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There's this related Helpful Zugzwang? but it's not quite what I am asking. I mean a double (or further) zugzwang.
So a player puts another player in zugzwang, and the other player makes a move. However, after that move, the first player doesn't have good moves either and it's a reverse zugzwang, or a self-zugzwang. Is it possible?

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So a player puts another player in zugzwang, and the other player makes a move. However, after that move, the first player doesn't have good moves either and it's a reverse zugzwang, or a self-zugzwang. Is it possible?

No. What you describe is incompatible with the definition of zugzwang. By definition if you place your opponent in zugzwang then any move they can make is a bad one which gives you the advantage. If they have a good move which puts you in zugzwang then, by definition, your previous move was not a good move which put your opponent in zugzwang.

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  • I suppose you could have a case where the player put in zugzwang has to make a move which makes their position worse than if they didn't have to move, but is still in a good position (just not as good)
    – Cort Ammon
    Jun 28 at 2:03
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You may be thinking of what is known as "reciprocal zugzwang" which are positions where either side would stand worse for having the move. They are very common in endgames, and feature prominently in the fundamental strategies of King and pawn play. Here is a simple example.

[FEN "8/8/1p2k3/p3Pp2/P4K2/1P6/8/8 w - - 0 1"]

Here is a more complex example.

[FEN "6k1/8/8/5PPP/ppp5/8/8/1K6 w - - 0 1"]
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  • I get your first example, but can you give a brief overview of how having the first move is bad in the second example? It's not obvious, at least not to me :)
    – John D
    Jun 27 at 0:55
  • 3
    The second position is actually pretty tricky, but basically the key is that the side not to move is in a perfect defensive position to meet any pawn thrust. For instance, if White is to play, 1.f6 is met by 1...Kf7!, or 1.g6 is met by 1...Kg7! Thus the side to move is essentially forced to compromise their king position or push a pawn that will then be immediately blocked. Jun 27 at 4:08
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If we had enough computing power, every board state could be assigned a score recursively according to these rules:

  1. A win is 1 for the winning player and 0 for the losing player.

  2. A draw is 0.5 for both players.

  3. The score for the player whose move it is is the maximum of their scores among all their possible moves, and the other player's score is the minimum among those scores.

I'll rewrite your question so the players and moves are labeled:

So in move N, White puts Black in zugzwang, and Black makes a move. However, after that move (that is, at move N+1), White doesn't have good moves either and it's a reverse zugzwang, or a self-zugzwang. Is it possible?

If, at move N.5 (that is, the half-move after move N), Black has a move that puts White in a losing position, then Black's score for that move is 1. And since Black's score in a position where it's their turn to move is the maximum of their score among all their moves, and one of their moves has a score of 1, it follows that their score in that position is 1. But a (full) zugzwang, by definition, is a position where the player whose turn it is has a score of 0. So Black was not in zugzwang.

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  • 1
    This is useful and interesting +1 Jun 26 at 16:40
  • 1
    I have always fancied the idea that theoretically every position from the start has a score like you mention.
    – Michael
    Jun 27 at 0:10
  • Note that such an exact definition also avoids sloppy use: Kf4 Pe5 - Ke6 Pf5 (Rewans position without the queenside pawns) easily gets called a reciprocal, but of course the game value is draw, even if the moving side loses a pawn. Jun 27 at 7:51
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Actually, what the poster describes is possible and not at all incompatible with the definition of zugzwang!

To avoid all references to concrete positions, let us define:

  • Full point zugzwang: If Black could pass this move, the position is won for Black. But any move loses for Black.
  • Half point zugzwang 1: If Black could pass this move, the position is drawn for Black. Any move loses for Black.
  • Half point zugzwang 2: If Black could pass this move, the position is won for Black. Any move draws for Black.
  • White zugzwang: Just reverse colors.

OK, now we just assume that White has one tempo move that puts Black into HPZ2, but lacks a second tempo move to turn HPZ2 to HPZ1. Thus the White tempo move avoids a loss, Black is in HPZ2, makes a move, White is in HPZ2 too since pass moves lack either, and game will be drawn. In that position, White also could have a move that actually wins, and thus putting Black in Zugzwang is a bad move. Observe:

[FEN "8/8/p7/P2p1k1p/3P3P/5K2/P7/8 w KQkq - 0 1"]

1.a4 HPZ1 for Black (passing wins), 1...Ke6! 2.Kf4 Kf6 HPZ1 for White (passing wins), drawn. Incidentally 1.a3! HPZ2, also puts Black in zugzwang and wins, as White has another tempo move. So in this case it was merely a "wrong" choice of zugzwang. It is easy to think of a position where White wins with PxP, but I'm too lazy to come up with one since I now have my first OTB game in years and must go :-)

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  • 3
    I don't understand your claim that 1. a4 pass is a win for Black; it looks like draw to me.
    – user21820
    Jun 26 at 9:03
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    I don't think this example is valid. Either side can easily draw no matter how many times the other side can pass; it's not very difficult to keep control over f4/f5.
    – D M
    Jun 26 at 11:52
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    The example was done in a haste and IS invalid. I deleted the pawns that block the king's ways. Sorry! Jun 26 at 14:55

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