Talk:Zugzwang

Does black lose in that immortal game if he moves first? Evercat 23:52 May 11, 2003 (UTC)

I'm sorry, I'd forgotten that zugzwang is not the same as reciprocal zugzwang. :-) Evercat 23:53 May 11, 2003 (UTC)

But thanks for reminding of the term "reciprocal zugzwang" - I'd forgotten that :) --Camembert

Please add the pronunciation of "zugzwang". --Juuitchan

second image/example

I think this example should not be there. It's not a zugzwang because Black loses no matter if it is Black or White's turn. Shouldn't it be removed? Alex.tan 06:33, August 30, 2005 (UTC)

No. It is zugzwang, for black only. Black would prefer not to move but has to (once the board reaches the appropriate position). —Simetrical (talk) 02:58, 26 December 2005 (UTC)

The second example was removed on Jan 1, 2006. I think it should be restored because mutual zugzwang is a special case of zugzwang. Most of the times when there is zugzwang, it is not mutual, so non-mutual zugswang is more common (and typical) than mutual zugswang. Bubba73 (talk), 18:18, 1 January 2006 (UTC)

The distinction between zugzwang and mutual zugzwang would be better demonstrated in some other game than chess, because in chess there is no distinction (in chess the term "mutual zugzwang" is a pleonasm). In a zero-sum 2-player game, when it is advantageous for one player to pass, then the same holds for the other side. In the first example demonstrates this principle: "black to move is in zugzwang, and loses" (black draws otherwise). From white's point of view the same diagram can be described as "white to move is in zugzwang, and draws" (white wins otherwise).

That is not correct, because White to move wins in that position. I think it would be a good idea to include examples from other games, but keep what is already in the article. Bubba73 (talk), 23:29, 14 April 2006 (UTC)

I overlooked. But in that case, isn't the example flawed? White to move wins, agreed. So when it is Black to move, he is not better off by passing. He loses either way, so it is no zugzwang after all?

I think it is correct. (I think it was given in one of the references, but I'm not sure.) If Black is to move, he is better off to just sit there, i.e. pass. If he moves he loses. If it is White's move, he triangulates to get to the same position in which Black has to move. So I think it is correct. Bubba73 (talk), 00:11, 16 April 2006 (UTC)

Mathematical reasoning tells it is the same. This is my last attempt before I move on: Think about this for the example position: Why is it better for Black to pass? If Black passes in this position, it becomes white to move. We have established that white to move wins. So in the example, black cannot improve the outcome by passing in this position: it is not a zugzwang.

Mathematically, the mutuality always holds in zugzwang positions for 2-player zero-sum games. There are 4 game scores to consider: 1. White to move ("WTM"), white's result (abbr. WTM-W), 2. White to move, black's result (WTM-B). Similarly, 3. Black to move, white's score (BTM-W) and 4. Black to move, black's score (BTM-B). Say that loss is 0, draw 0.5, and win is 1.0 . WTM-W + WTM-B = 1 and BTM-W + BTM-B = 1. In zugzwang, it is better to pass and obtain the result for the other position. Say for example that white is in zugzwang: If he moves, he gets WTM-W. When he passes, he obtains BTW-W. White prefers BTW-W over WTM-W: BTM-W > WTM-W. But then we also have 1 - BTM-B > 1 - WTM-B, from which follows BTM-B < WTM-B. Ergo: Black prefers not to be on move: Black is in zugzwang as well. The term "mutual zugzwang" is a pleonasm in chess. — Preceding unsigned comment added by 125.225.100.33 (talk • contribs)

Mutual/recripocal zugzwang isn't really a pleonasm in chess, the way most authors use the terms. In chess "zugzwang" normally means that one side is at a disadvantage if he has to move. Mutual or recropical zugzwang means that both sides are in zugzwang. It is used differently than in game theory. Bubba73 (talk), 01:36, 14 July 2007 (UTC)

It seems there is a logical fallacy in that argument: How people use a term doesn't preclude it from being a pleonasm. People just don't realize the two situations are always linked. — Preceding unsigned comment added by 125.225.100.33 (talk • contribs)

Excuse me, I made a big mistake. When I was talking about triangulation, I was looking at the first position, and the header was for the second position. Sorry, my error. Let me try to summarize. In the first position, if it is black's move, he loses. If it is white's move, white can triangulate to get to the same position with black to move, so white wins. That position is a win for white either way, but if it is white's move, he must triangulate to put black in zugzwang. This position is a win for white, regardless of who is to move. (If black could pass once, that wouldn't help him, but if he could pass whenever he wanted to, it would.) In the second position, if it is white's move it is a draw. If it is black's move, black loses. (If whoever is to move could pass one time, and there were no other passes allowed, the pass would change the outcome.) I hope this clarifies it and please discuss it more if you need to. Bubba73 (talk), 15:13, 16 April 2006 (UTC)

PS - from what you are saying, in 0-sum games, zugzwang may be defined more precisely than it is in chess, i.e. it is what is called mutual or reciprocal zugzwang in chess. Bubba73 (talk), 15:40, 16 April 2006 (UTC)

Chess is a 0-sum game. One's good is precisely the other's bad. A dictionary definition of "zugzwang" is: "a situation in which the obligation to make a move in one's turn is a serious, often decisive, disadvantage" (Oxford American Dictionaries). Try to find a position where this definition holds when White is to move, but doesn't hold when Black is to move. It is logically not possible to have such a position in 0-sum games, chess included.

Take the first example on the current main page (labeled "Flear 2004, page 11", 8/8/3k4/1p1p1p2/1P1K1P2/2P5/8/8 b - -). As the text explains, Black to move and Black loses, but allowing to pass once draws. So it is zugzwang. The same position with White to move is zugzwang as well: White to move draws, but allowing to pass once turns it back into win for White. So the obligation for White to move also gives him a disadvantage (a mere draw instead of a win). — Preceding unsigned comment added by 125.225.100.33 (talk • contribs)

1. As Elkies and Berlekamp et. al. point out (and the article states), game theory does not apply directly to chess.

2. As stated in the article, the term is used differently in chess than in game theory.

Ad 1 & 2: The relevant theory is sometimes called Combinatorial Game Theory, which certainly applies to chess. Sorry for the ambiguity, but the term "Combinatorial" is usually omitted when it is clear the context is chess and not economics or gambling. Under (Combinatorial) Game Theory, Zugzwang for 0-sum 2-player games is mutual.

3. You said "The same position with White to move is zugzwang as well: White to move draws" This is wrong. If white is to move in the first position, he is not obligated to make a move that weakens his position. (Kd3 and Ke3 do not hurt his position. Only c4 hurts his position, and he is not obligated to do that.) If it is white's move, white draws anyway. White is not in zugzwang, according to the way the term is used in chess. Bubba73 (talk), 18:20, 14 July 2007 (UTC)

Ad 3: Kd3, Ke3 and c4 all draw the game for White. None is better or worse than the other. The outcome is the same. However, that is not the point. The point is that if White would arrive in this position and is to move, he is forced to draw, no matter which move. If he could pass once, he would win. Therefore the obligation to move costs him half a point. So it is a zugzwang for White. (by applying the same definition we used for the original Black to move position: the obligation to move costs Black half a point if he were to move).

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

According to main article, Black to move is in zugzwang, and loses

This is a very poor example. White to move wins by 1. Ke5. If Black tries to maintain opposition by 1...Ke7, then 2. c6 forces promotion because the K has moved out of the square of the B6 pawn. If 1...Kc6, then 2 Kd4 Kd7 (if ... Kb5 then 3. Kd5-d6-c7 winning the Pb7) 3. Kd5, when the same position is reached with black to move.

It is black to move, not white. But I replaced it with an example from Flear. Bubba73 (talk), 04:16, 22 May 2006 (UTC)

I added two things to the article a week ago to make it clearer, a new position and the breakdown of the three types of positions in chess. What you are saying is that there are no positions of type #2. But there are positions of that type, and triangulation (chess) gives another good example. Bubba73 (talk), 13:37, 22 July 2007 (UTC)

Cut the complication

There's a classic zugzwang position, which I'm surprised you don't have in. It's very simple to understand. White king d6, white pawn e7, black king e8, white to move. Anything white does results in a draw, from a winning position. White will only get a half point instead of the full point he would have gotten if he had played so as not to get himself into that position. Instead of confusing the user with "black loses in 96 moves" put this example in. It's only three pieces and very elementary. 69.17.67.11 14:24, 18 July 2006 (UTC)

I think it used to be in there. Do you have a reference saying that particular position is Zugzwang? (I know it is but we need a source saying so.) Bubba73 (talk), 15:11, 18 July 2006 (UTC)

This is probably wikipedia heresy, but in my opinion a source shouldn't be necessary for something like that. The position is extremely simple, and anyone who knows anything at all about chess, applying the definitions given in the article, can see that it's mutual zugzwang. Krakatoa 16:48, 22 July 2006 (UTC)

Müller and Lamprecht citation

There is a cite in the article to "Müller and Lamprecht 2001:22." It's not clear to me what this source is, since it's not listed in the references at the end. Krakatoa 16:48, 22 July 2006 (UTC)

An omission, probably on my part. Fixed now. Bubba73 (talk), 23:53, 10 August 2006 (UTC)

Bourzutschky's trebuchet game

Am I going blind, or does black have two bishops on dark squares in that example? It would have to be a pretty convoluted game to get black to underpromote to a bishop instead of just getting a queen. Molimo 23:23, 10 August 2006 (UTC)

It is not from a game, it is a position discovered by computer. I've added a link to a page about it. Bubba73 (talk), 23:53, 10 August 2006 (UTC)

The link to the "page about it" no longer exists. It used to be http://216.25.93.108/forum/viewtopic.php?t=2860, but the relevant thread has disappeared. -Anon — Preceding unsigned comment added by 82.36.227.45 (talk • contribs)

I think Tim Krabbe in his Open Chess Diary discusses Bourzutschky's trebuchet positions. Bourzutschky discovered some more normal-looking trebuchet positions with knights on the board, and no same-colored bishops. Personally, I think one of those would be better to cite. The same-colored bishop position is ugly IMO; better to have a position that one could conceivably reach in a normal game. Krakatoa 01:35, 29 September 2006 (UTC)

I thought it was notable because it was the first one discovered that didn't involve knights or pawns. That's why I put it in there. But we are open to suggestions. Bubba73 (talk), 02:43, 29 September 2006 (UTC)

I know you noted that it didn't involve knights or pawns. I guess that is notable if one is a trebuchet scholar or something, but as a non-trebuchet scholar the "no knights or pawns!" thing doesn't excite me and I'd rather see something that looks like a more normal position. Your mileage may vary. Krakatoa 03:11, 29 September 2006 (UTC)

You're not the first to complain about that position, and I'm not married to it. Can you supply a better example? Or it we might just omit that position. Bubba73 (talk), 04:13, 5 October 2006 (UTC)

OK, I'm going to try substituting a position with four knights. Somehow that seems (slightly) more natural than one with two bishops on the same color. Not sure why. One would think there would be a full-point mutual zugzwang position without promoted pieces besides the simple one-pawn apiece trebuchet position. Krakatoa 05:19, 5 October 2006 (UTC)

Zugzwang the play?

I moved the following text here, as it seems out of place in the main article. Perhaps a move to University_of_Wollongong would be in order?

"Zugzwang" is also the name of a highly acclaimed theatrical performance by the talented University of Wollongong (Australia) performance students. The theatrical experience was revived several times and most recently is being transferred to Vietnam as part of the "Experimental Theatre Festival" in Hanoi. --85.139.186.98 15:13, 5 November 2006 (UTC)

Trebuchet

As I understand it a 'trebuchet' is a type of zugzwang - or perhaps vice versa. In any case the 'trebuchet' isn't mentioned or explained in the current version of the article - yet probably should be. Snori 10:35, 30 January 2007 (UTC)

It is discussed inder "recripocal zugzwang", in its own subsection: zugzwang#Trébuchet. Bubba73 (talk), 16:09, 30 January 2007 (UTC)