Talk:Two knights endgame

message: HELP!! It would be good if Search could find this article by what I think is the more common spelling in English, Troitsky, but I don't know how to do it.
Do you mean a redirect of the page name?  See WP:R for help if this is what you mean.  Stephen Compall 23:16, 11 May 2005 (UTC)
thread_title: old talk

message: Would it be better to have this article be about checkmate (or impossibility thereof) for two knights or two knights versus a pawn, rather than just the Troitzky line?  (I think so.)  The T. line would still play a prominant role.  Bubba73 (talk), 00:35, 16 July 2006 (UTC)
replies: text: If so, some material from checkmate can be moved to this article.  Bubba73 (talk), 05:28, 16 July 2006 (UTC)
replies: text:  Well, I did it, moving it from Triotzky line to this article, which is broader and can contain a little more material.  Bubba73 (talk), 21:17, 20 October 2006 (UTC)
thread_title:  Better name? 

message: Surely there's a better way to phrase
"There are also mating positions with the inferior side's king on the edge of the board rather than in the corner"
? Tar7arus 19:41, 12 January 2007 (UTC)
replies: text: How about taking out "rather than in the corner"? Bubba73 (talk), 23:17, 12 January 2007 (UTC)
replies: text:  I was actually more worried about "Mating positions"... Tar7arus 16:07, 13 January 2007 (UTC)
thread_title:  Rephrase required 

message: The caption accompanying the first diagram states that the position cannot be forced. The position can, however, arise (quite naturally) as the result of a forced mating sequence. E.g. from the position shown on the right, the sequence
:1. Nd5 e2
:2. Nb4+ Ka1
:3. Nd2 e1=N+
:4. Kb3 Nc2
:5. Nxc2#
is optimal play by both white and black and results in the mate shown. The caption should maybe also say, "... provided the same forces existed prior to the last half move", or something similar.
Of course the final position is one of several possible in the same number of moves, so cannot, strictly speaking be forced, but this would apply to most elementary mating positions (i.e. the weaker side generally gets to choose between alternative mates.) Martin Rattigan (talk) 13:38, 11 January 2010 (UTC)
replies: text: I think it is assumed that there was no other material on the board.  The position can't be forced if that is the only material on the board. And in some cases the knights win even if the pawn is past the Troitsky line - this is one of them.   Bubba73 (Who's attacking me now?), 18:25, 11 January 2010 (UTC)
thread_title:  forced mating position? 

message: The first two paragraphs could be clearer. The first paragraph defines the two knights ending as, "a chess endgame with a king and two knights versus a king, possibly with some pawns" (my italics). The next sentence then states, "... a king and two knights can not force checkmate". With the possibile pawns this is, of course, not necessarily true.
The second paragraph starts with the sentence, "Interestingly, if the lone king has a pawn (and sometimes with two pawns), then checkmate can be forced in some cases". Apart from looking very much like an oxymoron, the sequel spends some time on king and two knights v king and three pawns when checkmate can also be sometimes forced. (And why stop at three pawns - see "more pawns" below.)
The definition in the first paragraph that allows the opponent of the side with the two knights to have only pawns is no doubt taken from one of the references, but seems a little strange. I first realised there was a possibility of winning with only two knights when somebody left a chess magazine containing an endgame study something like that to the right in a hotel I was staying at circa 1976. You also include several examples which don't strictly speaking  fit within this definition. (Incidentally if anyone recognises the study I included - I think it was by Troitzky - I would be interested if they could correct the diagram, if necessary. I may have simplified it.) Martin Rattigan (talk) 18:01, 11 January 2010 (UTC)
replies: text: OK, I'll clarify the first thing.  It does need some cleanup.  Bubba73 (Who's attacking me now?), 18:28, 11 January 2010 (UTC)

text: Yes, some positions with two knights versus one knight are also considered, in contrast to an earlier statement.  I'll fix it.  Bubba73 (Who's attacking me now?), 18:35, 11 January 2010 (UTC)
replies: text:  PS, my daughter had a 2 knights versus 1 pawn position in a tournament when she was 6 years old.  I don't know if it was one of the theoretically won positions or not.  I didn't expect her to be able to win it - I was just hoping that she didn't let the pawn promote and then lose.  She had to exchange a knight for the pawn, draw.  Bubba73 (Who's attacking me now?), 19:23, 11 January 2010 (UTC)

text: She did better than Lilienthal then (Norman-Lilienthal Hastings 1934/5) who apparently managed to lose a won two knights v pawn ending in exactly the way you suggest. Martin Rattigan (talk) 19:56, 11 January 2010 (UTC)
replies: text:  Looks like he just failed to win it: game here.  Bubba73 (Who's attacking me now?), 20:57, 11 January 2010 (UTC)

text: Apologies for the misinformation. I was taking it from the book "Knight Endings" by Averbakh & Checkover, English translation published by Batsford 1977. In Ch. 14 covering two knights v. pawn, the position after white's move 72 is given (diag. 250) with the accompanying text, "Here victory, expedited by the young QNP, stymied Black.". Obviously I shouldn't believe all I read - it never did seem very plausible. Martin Rattigan (talk) 20:04, 26 February 2010 (UTC)
replies: text: I think he means that the win should be less difficult than usual because the pawn is not yet to the T. line, but he failed to win the game.  Bubba73 (You talkin' to me?), 20:58, 2 March 2010 (UTC)

text:  In another tournament game the same year, my daughter had a rook and 2 knights vs. a rook (no pawns), and exchanged rooks, down to the drawn endgame.  Bubba73 (Who's attacking me now?), 21:43, 11 January 2010 (UTC)
thread_title:  more rephrasing? 

message: I saw the ChessCafe article on the second Troizky line some years ago and it struck me at the time that the question that had been asked appeared to be the wrong question, but so obviously so that it was possibly just mis-stated. 
In the diagram to the right, for example, the pawn can be halted behind the second Troitzky line. The point is that it will take three moves before the knight blocks the pawn, so it's not of much interest that the win can then be achieved within the fifty move rule. We need to know that we can mate or force the pawn forward in forty seven rather than fifty moves.
As documented the second Troitzky line would seem to have limited relevance, i.e. only to games where the pawn is already blocked when the game crystalizes into a two knights v. pawn ending.
The text faithfully reproduces the ChessCafe article, but do you think the article was itself correctly stated? Or am I missing something? Martin Rattigan (talk) 21:15, 28 February 2010 (UTC)
replies: text: Yes, I made the change in the article.  Bubba73 (You talkin' to me?), 15:59, 1 March 2010 (UTC)

text: The only reference to the Second Troitzky line that I know of is the ChessCafe PDF.  Bubba73 (You talkin' to me?), 21:25, 1 March 2010 (UTC)

text: The tablebase shows the pawn being blocked on c4 after six moves.  Tablebases do not take the 50-move rule into account.  As far as defense, they try to delay checkmate as long as possible (or maybe the conversion to a simpiler endgame). Reading the ChessCafe article, he says that if the pawn is securly blocked on or before those squares, the knights can win within the 50-move rule.  (Recall that the pawn is released near the end so that can affect the count.) Bubba73 (You talkin' to me?), 02:57, 2 March 2010 (UTC)

text: I'll have to read this more in-depth later.  When I said that the tablebase blocked the knight on the sixth move, I was in a program making the moves that were the top-rated.  One thing - I'm worried that this is getting into the area of wp:OR ofiginal research and it might be best for the article to state what the ChessCafe article says and leave it at that, since I don't know of anything else published on the second T. line.  Bubba73 (You talkin' to me?), 17:31, 2 March 2010 (UTC)

text: I, having changed my opinion during the discussion, would concur. I now think, for the reasons I mentioned above, that the enunciation of the rule in the ChessCafe article does indeed say what it was intended to say. My original feeling to the contrary was just the result of a lack of chess expertise. Martin Rattigan (talk) 18:30, 2 March 2010 (UTC)
thread_title:  Second Troitzky line - is it properly reported (or alternatively any use)? 

message: The reference to Benko 2007 is missing.  It looks like I forgot to put it in, in June 2009.  It was probably in Chess Life.  Bubba73 You talkin' to me? 23:55, 28 March 2013 (UTC)
replies: text: I looked through Chess Life online and didn't find it.  I thought that it was likely in his book Endgame Laboratory, since I got the book the month before the edits (you can usually tell what book I've gotten recently by my additions), but it isn't there either.  Bubba73 You talkin' to me? 00:39, 29 March 2013 (UTC)
replies: text:  The comment at ChessGames.com says that his CL column says <"I recall my first meeting over the board with Bronstein. I escaped to an endgame with one Knight against his two. It was a well-known theoretical draw, even without my Knight. I chased one of his Knights with mine, till the audience started to laugh. At that point he agreed to a draw.", so it must be in his CL column somewhere.  Bubba73 You talkin' to me? 00:49, 29 March 2013 (UTC)
thread_title:  reference missing 

message: The article claims that Yue's pawn is past the Troitsky line in the position 8/8/2k5/K1n5/2P5/5n2/8/8 w - - 3 63, but it's Black who has the two knights, so the Troitsky line is reflected and the pawn is blocked on its fourth rank.  I don't see how this is an example of the two knights winning with the pawn beyond the line. Also, the article isn't making it clear that Anand actually played 61... Kc5. Infenwe (talk) 13:10, 5 May 2014 (UTC)
replies: text: Yes, after the pawn gets to c4 it is on the T. line.  I'll look at this in a few days.  Bubba73 You talkin' to me? 23:58, 5 May 2014 (UTC)

text: OK, I looked up the original article.  Some changes have to be made to that section.  I'll do it in a few days.  Bubba73 You talkin' to me? 01:29, 10 May 2014 (UTC)
thread_title:  Wang Yue - Anand 

message: About the fifty-move rule - there are some pawn moves in there that reset the counter.  Bubba73 You talkin' to me? 15:37, 11 May 2014 (UTC)
thread_title:  Fine & Benko, diagram 201 - 96 moves 

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thread_title:  External links modified 

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

text:  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)
replies: text: 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)

text: I have read BRD as you suggest in your reversion comment. It says among other things.
#BRD is not a valid excuse for reverting good-faith efforts to improve a page simply because you don't like the changes.
#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)

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

text: 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)
replies: text: 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)

text: The above ping did not work because the comment was not signed. Johnuniq (talk) 09:28, 2 October 2017 (UTC)
thread_title:  Third reversion by Jasper Deng. 

message: 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.
This can be forced from the position below by the sequence shown.
1.Nd7+ Kd8
2.Kc8 b6
3.Nxb6#
  
This can be forced from the position below by the sequence shown.
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)
replies: text: 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)
thread_title:  Impossibility of forcing checkmate 

message: 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. 
(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)
thread_title:  Second Troitzky line section - delete?