user27718: 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?

user11144: 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 :-)

user15221: If we had enough computing power, every board state could be assigned a score recursively according to these rules:

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

A draw is 0.5 for both players.

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.

user28101: 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"]


user4418: 
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.

27718: <p>There's this related <a href="https://chess.stackexchange.com/questions/22240/helpful-zugzwang">Helpful Zugzwang?</a> but it's not quite what I am asking. I mean a double (or further) zugzwang.<br>
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?</p>
 11144: <p>Actually, what the poster describes is possible and not at all incompatible with the definition of zugzwang!</p>
<p>To avoid all references to concrete positions, let us define:</p>
<ul>
<li>Full point zugzwang: If Black could pass this move, the position is won for Black. But any move loses for Black.</li>
<li>Half point zugzwang 1: If Black could pass this move, the position is drawn for Black. Any move loses for Black.</li>
<li>Half point zugzwang 2: If Black could pass this move, the position is won for Black. Any move draws for Black.</li>
<li>White zugzwang: Just reverse colors.</li>
</ul>
<p>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:</p>
<pre><code>[FEN &quot;8/8/p7/P2p1k1p/3P3P/5K2/P7/8 w KQkq - 0 1&quot;]
</code></pre>
<p>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 &quot;wrong&quot; 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 :-)</p>
 15221: <p>If we had enough computing power, every board state could be assigned a score recursively according to these rules:</p>
<ol>
<li><p>A win is 1 for the winning player and 0 for the losing player.</p>
</li>
<li><p>A draw is 0.5 for both players.</p>
</li>
<li><p>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.</p>
</li>
</ol>
<p>I'll rewrite your question so the players and moves are labeled:</p>
<blockquote>
<p>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?</p>
</blockquote>
<p>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.</p>
 28101: <p>You may be thinking of what is known as &quot;reciprocal zugzwang&quot; 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.</p>
<pre><code>[FEN &quot;8/8/1p2k3/p3Pp2/P4K2/1P6/8/8 w - - 0 1&quot;]
</code></pre>
<p>Here is a more complex example.</p>
<pre><code>[FEN &quot;6k1/8/8/5PPP/ppp5/8/8/1K6 w - - 0 1&quot;]
</code></pre>
 4418: <blockquote>
<p>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?</p>
</blockquote>
<p>No. What you describe is incompatible with the definition of <a href="https://en.wikipedia.org/wiki/Zugzwang" rel="noreferrer">zugzwang</a>. 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.</p>
