Talk:Two knights endgame

Two knights versus one knight

I have deleted the section "Two knights versus one knight". This was introduced by an anonymous user on 21Aug2012 and a citation needed flag was correctly added by Bubba73. I can't find the original discussion, but the citation flag is in line with Bubba73's comments here. The last change (by another anonymous user) deleted the citation needed flag on the grounds that the mate given is obvious, but the point of the citation needed flag is that a citation is needed. How obvious the material is is not relevant; it should have a reliable and verifiable source. Since no citation has been added in the intervening three years (in any case a cited example immediately follows) it seememed to me to be time to delete it.

Third reversion by Jasper Deng.

Reason given for reversion was, "Do not restore disputed content when you know well it is disputed." In fact that is exactly what this user just did, so I have undone his reversion.

To be factual I did not restore anything. I am re-adding my changes in stages to determine which are disputed.

User also did not conserve the improvements to the "Checkmate in problems section, nor the inserted "citation needed" flags.

I also note the user has not deigned to answer the questions I posed after his first two reversions. Martin Rattigan (talk) 22:48, 1 October 2017 (UTC)

@Martin Rattigan: You were the one who inserted the original content that is under dispute above, therefore, you should not be reverting: if a dispute occurs, then the status quo, i.e. what was there before, is restored. Stop edit warring, and also, as others have said above, please be more concise and not wikilawyer.--Jasper Deng (talk) 23:15, 1 October 2017 (UTC)

@Jasper Deng:: Well the D bit of BRD is discussion which you appear to have broken off.Martin Rattigan (talk) 00:41, 2 October 2017 (UTC)

Did you really intend to insert two cn in this edit? With one of them being the first thing in the article? That does not look very helpful. By the way, a section heading at an article talk page should not name another editor, and should not end with a period. This page is for calm discussion of actionable proposals to improve the article. Johnuniq (talk) 02:54, 2 October 2017 (UTC)

@Johnuniq: Yes the cn are deliberate. I think the meaning of the endgame has been revised by Wikipedia. Did you notice the last but one section heading? You don't appear to have commented on it. I shall leave out the full stops in future.Martin Rattigan (talk) 03:11, 2 October 2017 (UTC)Martin Rattigan (talk) 03:47, 2 October 2017 (UTC)

@Johnuniq: You say, "This page is for calm discussion of actionable proposals to improve the article". It would seem not many of its users agree with you.Martin Rattigan (talk) 03:47, 2 October 2017 (UTC)

Since 28 September 2017 Martin Rattigan has edited this talk page 149 times, Bubba73 23 times, and two others have edited it 3 times each, and after this I will have made 2 comments. Please try to engage more with the points raised in the helpful outline at 07:23, 1 October 2017 above by Quale. Dismissing points 1 and 2 as "lecturing" indicates a WP:BATTLEGROUND approach, and such an approach will eventually lead to a topic ban at WP:ANI. Putting citation needed at the very top of the article, before any other text, is either a mistake or a significant misunderstanding. Rather than sprinkling tags around, why not discuss problems on this talk page, slowly and one section at a time? Johnuniq (talk) 06:58, 2 October 2017 (UTC)

@Jasper Deng:: I have read BRD as you suggest in your reversion comment. It says among other things.

1. BRD is not a valid excuse for reverting good-faith efforts to improve a page simply because you don't like the changes.
2. BRD is not an excuse to revert any change more than once. If your reversion is met with another bold effort, then you should consider not reverting, but discussing. The talk page is open to all editors, not just bold ones. The first person to start a discussion is the person who is best following BRD.

Could I invite you to continue the discussion from where we left off?

Martin Rattigan (talk) 04:27, 2 October 2017 (UTC)

Anyone proposing a change should explain reasons supporting the change on this talk page. Johnuniq (talk) 06:58, 2 October 2017 (UTC)

Which is exactly what I did with the "Checkmate in problems" section. It makes no difference. Someone will immediately revert it.Martin Rattigan (talk) 08:36, 2 October 2017 (UTC)

You may notice that Bubba73 who reverted that change has made 15 updates today without any comments on the talk page and without rebuke.Martin Rattigan (talk) 08:40, 2 October 2017 (UTC)

Unfortunately people get exhausted and may not give sufficient attention to every comment. The section in question starts with six numbered points, but has additionial comments that make the section a bit hard to follow. The two unsigned comments also make the section uninviting. It might be better to start again because no progress can occur if everyone keeps referring to past problems. Any new proposal should be focused on a small number of digestible points. Bear in mind that collaborative editing is a requirement at Wikipedia. That means a highly prolific editor might have to lower their output so others can keep up. Regarding the "White to play and mate in 50" position in the section, I can see why people might not have wanted to respond. No one doubts that positions can be found where one side has notionally weak material strength yet is able to win. My understanding of the topic is that a lot has been written in reliable sources regarding what is known as the "two knights endgame", and almost none of that would resemble the "White to play and mate in 50" position. Johnuniq (talk) 09:28, 2 October 2017 (UTC)

@Johnuniq:I think the problem is very succinctly described here https://www.technologyreview.com/s/520446/the-decline-of-wikipedia/. But for the moment I have better things to do. — Preceding unsigned comment added by Martin Rattigan (talk • contribs) 09:22, 2 October 2017 (UTC)

The above ping did not work because the comment was not signed. Johnuniq (talk) 09:28, 2 October 2017 (UTC)

Impossibility of forcing checkmate

Deleted the sentence "Although there are checkmate positions with two knights against a king, they cannot be forced." because:

(a) There is no citation for it.

(b) It's incorrect

Below are two examples of such positions and a forced mate resulting in each.

	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

This can be forced from the position below by the sequence shown.

	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

1.Nd7+ Kd8

2.Kc8 b6

3.Nxb6#

	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

This can be forced from the position below by the sequence shown.

	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

1...Ne7+

2.Kb8 N5c6+

3.Ka8 Nd5

4.cxb6 Nxb6#

Removed the full stop between "The player with the lone king has to make a blunder to be checkmated" and "In this position ..." in Keres' example.

Removed @Bubba73's reinsertion of the sentence, "Although there are checkmate positions with two knights against a king, they cannot be forced.". Still no citation. Still incorrect as explained above.

I assume his note in parentheses refers to the Seirawan position shown. Seirawan says of this (Diagram 20 in the reference included in the diagram)

Take a look at Diagram 20 and imagine that White’s c2-Knight is on the e2-square, covering the c1-square. White’s last move, Nd2+, forced Black’s King into the corner. Now the coup de grace is to play Ne2-d4-c2 checkmate. But, unfortunately, Black’s King is left stalemated! If Black could only move, checkmate would be a cinch. No matter how I tried, the only way I could checkmate Black’s King was with his cooperation. I couldn’t do it by force. Spend a while on this confounded ending and see for yourself.

That does not, by any stretch of the imagination, mean "Although there are checkmate positions with two knights against a king, they cannot be forced".

Again removed @Bubba73's incorrect OR. This time there is an attempted reference in the form of a repetition of the first diagram but with the footnote deliberately edited from the correct version of what Seirawan says to what @Bubba73 wants him to say. But even with the edit that would not justify @Bubba's statement, "Although there are checkmate positions with two knights against a king, they cannot be forced." because it refers to only one such position. It also looks ridiculous to have the first two diagrams on the page identical and smacks of vandalism. --Martin Rattigan (talk) 00:37, 13 September 2021 (UTC)

Regarding the "Although there are checkmate positions, ... , they cannot be forced" issue, it looks like you have arrived at a satisfactory compromise. I wouldn't have taken issue with the original wording, since I doubt that it has caused any real confusion in the last 15 years, but it is just as well that somebody has replaced passive voice with active voice there. Bruce leverett (talk) 04:37, 13 September 2021 (UTC)

Info and references

There are often a very small number of pathological positions in which a general rule doesn't hold. There are rules that hold generally, but hold in 99.9+% of the cases instead of exactly 100%.

To illustrate this, take, for instance, some cases in Secrets of Pawnless Endings, second edition, by John Nunn, page 284: "The ending of Q vs B+N is generally won but there is one important drawing fortress position." And on page 290, about Q vs. B+B "there is precisely one fortress position which is genuinely drawn." And on page 328, queen vs. three bishops on the same color: "General result is a win [for the queen], but there is a fortress with Black's king in a corner controlled by the bishops."

There are positions that can be set up with two knights where Black has been checkmated. There are positions that can be set up in which White to move checkmates in one move. But these are not forced checkmates. A forced checkmate is one in which checkmate can be forced against any defense by Black. "White to mate in one" doesn't give Black any chance for defense. Back these positions up to where Black has a choice of defensive moves and see what happens. All the defender has to do is not move the king where it can be checkmated on the next move. (This is in some of the sources.) So it isn't a forced checkmate.

On just one of my shelves, I found 11 books stating that checkmate with two knights can't be forced (in general). Some of them also state that a checkmate position can be set up, but they can't be forced against good defense ("forced" means against good defense, obviously). Some also state that stalemate can be forced.

• Ruben Fine, Basic Chess Endings, revised by Benko, p. 6
• Yuri Averbackh, Chess endings - essential knowledge, p. 14
• Paul Keres, Practical Chess Endings, (algebraic edition) p. 2
• Edmar Mednis, Advanced Endgame Strategies, pp. 40-41
• Lev Albert and Nikolay Krogus, Just the Facts!, 2nd edition, p. 312
• James Howell, Essential Chess Endings, p. 136
• Mark Dvoretsky, Dvoretsky's Endgame Manual, 3rd edition, p. 283
• Jon Speelman, Jon Tisdall, and Bob Wade, Batsford Chess Endings, p. 11
• Ilya Rabinovich, The Russian Endgame Handbook, p. 76
• Yasser Seirwan, Winning Chess Endings, p. 17
• Karsten Muller and Frank Lamprecht, Fundamental Chess Endings, p. 19.

Bubba73 ^{You talkin' to me?} 15:12, 13 September 2021 (UTC)

Regarding your first two paragraphs, John Nunn is an expert on the endgame and feels he should include the positions you mention. Wikipedia is intended to summarise expert opinion so if you're reporting on these endgames you should include the author's caveats. I wouldn't describe the fortresses as pathological. In the KQKBB and KQKBN endgames they appear to be the only chance for Black to draw against perfect play short of taking the queen. (Never looked at queen v three same coloured bishops.)

As for the third paragraph a reader who is not conversant with chess literature would say that White to play can force mate in this position.

	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

White to play and mate in 1.

Conventionally in chess literature a mating sequence is referred to as forced only if it is at least two ply. That's why I linked the word "force" to the chess glossary in my changes. It's used in the chess literature sense.

I haven't said that any of the positions you talk about give a forced mate. A forced KNNK mate necessarily involves the capture of a black piece on the mating move. But I haven't made any changes to that effect because I don't know of a suitable reference.

Your fourth paragraph demonstrates the root of the disagreement regarding the recent change I made.

The statement I deleted is demonstrably false. I proved that in the previous section when I made the deletion. (Did you read it?) No reputable reference will assert it.

The problem appears to be that you haven't grasped the distinction between:

(a) A checkmate position is impossible to force with two knights and a king against a lone king. (True)

and

(b) A checkmate position with two knights and a king against a lone king is impossible to force. (False)

(a) is equivalent to "two knights and a king cannot force checkmate against a lone king" which many references (and the article) correctly claim.

(b) is the sentence I deleted.

You say your books say, "checkmate with two knights can't be forced". I think if you read them correctly they actually say, "checkmate can't be forced with two knights". If a book says, "a checkmate position can be set up, but they [sic] can't be forced", without establishing that "forced" in the context means "forced by two knights and a king against a lone king", then it's incorrect. There are plenty of correct references.

I don't have all the books you mentioned but I have Batsford Chess Endings, Winning Chess Endings, Fundamental Chess Endings and Basic Chess Endings (unrevised). All of these are correct. I can't speak for your remaining books, but I imagine the same applies.

I didn't understand the relevance of your reference to stalemate as far as this page is concerned.

Martin Rattigan (talk) 20:10, 14 September 2021 (UTC)

Second Troitzky line section - delete?

This section describes the content of a chess café article where Helmut Konrady supplied a "second Troitzky" line such that if a pawn is securely blocked on or behind the line the two knights can win within the fifty move rule.

There are some problems both with the reporting of the article in Wikipedia and with the article itself. The link is now a pay site, so I have to speak from memory regarding the article contents. Perhaps someone with a chess cafe account could check what I say about it.

Firstly the problem with the Wikipedia reporting. The section says:

If Black's pawn is blocked by a white knight on or behind one of the dots, White can force a win within fifty moves. If the pawn can be blocked on or behind one of the Xs, White can force a win within fifty moves more than 99 percent of the time.

I'm pretty sure the article mentioned that the pawn should be securely blocked, not just blocked. Also, winning without the fifty move rule coming into effect in this endgame is not the same as winning within fifty moves. If "securely blocked" is taken to mean there is a knight immediately in front of the pawn protected by the other knight (as in M&L's statement of the Troitzky line rule) there are in fact 176892 positions on or behind the line shown which require more than 50 moves and around half of the positions on the X marked squares also require more than 50 moves (according to Nalimov).

The problems with the original article are several.

(a) Helmut Conrady said the results were based on endgame tablebases but there were no DTx50 EGTBs produced at the time and the information can't be extracted without these. I believe people working on EGTBs at the time believed his methodology was flawed. (User Syzygy expressed that opinion to me in conversation on the CCRL site.)

(b) Even if the line is accurate (this would be possible despite flawed methodology - it can now easily be checked from syzygy-tables.info in conjunction with Nalimov that the king, queen and bishops' files are correct) it would seem to have virtually no application. It can easily be seen that the two knights can securely block the b7 pawn in this position in five moves, but not less. The ply count under the 50 move rule is by then at least 10 and the information that the same position with ply count 0 could be won within the 50 move rule tells you nothing.

	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

White to play

(c) If the 50 move rule is to be taken into account the ply count then becomes part of the position, which increases the number of positions by a factor of 100. It would then be true that a large majority of positions with a securely blocked pawn on or behind the Troitzky line and the second Troitzky line could not be won within the 50 move rule, indeed many could not be won at all under the 75 move rule. (But the latter rule didn't exist at the time the article was written.)

(d) I don't think that "securely blocked" in the article was elucidated as clearly as it is in Fundamental Chess Endings. With M&L's statement in the book, the Troitzky line rule becomes more of a rule and less an approximate rule of thumb. Without it the "second Troitzky line rule" could only also ever be an approximate rule of thumb. Even with M&L's version there are 1000 or so dead positions behind the second Troitzky line.

My personal view is that the rule is not a proper part of the theory of the two knights v pawn ending, more an historical glitch that Dr. Müller and Herr Konrady would probably prefer forgotten, so if there are no objections I will delete the section in about a week. Martin Rattigan (talk) 21:48, 19 September 2021 (UTC)

No objections, so deleted section and reference under "Troitzky line". Left in links under "External links" because PDFs contain info other than the second Troitzky line. --Martin Rattigan (talk) 17:53, 26 September 2021 (UTC)