 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?

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. — Laska, Oct 11 '17 at 15:28
The trebuchet is symmetrical if you are playing on a 7x8 board! :D — Laska, Oct 11 '17 at 15:29
@Laska I think maybe the wiki article has been updated and expanded since I asked this question. — Dag Oskar Madsen, Oct 11 '17 at 19:49
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. — dbdb, Nov 16 '23 at 01:04

score 23 · Accepted Answer · answered Dec 01 '16 at 18:41

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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.

answered Dec 01 '16 at 18:41

GloriaVictis

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What about: Kd1 f2 Ke1 f1=Q Kxf1 d2 Ke1........ – AAM111 Dec 02 '16 at 00:05
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@OldBunny2800: Your king uses an invisibility cloak at Ke1 so the pawn at f2 can't see it? – user21820 Dec 02 '16 at 01:33
@user21820 ???? – AAM111 Dec 02 '16 at 01:43
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@OldBunny2800: Your suggestion in your comment is invalid because you moved the king into check. – user21820 Dec 02 '16 at 02:14
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@user21820 ohhhh, my bad. – AAM111 Dec 02 '16 at 03:04

Evargalo · Answer 2 · 2021-05-06T08:22:08.290

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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.

edited May 06 '21 at 08:22

answered Oct 12 '17 at 08:37

Evargalo

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That's a cool position, unfortunately it doesn't have mirror symmetry – klm123 May 04 '21 at 10:49
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@klm123 No mirror symetry, but a point symmetry. – Evargalo May 06 '21 at 08:21
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 (:). – dbdb Nov 16 '23 at 01:12
@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. – Evargalo Nov 16 '23 at 14:39

Are there any symmetric zugzwang positions?

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