Talk:Two knights endgame

old talk

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)[reply]

Yes, that is what I mean. Thank you for the pointer! Now I can do it. Bubba73

Better name?

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)[reply]

If so, some material from checkmate can be moved to this article. Bubba73 (talk), 05:28, 16 July 2006 (UTC)[reply]

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)[reply]

Rephrase required

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)[reply]

How about taking out "rather than in the corner"? Bubba73 (talk), 23:17, 12 January 2007 (UTC)[reply]

I was actually more worried about "Mating positions"... Tar7arus 16:07, 13 January 2007 (UTC)[reply]

This phrase needs rephrasing: "Andor Lilienthal failed to win it twice in a six-year period, see Norman vs. Lilienthal and Smyslov vs. Lilienthal." In the game vs Smyslov Lilienthal never had a theoretically winning position, regardless of what Botvinnik claimed. I checked the game score with Nalimov tablebases, Smyslov never strayed from the drawing territory. AndreyTe 19 April 2021

forced mating position?

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White to play

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)[reply]

Maybe I should have understood the previous entry before I typed the foregoing. Martin Rattigan (talk) 18:01, 11 January 2010 (UTC)[reply]

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)[reply]

more rephrasing?

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White to play and win. Troitzky and Aizenshtadt 1940.

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) (Found this in another source. It is essentially the same, but I have corrected diagram and attribution.)Martin Rattigan (talk) 15:20, 9 September 2015 (UTC)[reply]

OK, I'll clarify the first thing. It does need some cleanup. Bubba73 ^{(Who's attacking me now?)}, 18:28, 11 January 2010 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

Looks like he just failed to win it: game here. Bubba73 ^{(Who's attacking me now?)}, 20:57, 11 January 2010 (UTC)[reply]

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)[reply]

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)[reply]

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)[reply]

more pawns

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White to play and win (J. Mendheim 1832)

"The knights cannot set up an effective blockade against four connected pawns, so the position is a draw" - seems to be too dogmatic. E.g. add an extra white knight almost anywhere to the position on the right, which is already a win for white. Martin Rattigan (talk) 18:01, 11 January 2010 (UTC)[reply]

The statement about four pawns is from Basic Chess Endings and is true in the vast majority of cases. There are exceptions to almost all "rules". This position was composed to be an exception. Bubba73 ^{(Who's attacking me now?)}, 18:21, 11 January 2010 (UTC)[reply]

Most composed positions are designed to be exceptions to the general rule. Bubba73 ^{(Who's attacking me now?)}, 19:02, 11 January 2010 (UTC)[reply]

Agreed - "... so the position is usually drawn" - would express that perhaps better. Martin Rattigan (talk) 18:36, 11 January 2010 (UTC)[reply]

Maybe, because it isn't an immediate draw. But the source says "... so the result is a draw". Often "draw" is used to mean theoretical draw - it will result in a draw if both sides play correctly. But the original source makes this clearer so I'll try to fix it.

I think that takes care of all of your suggestions, thanks. Bubba73 ^{(Who's attacking me now?)}, 19:12, 11 January 2010 (UTC)[reply]

PS - this part of the article talks about blocking the pawns with the two knights and then capturing all of them except one to get to a winning position, and that is quite different from this composed position. Bubba73 ^{(Who's attacking me now?)}, 19:16, 11 January 2010 (UTC)[reply]

Just to make sure I'm not accidentally spreading misinformation, I should make clear that Mendheim never intended this as an example of the two knights ending. The composition had one knight exactly as shown. The suggestion to add an extra (irrelevant) knight was mine. I just used Mendheim's composition because it happened to have four connected pawns (at least in the sense of occupying adjacent files) and could obviously therefore be extended to an (admittedly atypical) counterexample to the rule given in the wiki article.

The winning method, unsurprisingly, doesn't exactly correspond with that suggested in the text, but I don't see that this invalidates it as a counterexample. In any case I think the text now reads better. Martin Rattigan (talk) 20:28, 11 January 2010 (UTC)[reply]

Yes, this is a special situation. Usually the knight would lose, and it doesn't illustrate the method described in the article of blocking the pawns, winning all but one, and then have a winning 2N vs. P endgame. Bubba73 ^{(Who's attacking me now?)}, 20:55, 11 January 2010 (UTC)[reply]

Second Troitzky line - is it properly reported (or alternatively any use)?

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White to play

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)[reply]

To clarify what I wrote. Should the second Troitzky line result be stated, "if the pawn can be stopped behind the second Troitzky line, the mate can be achieved within the fifty move rule by stopping the pawn behind the second Troitzky line"? The limited usefulness of the result as actually stated suggests this was what Karsten Müller / Helmut Conrady really had in mind / investigated. Martin Rattigan (talk) 08:16, 1 March 2010 (UTC)[reply]

I've changed the diagram and the wording in my original text because both were incorrect. (The pawn would originally move before it was blocked). Martin Rattigan (talk) 14:24, 1 March 2010 (UTC)[reply]

Yes, I made the change in the article. Bubba73 ^{(You talkin' to me?)}, 15:59, 1 March 2010 (UTC)[reply]

OK, I see the change. This applies to the knights' files only and effectively says that the stronger side can win within the fifty move rule in over 99% of cases even if any (minimum number of) moves needed to effect the blockade are counted within the first allocation of fifty moves. Does this mean that this definitely doesn't apply to the other files? And did you find a reference for the change - I've tried googling, but only found repetitions of the original?

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White to play and mate within the fifty move rule

Incidentally the position, that prompted the question is as shown on the right. In this case the pawn is securely blockaded (on a "dot") in two moves, so white then has 48 moves to mate or force the pawn forward.

If Wilhelm with the DTM EGTB connected plays this against himself, he fails to mate. He gives it as mate in 52 and stops after fifty moves with two moves still needed to mate. However I'm fairly sure that the mate is possible within the 50 move rule,

[Have to say I disagree with myself on this point] Martin Rattigan (talk) 11:56, 1 May 2015 (UTC)[reply]

and the problem is the DTM EGTB. This should be a DTR50 EGTB for playing real chess, but these are difficult to get hold of. I can beat Wilhelm DTM EGTB within the 50 move rule if I play the white pieces myself, but it's conceivable that this is because he's not taking the 50 move rule into account when defending. (I can't see where this would apply, but that doesn't prove too much).

As stated in the Wiki, the second Troitsky line rule would not say one way or the other whether a mate is possible within the 50 move rule from the given position. This illustrates why I think the second Troitsky line rule is pretty useless if it's meant to read as it does. If it were meant to read as I suggested above it would classify the position as a win within the 50 move rule. Martin Rattigan (talk) 21:18, 1 March 2010 (UTC)[reply]

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)[reply]

Shame. But then perhaps you had better reverse the change to the main text, since it sounds like there's no guarantee that it's now correct and the previous strict reading is safer. Martin Rattigan (talk) 22:12, 1 March 2010 (UTC)[reply]

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)[reply]

Before commenting on your reply I should mention that I can, after further reflection, answer at least one of my own questions in the affirmative, viz. "am I missing something?".

What I was missing and Dr. Müller, being a real chess player, was no doubt not, is that the play leading up to a two knights v. pawn endgame will predispose the conversion into this endgame to occur with the pawn already blocked. For example, if the conversion to the ending occurs by the weaker side exchanging his last piece for the stronger side's last pawn in a situation where there are two mutually blocking pawns and the piece is retaken with a knight, this results in the remaining pawn being blocked (possibly securely).

Somebody referred to as "Resignation Trap" has compiled a list of games that finished up in this ending here. A large percentage of the games (on a quick scan through I make it nearly half) converted into the ending with the pawn already securely blocked. So, while the second Troitzky line as stated would seem to be almost totally irrelevant when "disembodied" positions such as the ones I inserted are considered, when positions that actually occur in chess games are considered it becomes much more relevant. It would obviously still be nice to know whether the rule as I rephrased it holds, but c'est la vie. (Incidentally while I was doing the scan I couldn't help noticing that something very strange seemed to be going on in Gurevich-Rowley 1990. What is white doing on moves 74 and 90? Not very germane, admittedly, but I'd appreciate any enlightenment.)

Coming back to what you said, the point I have been making is the distinction between "is securely blocked" and "can be securely blocked", and the few moves difference this makes, in view of the fact that many positions in this ending fall inconveniently close to requiring exactly fifty moves.

By "is securely blocked" in this context, I would understand that the blockading knight (knight it must be) is already in the path of the pawn and the pieces are so arranged that the stronger side can either permanently prevent a direct attack by the weaker side's king on the blockading knight, or one of the stronger side's remaining pieces can defend the blockading knight in time to stop the weaker side's king actually taking it (except for the special situations with a rook's pawn where this can be allowed). By "can be securely blocked", I would understand that the stronger side can bring about a position in which the pawn "is blocked", but of course this may take a move or two and blocking the pawn won't reset the move counter under the fifty move rule.

The ChessCafe article says, "is blocked", in the case of the non knight's files and at least strongly implies "is blocked" for the 99% result relating to the knight's files. This means it can't be reliably used to evaluate positions in a "can be blocked" situation (at least if the reading is taken at face value). For example, it sheds no light on the second position I gave, even with the extra information from the DTM EGTB that the position is mate in 52, since the DTM EGTB ignores the 50 move rule. I understood that the second Troitzky line result had been obtained using DTR50 EGTBs (or possibly at that time DTZ50 EGTBs), which take the 50 move rule into account.

When you say that your tablebase shows the pawn being blocked on c4 after 6 moves, I assume you mean the knight is blockading on c4 and the pawn is on c5, and that you have taken the pawn to be securely blockaded only when it's actually been defended by the second knight. This is, strictly speaking, another point where the statement of the second (and indeed the first) Troitzky line rule could benefit from clarification, but given that the blockading knight in general may never actually need to be defended, I think the meaning I have given must be the one intended (in both cases). I would be surprised if your database lets the pawn through to c4 by move 6, because it's difficult to see how it could then complete the mate in 52 moves, which explains the other part of my assumption.

You are right when you say that the databases (DTM) that are generally available don't take into account the 50 move rule. For some endings (this one) this can mean that these databases get it wrong. The second diagram above is a case in point. Because different paths can be taken through the database, the results obtained can be inconsistent. I include the Wilhelm PGN below. The mainline shows Wilhelm failing to reach a mate under the 50 move rule. I have reloaded and played white's moves 15 to 20 myself, at which point Wilhelm (or any program using a DTM ETGB) can mate under the 50 move rule because the pawn has moved forward and the mate according to the DTM EGTB now occurs within 50 moves of that event. Morover the mate still occurs on move 52 so the path was already in the DTM EGTB, it just hasn't been used. For completeness I have also made all the alternative moves for black at the point the pawn moved forward. Wilhelm's comments show that the pawn would have been forced forward at that point even had the database respected the 50 move rule, because in all cases mate would be possible within 50 moves from the starting position.

Unfortunately this still doesn't tell me, and neither, as stated, does the second Troitzky line rule, whether the position shown is won for white. In practise I can generally win it against a DTM EGTB (there is a useful site here for trying out variations - Wilhelm gets stuck in a rut - but it is obvious from the results that it is also attached to a DTM EGTB). Besides getting the attack wrong the DTM EGTBs may also get the defence wrong for the same reason. To get a definitive answer would really need an EGTB that works correctly with the 50 move rule. This would be a DTR50 EGTB but as I said these are hard to get hold of, if indeed anybody has generated one for this ending.

[Event "?"] [Site "?"] [Date "2010.22.2"] [Round "?"] [White "?"] [Black "?"] [Result "1/2-1/2"] [SetUp "1"] [FEN "K1k5/8/8/2p5/4N3/8/8/N7 w - - 0 0"]

1.Ne4-d6 {64/1/0 #52} Kc8-d7 {64/1/0 #51} 2.Nd6-c4 {64/1/0 #51} Kd7-c6 {64/1/0 #50} 3.Na1-c2 {64/1/0 #50} Kc6-d5 {64/1/0 #49} 4.Nc2-e3 {64/1/0 #49} Kd5-c6 {64/1/0 #48} 5.Ka8-b8 {64/1/0 #48} Kc6-b5 {64/1/0 #47} 6.Kb8-c7 {64/1/0 #47} Kb5-a4 {64/1/0 #46} 7.Kc7-d6 {64/1/0 #46} Ka4-b3 {64/1/0 #45} 8.Kd6-e5 {64/1/0 #45} Kb3-b4 {64/1/0 #44} 9.Ke5-f4 {64/1/0 #44} Kb4-b3 {64/1/0 #43} 10.Kf4-f3 {64/1/0 #43} Kb3-b4 {64/1/0 #42} 11.Kf3-f2 {64/1/0 #42} Kb4-b3 {64/1/0 #41} 12.Kf2-e1 {64/1/0 #41} Kb3-c3 {64/1/0 #40} 13.Ke1-e2 {64/1/0 #40} Kc3-d4 {64/1/0 #39} 14.Ke2-d2 {64/1/0 #39} Kd4-e4 15.Nc4-d6 {64/1/0 #38} ( 15.Kd2-c3 Ke4-f3 {64/1/0 #37} 16.Kc3-d3 Kf3-f4 {64/1/0 #36} 17.Ne3-d5 Kf4-f3 {64/1/0 #35} 18.Nc4-e5 Kf3-g3 {64/1/0 #34} 19.Kd3-e4 c5-c4 {64/1/0 #33} ( 19...Kg3-h4 20.Ne5-c4 {64/1/0 #31} ) ( 19...Kg3-h3 20.Ne5-c4 {64/1/0 #30} ) ( 19...Kg3-h2 20.Ke4-f3 {64/1/0 #8} ) ( 19...Kg3-g2 20.Ke4-f4 {64/1/0 #27} ) ( 19...Kg3-f2 20.Ne5-c4 {64/1/0 #29} ) 20.Nd5-c3 Kg3-h4 {64/1/0 #32} ) Ke4-f3 {64/1/0 #37} 16.Ne3-c4 {64/1/0 #37} Kf3-f2 {64/1/0 #36} 17.Nd6-e8 {64/1/0 #36} Kf2-f3 {64/1/0 #35} 18.Ne8-f6 {64/1/0 #35} Kf3-f2 {64/1/0 #34} 19.Nf6-d5 {64/1/0 #34} Kf2-f3 {64/1/0 #33} 20.Kd2-d3 {64/1/0 #33} Kf3-g3 {64/1/0 #32} 21.Kd3-e4 {64/1/0 #32} Kg3-f2 {64/1/0 #31} 22.Nd5-c3 {64/1/0 #31} Kf2-g3 {64/1/0 #30} 23.Nc3-d1 {64/1/0 #30} Kg3-g4 {64/1/0 #29} 24.Nd1-f2 {64/1/0 #29} Kg4-g5 {64/1/0 #28} 25.Ke4-e5 {64/1/0 #28} Kg5-g6 {64/1/0 #27} 26.Nf2-e4 {64/1/0 #27} Kg6-h5 {64/1/0 #26} 27.Ke5-f4 {64/1/0 #26} Kh5-g6 {64/1/0 #25} 28.Kf4-g4 {64/1/0 #25} Kg6-f7 {64/1/0 #24} 29.Kg4-f5 {64/1/0 #24} Kf7-f8 {64/1/0 #23} 30.Ne4-d6 {64/1/0 #23} Kf8-e7 {64/1/0 #22} 31.Kf5-e5 {64/1/0 #22} Ke7-d7 {64/1/0 #21} 32.Ke5-f6 {64/1/0 #21} Kd7-c7 {64/1/0 #20} 33.Kf6-e7 {64/1/0 #20} Kc7-c6 {64/1/0 #19} 34.Ke7-e6 {64/1/0 #19} Kc6-c7 35.Nd6-e4 {64/1/0 #18} Kc7-d8 {64/1/0 #17} 36.Ne4-f6 {64/1/0 #17} Kd8-c7 {64/1/0 #16} 37.Ke6-d5 {64/1/0 #16} Kc7-c8 {64/1/0 #15} 38.Kd5-c6 {64/1/0 #15} Kc8-d8 {64/1/0 #14} 39.Kc6-d6 {64/1/0 #14} Kd8-c8 40.Nf6-e8 {64/1/0 #13} Kc8-d8 {64/1/0 #12} 41.Ne8-c7 {64/1/0 #12} Kd8-c8 42.Nc7-e6 {64/1/0 #11} Kc8-b7 {64/1/0 #10} 43.Kd6-d7 {64/1/0 #10} Kb7-a7 {64/1/0 #9} 44.Kd7-c7 {64/1/0 #9} Ka7-a6 {64/1/0 #8} 45.Kc7-c6 {64/1/0 #8} Ka6-a7 46.Kc6-b5 {64/1/0 #7} Ka7-b7 {64/1/0 #6} 47.Nc4-d6 {64/1/0 #6} Kb7-b8 {64/1/0 #5} 48.Kb5-b6 {64/1/0 #5} Kb8-a8 {64/1/0 #4} 49.Ne6-d8 {64/1/0 #4} Ka8-b8 {64/1/0 #3} 50.Nd8-c6 {64/1/0 #3} Kb8-a8 1/2-1/2

By the way information on the different flavours of EGTB can be found on the CCRL Endgame Tablebases forum. —Preceding unsigned comment added by Martin Rattigan (talk • contribs) 14:42, 2 March 2010 (UTC) Sorry - forgot the twiddles again - that was me above. Martin Rattigan (talk) 14:57, 2 March 2010 (UTC)[reply]

P.S. I have thought some more about your last comments.

There are in fact only a few DTM optimal paths for the first few moves. These all start Nd5 ,c4 for white, resulting in what I would call a securely blocked pawn on move 2 (i.e. knight in place and defensible), but also all paths lead to the knight also being defended by the second knight on move 4 and surely this would count as securely blocked under any interpretation of the phrase.

If I enter Nc3 (quickest block) into Wilhelm (DTM)EGTB and then let it play by the database this results in the pawn being blockaded by the knight on c3 and occupying c4 after move 5 , the blockading knight being, in addition, defended by the second knight after white's move 6. This may be what you are referring to, which brings up other possible interpretations of "securely blocked".

I would use the phrase immediately after Nc3 in this instance, but I realise that others, apart from requiring the knight to be defended, which I discussed already above, might not use the phrase unless the knight is immediately in front of the pawn. (This would seem to be quite logical, correct even, because really and truly the pawn is not otherwise blocked at all, strictly speaking, just potentially blocked.) How would you interpret the phrase?

Nc3 must be entered manually because it results in mate in 60 instead of 52, but Wilhelm finishes up only one move further adrift of mating than in the PGN above, because the pawn moves forward on move 5, resetting the move counter. Because Wilhelm is using a DTM EGTB, the 50 move rule will never give him reason to hold back the pawn; an obvious question is, "would a DTR50 EGTB also push the pawn at that point?". Martin Rattigan (talk) 16:57, 2 March 2010 (UTC)[reply]

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)[reply]

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)[reply]

reference missing

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)[reply]

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)[reply]

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)[reply]

More references missing. I have inserted a reference for the first sentence of the subsection On the edge of the section Two knights cannot force checkmate.

Wang Yue - Anand

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)[reply]

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)[reply]

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)[reply]

Fine & Benko, diagram 201 - 96 moves

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)[reply]

Draws on and behind the Troitsky line.

You write:

Troitsky established that if a black pawn is blockaded (by one of the white knights) on a square no further forward than the line a4–b6–c5–d4–e4–f5–g6–h4, then White can win the resulting endgame (and similarly in reverse for Black), no matter where the other pieces are placed.

This is not true. Even neglecting the positions where the black king can immediately take a knight or effectively attack both, there are drawn positions with the pawn (securely) blockaded on every square on or behind the Troitsky line.

	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

A. Black to play and draw.

On most of the squares, the draws I can think of are variations of the cornered knight motif shown in diagram A. Some of these are more trivial than others; e.g. if the f and g columns in diagram A were flipped vertically black would be able to play his king to f3-g2-h1, taking the knight without hindrance.

I include below a pgn file showing a couple of lines in A. It is fairly obvious that white can only draw by repetition, lose a knight or take the pawn, otherwise the pawn queens or at least reaches c2 with black in the h8 corner with a clear draw.

[Event "?"] [Site "?"] [Date "2015.05.28"] [Round "?"] [White "Rybka 2.3.2a mp 32-bit "] [Black "martin"] [Result "*"] [FEN "7N/2p5/2N5/3K2k1/8/8/8/8 b - - 0 1"]

1... Kf6 2. Nd8 Ke7 3. Ne6 (3. Ndf7 {Rybka 2.3.2a mp 32-bit -martin} Kf6 4. Nh6 Kg7 5. N8f7 c5 6. Kxc5) 3... Kf6 4. Nxc7 *

I can also think of some positions where the knight is not in the corner. These are variations on diagram B. Play is obvious.

	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

B. Black to play and draw.

If the blockaded pawn is a bishop's pawn that hasn't moved and the other knight in the nearest corner (admittedly unlikely in play), then almost all such positions are drawn. I think the position in diagram C and the same position with white's king on the dotted square (both white to play) are the only positions that white can win. Play is again obvious in the shown 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

C. White to play and win.

With the a8 knight and c7 pawn as shown, there is indeed a relatively small percentage of positions that can be won by white, whether the other knight is blockading the pawn or not. The other two white pieces must be able to immobilize the black king in a1, h1 or h8 unaided, otherwise black can simply leave the pawn where it is. Position D and its reflection are the sole exceptions.

	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

D. White to play and mate in 1.

I think it means with White to move. Bubba73 ^{You talkin' to me?} 03:14, 28 May 2015 (UTC)[reply]

I assume you mean the Troitzky line statement should read "if the black pawn is blockaded on or behind the Troitzky line and it is white to move then etc. This would only be relevant for an initial capture into an already blockaded two knights v pawn ending. I don't think this affects anything I've written. Martin Rattigan (talk) 08:18, 28 May 2015 (UTC)[reply]

In endgames, it is generally understood that it is the stronger side's turn to move - otherwise there could be an immediate capture. I've made some changes. The text did say "with White on the attack" but I've changed that to "White to move". Bubba73 ^{You talkin' to me?} 20:07, 28 May 2015 (UTC)[reply]

Sorry to be a pain, but I think the change in wording is retrograde. I believe that the statement of the Troitzky line statement that you had, subject to the qualification "securely" of the word "blockaded" and exceptions some of which are the subject of this discussion, was correct irrespective of who has the move. — Preceding unsigned comment added by 77.58.143.123 (talk) 15:04, 30 May 2015 (UTC)[reply]

(a) These are draws (with black to move in the A and B positions, mostly with either side to move in the C positions). There is no stronger side.

(b) In endgames where both sides have pieces other than the king there could be an immediate capture whoever has the move.

(c) If you want the side with the two knights to move first then you need only move forward one ply in diagrams A and B. (You get the diagrams A' and B' I've shown.)

(d) I don't think it is generally understood that it is the stronger side's turn to move. You yourself talk about black to move in the diagram shown under "Position of mutual zugzwang"; indeed such positions would be very hard to discuss if you weren't allowed to consider black moving first.

In positions A and B black's decision determines the outcome of the game. After he moves the outcome is already determined. Therefore the positions are of more interest on this ply than they are in A' and B'.

Of the diagrams in the Batsford translation of Averbakh's chapter on two knights v pawn (which used to be the standard reference before EGTBs happened), 14 are with either side to move, 7 are the side with the two knights to move and 17 are the side with the pawn to move.

At any rate chess allows both sides to move and the fact remains that there are draws behind the Troitzky line whoever plays first.

	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

A'. White to play and black to draw.

	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

B'. White to play and black to draw.

	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

C'. White to play and black to draw. (For completeness.)

(That was me by the way - I forgot to add the twiddles.)Martin Rattigan (talk) 11:52, 29 May 2015 (UTC)[reply]

Well, with the black pawn blocked behind the T. line, Black has no chance of forcing checkmate whereas White does. So White is the stronger side and so it is assumed that White is to move. That is in the article. Bubba73 ^{You talkin' to me?} 16:46, 29 May 2015 (UTC)[reply]

Positions A', B' and C' are white to move so the discussion of conventions for endgame diagrams is probably pointless so far as the wording of the article is concerned. The positions I described are draws with the pawn blockaded behind the T line.

Martin Rattigan (talk) 17:47, 29 May 2015 (UTC)[reply]

But they are with BLACK to move, and he can trap and capture a knight. I don't think they are draws with WHITE to move. Bubba73 ^{You talkin' to me?} 19:53, 29 May 2015 (UTC)[reply]

I think you must have misread what I said. Read the captions under the A', B' and C' diagrams. Black cannot trap and capture a knight in any of them. In A' after white plays ne5, n(either)f7 then as long as he never moves the knights again black can never capture either of them. In B' after white plays nxp, ng5, n(either)f7 and so long as he never moves the knights again black can also never capture either of them. And how is he going to trap and capture a knight in C'?

In retrospect I think it might have been clearer just to label positions A', B' and C' simply as "Draw", because neither side can force a win win whoever moves first (with correct play). I adopted the actual wording in an attempt to make it clear that they were in fact drawn with white to move (in consideration of the previous discussion), but on rereading I think I may have achieved the opposite of what I intended.

Martin Rattigan (talk) 22:04, 29 May 2015 (UTC)[reply]

In your original A, White to move wins in 35 moves. In your revised A, Black has the knight trapped. Obviously the statement doesn't apply if Black can immediately win a knight. Bubba73 ^{You talkin' to me?} 23:23, 29 May 2015 (UTC)[reply]

You're correct (though I haven't counted the moves). That's why I labelled it "Black to play and draw". Black cannot capture the knight in either A or A' if white doesn't want him to (see the previous explanation).

Martin Rattigan (talk) 00:09, 30 May 2015 (UTC)[reply]

I didn't read all of that (too long), but in A', I don't see how White (to move) can prevent Black from capturing the knight that is on h8 on his first or second move. Bubba73 ^{You talkin' to me?} 00:20, 30 May 2015 (UTC)[reply]

Well the black king has to be adjacent to h8 to capture on h8 and a black pawn can never capture on the eighth rank, so we can discount a capture on black's first move. In A' it is white to move first so he can play his blockading knight from c6 to either d8 or e5 to cover one or both of the h8 knight's exit squares. Then if the black king moves to g7, either the h8 knight can move out to a protected exit square or the erstwhile blockading knight can move to (one of) the exit squares it protects. In either case the knights are then mutually protecting. Hope this helps.

Martin Rattigan (talk) 01:09, 30 May 2015 (UTC)[reply]

)

But in that case White has to unblock the pawn. Bubba73 ^{You talkin' to me?} 01:18, 30 May 2015 (UTC)[reply]

Exactly. In A', black uses the threat of an attack on the h8 knight to break the blockade on his pawn. White can then no longer win. That is why the position is a draw.

84.73.190.173 (talk) 01:28, 30 May 2015 (UTC)[reply]

If it is no longer blocked, then it isn't "blocked behind the Troitsky" line, so it obviously doesn't apply. The pawn can advance and draw. If White has to give up a knight, then it is no longer "two knights versus pawn". F&M use the word "securely", so I'll add that. Bubba73 ^{You talkin' to me?} 01:33, 30 May 2015 (UTC)[reply]

I noticed that you added "securely" in the preamble, but not in the section on the Troitzky line. I assume this was an oversight, so I have taken the liberty of adding it myself - I hope you don't mind. I didn't make any of other changes that I think are necessary - I'm waiting for you to mull it over and respond to the discussion to date. Martin Rattigan (talk) 18:31, 31 May 2015 (UTC)[reply]

Well I also used the word securely. I think by "securely" they mean either that the blockading knight is protected or the remaining pieces can stop the opposing king from reaching an attacking square. In each of the examples the blockading knight is protected.

But in any case what you say doesn't apply in situations of the type B and C' (B' and C' if you prefer). Would you agree that these are exceptions?

84.73.190.173 (talk) 02:25, 30 May 2015 (UTC)[reply]

By the way white does give up a knight in a lot of the two knights v pawn endings with a rook's pawn, but the play still comes under two knights v pawn in expositions of the subject. I would say that what is relevant is the material in the starting position.

84.73.190.173 (talk) 02:37, 30 May 2015 (UTC)[reply]

I would also say that it is only whether the pawn is securely blocked in the starting position that is relevant to the rule. In all positions with a blockaded pawn (behind or in front of the T line) white is forced to abandon the blockade if he wants to win.

77.58.143.123 (talk) 12:58, 30 May 2015 (UTC)[reply]

I should retract my assertion, "In A', black uses the threat of an attack on the h8 knight to break the blockade on his pawn".

In position A' white (to play) has no winning moves, but also no losing moves. Therefore he is not forced in any way. In particular he is not forced to break the blockade.

Neither, with best play by both sides, does he necessarily lose the knight if he chooses not to break the blockade.

For example after 1. Kc5 Kg7 2.Kd5, black has two options; KxN and Kf6. Both of these are optimal moves, so he has nothing to gain by taking the knight (also nothing to lose).

With best play by both sides, the pawn may remain blockaded and the material may remain unchanged until a draw is agreed, however long that takes.

I trust this resolves the objections you raised to position A(A').

REMOVED SUBSTANTIAL SECTION HERE BECAUSE I WAS TALKING RUBBISH. THE KNIGHTS COULD BE FORKED BY THE BLACK KING IN THE POSITION I GAVE. Martin Rattigan (talk) 23:55, 23 June 2015 (UTC)[reply]

I've never been sure whether "blockaded" implied there was a piece immediately in front of the pawn, or whether it could be used in the weaker sense that the piece was one or more squares in front of the pawn on the same file. I've just noticed that the main statement of the Troitzky line rule links to a definition of "blockaded", so now I know. I have deleted some of the text I wrote that referred to positions blockaded in the weaker sense on clarity and relevance grounds.

__________________________________________________________________________________Martin Rattigan (talk) 17:23, 3 June 2015 (UTC)[reply]

Anyway I think the quoted phrase should be amended in a way similar to the amendment you made to the bishop and knight ending. The two situations are very similar.

Martin Rattigan (talk) 02:17, 28 May 2015 (UTC)[reply]

I don't know if I wrote that about the bishop and knight endgame - others did a lot of work on that article too. Bubba73 ^{You talkin' to me?} 00:21, 30 May 2015 (UTC)[reply]

I deleted the sentence "Therefore the ending is more of theoretical than practical interest." and the sentences "If a pawn is beyond the Troitsky line, the result usually depends on the location of the defending king. Usually there is a "drawing area" and a "losing area"" previously flagged as "citation needed". Martin Rattigan (talk) 22:31, 7 July 2015 (UTC)[reply]

Role of the pawn in two knights v pawn ending.

	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) White to play and mate in 11; Black to play and mate in 11. (Mutual Zwang?)

	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

(2) White mates from position (1)

In the preamble you write:

The reason that checkmate can be forced is that the pawn gives the defender a piece to move and deprives him of a stalemate defense (Müller & Lamprecht 2001:19–20).

This is the most common reason but not the only one.

For example in position (1) shown white to move can win. The only possible mating position is position (2).

You will notice that the position of the pawn is unchanged. White cannot afford to immobilize the king prior to mate, otherwise if the pawn is still blocked it will be stalemate and if the pawn is not still blocked it will immediately queen, resulting in a draw.

The pawn throughout play, in fact, does nothing in particular and does it very well. Its role is simply to be there.

You should maybe add something like, "or provides extra mating positions".

Martin Rattigan (talk) 23:59, 29 May 2015 (UTC) [reply]

(1) An encyclopedia/Wikipedia article is not to be a completely comprehensive discussion of a subject, and (2) information must come from reluable and verifyable sources. Bubba73 ^{You talkin' to me?} 00:26, 30 May 2015 (UTC)[reply]

Ok, but could I suggest you change "The reason ..." to "One reason ..." which would make it a little more accurate without violating the terms of your contract?

84.73.190.173 (talk) 03:50, 30 May 2015 (UTC)[reply]

	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 win. Black pawn does not move.

For a reliable and verifiable source, I.Kling and B.Horwitz 1851 give the position to the right in which the pawn also does not move.

The main variation given is:

1. K-R4 K-N7

2. K-N4 K-N8

3. K-R3 K-R8

4. N-N3 KN8

5. N-B3 mate.

Made the change. Martin Rattigan (talk) 22:03, 7 July 2015 (UTC)[reply]

I have reverted the change. I would accept changing "The reason" to "The most common reason" per the previous discussion, but the place for giving exceptions to general rules of thumb is not in the lead section of an article, which should summarize the article's contents. Plus algebraic notation should be used, and Kling and Horwitz's position was most certainly not composed in 1986, which would be the implication of the caption as given. Cobblet (talk) 00:00, 8 July 2015 (UTC)[reply]

Cobblet, I don't disagree with your points, but just to be clear, when you say, "I would accept ...", do you mean at a personal level, or do you have some special authority within Wikipedia? Also, I'm new to this but would reverting the whole change be the normal action in this case? The first sentence of DR - Normal Protocol seems to suggest that relocating the offending material and correcting as you think necessary would be more appropriate. [[Martin Rattigan (talk) 08:56, 8 July 2015 (UTC)[reply]

I considered your initial edit to be so poor as to constitute vandalism, and therefore reverted it. Your second effort is a significant improvement. Cobblet (talk) 14:14, 8 July 2015 (UTC)[reply]

From this I take it that you don't have special authorities. As for your first sentence, I can only say, "what a heap of cobblers". You made no mention of this at the time you made your reversal. It should have been clear that the addition was intended to add value to the article. Given that there is no major difference between the content of the first and second edits, only the placement, your accusation of vandalism is clearly untenable. It would be better applied to your summary removal of the change. — Preceding unsigned comment added by Martin Rattigan (talk • contribs) 21:34, 8 July 2015 (UTC)[reply]

Then be careful what you wish for – I'm only clarifying my actions because you're asking me to. Reverting edits that add no value to Wikipedia is standard practice and occurs frequently between established editors. And now you're also asking me to assume good faith. I find it rather hard to do so when the user in question pays more attention to the formatting of their own comments on talk pages than their edits in article space. You've been posting here since 2009 – you've had plenty of time to familiarize yourself with Wikipedia policies. The problems with your initial edit should have been equally clear to you. Cobblet (talk) 22:47, 8 July 2015 (UTC)[reply]

All the points you made in the paragraph starting "I have reverted your change" could and should have been discussed here before making the reversion. See WP:Revert only when necessary.

After the fact I will discuss the points you raise.

(1) You say "I would accept changing "The reason" to "The most common reason""

This would be altering the meaning of the citation so I have not complied.

(2) You say "the place for giving exceptions ... is not in the lead section of an article ..."

The material I inserted was to qualify the sentence, "The reason that checkmate can be forced is that the pawn gives the defender a piece to move and deprives him of a stalemate defense (Müller & Lamprecht 2001:19–20).". This occurs in the lead section, so that is where I placed it to avoid a long range forward reference which would be awkward for the reader. I dropped this to the main Troitsky line section (to satisfy you) and qualified the similar (but unsupported) statement, "The reason for this is that a common technique in this endgame is that of reducing the defending king to a position that would be a stalemate except for an available pawn move, and allowing the pawn to move can allow the attacking knights to move in for the checkmate.". The problem here is that the statement in the lead section is now unqualified. I suggest a solution to this in (6).

(3) You say "algebraic notation should be used".

The descriptive notation I used was historically accurate and intended to make clear that the line given was taken from the source and not my own analysis. Though I do not agree, I have complied with your demand because this is a minor point.

(4) I think we can agree that the date of composition rather than the date of publication of a source is more appropriate in the diagram.

(5) In the meantime Bubba has moved the diagram (again without any discussion) from close to the point where it is referenced to the end of the "Pawn beyond the Troitsky line" section where it is not close to the point where it is referenced. While it is an instance of the pawn beyond the Troitsky line, its purpose is to qualify the second statement referred to in (2), so the move is inappropriate.

(6) Unless anyone has germane objections, I propose to replace the uncited statement, "The reason for this is that a common technique in this endgame is that of reducing the defending king to a position that would be a stalemate except for an available pawn move, and allowing the pawn to move can allow the attacking knights to move in for the checkmate." in the Troitsky line section by the cited statement "The reason that checkmate can be forced is that the pawn gives the defender a piece to move and deprives him of a stalemate defense (Müller & Lamprecht 2001:19–20)." from the lead and delete the statement from the lead. Also to return the Kling & Horowitz diagram to the main Troitzky line section.

Martin Rattigan (talk) 00:12, 9 July 2015 (UTC)[reply]

You made the bold edit, I reverted, and then we had a discussion per WP:BRD. Of course that's not policy, but then neither is WP:ROWN.

I believe M&L's statement is in line with what is generally said about this endgame in the literature and that no qualification of it is necessary in the lead. The "exception" you give applies to a situation where the Troitzky line also does not apply, and I interpret M&L's statement to be commentary on why the Troitzky line exists, not as a general statement about the significance of the pawn in all 2NvP positions where mate is possible. That being said, if you want to remove M&L's statement from the lead entirely, I have no problem with that.

Given that the very first example in the "Troitzky line" section already features a pawn past the Troitzky line, I don't see a problem with your original placement of the Kling and Horwitz position. But I'd consider rephrasing the caption to more clearly say what you're trying to explain, e.g. "White to play mates with 1. Kh4 Kg2 2. Kg4 Kg1 3. Kh3 Kh1 4. Ng3 Kg1 5. Nf3# – the pawn on f2 prevents Black's king from escaping from the corner." I would also use Template:Chess diagram small, make "Kling & Horwitz, 1851" the title of the diagram (compare the other literature positions quoted in the article) and not write each ply-pair on its own line, to reduce the height of the diagram and the amount of displacement of subsequent diagrams.

Understand that these are not "demands" I'm making of you, but rather comments intended to drive the consensus-building process forward. If you can let go of the need to "convince" others of your point of view at every turn (which causes you to write lengthy defences of yourself that nobody gains anything by reading, and makes others suspect you're here more to soapbox than to actually work on content), we can work together. Cobblet (talk) 01:34, 9 July 2015 (UTC)[reply]

Encouraged by the fact that Bubba has not, as yet, reverted the latest change I made, I will try proceeding with the changes as discussed above. Martin Rattigan (talk) 13:23, 12 July 2015 (UTC)[reply]

Since you joined the discussion I have belatedly started to read the Wikipedia policy documentation. Since the quote as it stands is a citation, I don't think it is appropriate to change its meaning, even if only slightly. I will just drop the exception to the Troitzky line section. Martin Rattigan (talk) 04:01, 8 July 2015 (UTC)[reply]

I asked you to read those things on May 30 (above) and again on June 26 on the chess project talk page. Bubba73 ^{You talkin' to me?} 04:07, 8 July 2015 (UTC)[reply]

I read the things you mentioned above, but there is more. It takes some mulling over. After all you, by your own admission will not bother to read the points you are responding to if there are more than five sentences involved.

Cobblet joined the discussion on 23rd. June, so what you are referring to on the 26th. is probably not relevant, but I couldn't actually find it. Martin Rattigan (talk) 05:05, 8 July 2015 (UTC)[reply]

Typo - June 28. Bubba73 ^{You talkin' to me?} 05:16, 8 July 2015 (UTC)[reply]

Yes, still after Cobblet joined, but there is also more to read.Martin Rattigan (talk) 05:30, 8 July 2015 (UTC)[reply]

You could have read it before Cobblet joined the discussion, say, when I gave you links to them and alluded to general guidelines. Bubba73 ^{You talkin' to me?} 05:35, 8 July 2015 (UTC)[reply]

As I thought I'd already said, I did.

Is there any point to this discussion or do you just feel an urge to say I'm a naughty boy? Martin Rattigan (talk) 05:40, 8 July 2015 (UTC)[reply]

I added h1 as a possible mating corner in Averbakh p119 diagram. — Preceding unsigned comment added by Martin Rattigan (talk • contribs) 19:04, 11 July 2015 (UTC) Also added "White to play draws; Black to play loses" to the diagram. — Preceding unsigned comment added by Martin Rattigan (talk • contribs) 19:20, 11 July 2015 (UTC) And added Black to play also in the text for clarity. Martin Rattigan (talk) 19:51, 11 July 2015 (UTC) I left in a1 as one of the corners, but I don't see how it can be forced at the moment. Martin Rattigan (talk) 19:51, 11 July 2015 (UTC)[reply]

Averbakh & Chekhover page 119 diagram

Do Averbakh & Chekover say that checkmate CAN be forced in the h1 corner? IIRC, the authors don't say about h1. Bubba73 ^{You talkin' to me?} 20:01, 11 July 2015 (UTC)[reply]

It's implicit in the theory leading up to this diagram. They don't say anything about which corners Black can be mated in with specific reference to this diagram. Bubba inserted a1 and h8 on 28 Nov 2012, presumably from his own analysis, but I'd like to see how he proposes to force mate on a1. Martin Rattigan (talk) 20:19, 11 July 2015 (UTC)[reply]

Well I've had a look at it and I'm certain Bubba's analysis was just wrong. Here we have more flawed material produced by Bubba and passed off as grandmaster work. I would delete the whole of this sentence, but I suspect Bubba will just revert it if I do. — Preceding unsigned comment added by Martin Rattigan (talk • contribs) 21:59, 11 July 2015 (UTC)[reply]

No, NONE of that is my analysis. If I put in that the mate can be forced in a1 and h8 and cited Averbakh & Chekhover then that is what Averbakh & Chekhover said. Bubba73 ^{You talkin' to me?} 23:20, 11 July 2015 (UTC)[reply]

Well that's tosh I'm looking at the book. And Averbakh & Chekhover were endgame experts, so they wouldn't be saying any such thing anyway. — Preceding unsigned comment added by Martin Rattigan (talk • contribs) 23:54, 11 July 2015 (UTC)[reply]

And you had Muller and Lamprecht saying "Checkmate can be forced in at most thirty-three moves from any starting position (unless the defender can immediately win one of the pieces) (Müller & Lamprecht 2001:19)" for years in the sentence you reverted in the Bishop and knight checkmate article, which is a beginners mistake. And it still says nothing like anything in Muller and Lamprecht.

And you have avoided at all stages actually giving a quote from Speelman et al to support your list of exceptions to your current version of the sentence.

Martin Rattigan (talk) 00:05, 12 July 2015 (UTC)[reply]

Rattigan, if you wonder why people often don't respond to you, then you lack self awareness. I think your snide and sarcastic attitude is enough reason for anyone to try to avoid you. Add that to your lack of understanding of Wikipedia policy and unwillingness to abide by community guidelines, and it makes trying to engage you an invitation for abuse. I'm not surprised that most editors don't care to be abused and think they can make better use of their time. BTW, "it's implicit in the theory" is precisely the sort of thing that WP:OR prohibits. Didn't you say that you had read the key Wikipedia policies? (That was a rhetorical question. I don't really care to know the answer, so you don't have to answer.) Quale (talk) 07:39, 12 July 2015 (UTC)[reply]

Thank you for the counselling.

You will please note my sentence, "I would delete the whole of this sentence, but I suspect Bubba will just revert it if I do.". That is to say I agree that the addition of h1 was prohibited by WP:OR and I'm not objecting to the fact that Bubba has now immediately removed it.

But at least my original research in inserting h1 was correct. Bubba's original research in specifying a1 and h8 was not.

Bubba has not removed his own original research, so the material in question remains incorrect and bogusly attributed to Averbakh and Chekhover. He gives the reason for his change as "(→‎Pawn beyond the Troitsky line: let's stick to what the reference says)", but as he must by now be aware his change does not do that.

I will now try deleting the sentence containing Bubba's OR. If Bubba attempts to reinstate it then given that his error has already been pointed out above, that would, I believe, constitute vandalism. We will wait and see. Martin Rattigan (talk) 08:48, 12 July 2015 (UTC)[reply]

Further, we can agree to dislike each other Quale, if you so wish, but please do not bring this into the discussions. It tends to obscure the serious points.

The issues concerning Martin's most recent edits have been resolved and subsequent conversation has not been productive, so I'm closing this discussion Cobblet (talk) 00:33, 14 July 2015 (UTC)[reply]

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

recent edits

I had to undo four recent edits to fix a destructive one. Bubba73 ^{You talkin' to me?} 15:14, 12 July 2015 (UTC)[reply]

Which one was the destructive one? Cobblet (talk) 18:36, 12 July 2015 (UTC)[reply]

Assuming the earliest one was the "destructive" one, this was the one that deleted the sentence, "With Black to move checkmate can be forced in the a1 or h8 corners (Averbakh & Chekhover 1977:119).". This was a correct removal because, as already indicated above it is (i) original research, (ii) incorrect and (iii) bogusly sourced. Averbakh has no list of possible mating corners for this position. (I think Averbakh has been out of print for many years, so I will upload photocopies of pp.119-120 tomorrow, so interested parties may check this).

I request Bubba to reinstate the reverted changes. These include the changes concerning the role of the black pawn I discussed with Cobblet above.

Martin Rattigan (talk) 21:03, 12 July 2015 (UTC)[reply]

I've already reinstated your changes. Copies of A&C would be most helpful in clearing this up. Cobblet (talk) 21:05, 12 July 2015 (UTC)[reply]

Thanks very much. I'll get them copied & uploaded tomorrow.Martin Rattigan (talk) 22:49, 12 July 2015 (UTC)[reply]

Martin Rattigan removed sourced material with the edit comment "Removed incorrect sentence bogusly attributed to Averbakh and Chekhover." Elsewhere he accused me of putting in my original research, which isn't true. I can't AGF if he didn't even bother to check the reference. I've scanned Averbakh & Chekhover, p. 119, diagram 251 and this is a DropBox link to it. Bubba73 ^{You talkin' to me?} 22:52, 12 July 2015 (UTC)[reply]

We're going to need p. 120 as well. Martin has stated that he has in fact checked the reference, and right now I don't see any mention of the corners in which the king can be mated, only that he can't be mated on a8. Cobblet (talk) 23:06, 12 July 2015 (UTC)[reply]

I'll get it later. A&C state that this is based on the work of Triotsky. In the 2006 reprint of his Collection of Chess Studies, the section "Play against Pawn on KR6", p. 245-50 is relevant, especially diagram # 45, which gives the drawing zone in A&C position 251. Bubba73 ^{You talkin' to me?} 23:42, 12 July 2015 (UTC)[reply]

Here is Averbach & Chekover, pp. 120-21. Bubba73 ^{You talkin' to me?} 23:49, 12 July 2015 (UTC)[reply]

And the Encyclopedia of Chess Endings, the volume on bishop endings and knight endings, position # 1740 is similar (pawn on h3 blocked by a knight, and it demonstrates a checkmate in the a1 corner and a checkmate in the h8 corner. Bubba73 ^{You talkin' to me?} 00:41, 13 July 2015 (UTC)[reply]

A&C explicitly notes in position 253 that mate is possible on h1 or h8. And certainly positions exist (rare and unlikely as they may or may not be; I don't have ECE) where the quickest mate occurs on a1, e.g. W:Kc3, Nd3, h2; B: Ka1, Ph3 is mate in five beginning with 1.Kb3. What the article currently says about positions with the rook pawn on its 6th rank seems accurate. Cobblet (talk) 01:19, 13 July 2015 (UTC)[reply]

There is also relevant information on preceding pages. On page 111, they say "So, the black king lapses into KR1 [a8] and the well-known valley of doom." On page 114, "Since White wins here, regardless of which hideout the black king chooses (QR8 or QR1) [a1 or a8]..." (but that is a position with the black pawn on h4). Bubba73 ^{You talkin' to me?} 01:27, 13 July 2015 (UTC)[reply]

PS - what the article currently says has a sentence that was referenced to A&C p. 119, but now is unreferenced (that MR called "bogus" and my OR). It needs to be referenced, but maybe more pages need to be included (not just 119). Bubba73 ^{You talkin' to me?} 01:30, 13 July 2015 (UTC)[reply]

Obviously the placement of the rook pawn can make a difference. I've done what I can to fix the reference. Cobblet (talk) 02:05, 13 July 2015 (UTC)[reply]

A&C pp119-120 should be up in a jiff. I Don't have a scanner so I had to go out & get these done. Martin Rattigan (talk) 11:31, 13 July 2015 (UTC)[reply]

I gost a bit worried about copyright, so probably best to use Bubba's files. — Preceding unsigned comment added by Martin Rattigan (talk • contribs) 11:41, 13 July 2015 (UTC)[reply]

(a) Re Bubba's point here, if you look at the removed sentence in the edit I so commented you will see it is, "With Black to move checkmate can be forced in the a1 or h8 corners (Averbakh & Chekhover 1977:119).". I repeat this is (i) OR, (ii) incorrect and (iii) bogusly attributed to A&C. This assumes of course that the sentence applies to the printed diagram (essentially 251) and this is stated ("In this diagram ..." at the beginning of the line.). Martin Rattigan (talk) 11:59, 13 July 2015 (UTC)[reply]

(b) Re Bubba's point here:

(i) The reference to other books is not relevant. The citation is for A&C p.119. If anything is inserted based on other material this is OR as stated in my edit.

(ii) Diagram Troitsky Chess Studies # 45 contains only the h2/h3 pawn and knight, so is not too relevant to the printed position.

(iii) I don't have Encyclopedia of Chess Endings, but position # 1740 is not the position printed. Mate in a1 cannot be forced from the position printed. Martin Rattigan (talk) 12:32, 13 July 2015 (UTC)[reply]

(c) Re Cobblet's point here:

(i) I have never said that there are no positions with the pawn on h3 and a knight on h2 in which white can force mate on a1; only that the printed position is not one of them.

(ii) In position 253, just as in position 251, mate can be forced only on one of h1 and h8 (Black's choice of which).

(iii) The post seems to be straying into the area of "future" rather than "recent" edits. If you agree I'll open a new section for enhancements to this paragraph.Martin Rattigan

(talk) 12:59, 13 July 2015 (UTC)[reply]

(d) Re Bubba's point here:

(i) This is arguably also straying into the area of "enhancements" I mentioned.

(ii) In A&C p.111, the "Valley of doom" refers to Bolton's position 235. This is part of what I referred to in my phrase "it's implicit in the theory ..." in the section "Averbakh & Chekhover page 119 diagram". Quale argues here that using this is OR, and I have to say I agree.

(iii) P.114 is irrelevant because, as you say, the pawn is on h4.

Martin Rattigan (talk) 13:48, 13 July 2015 (UTC)[reply]

(e) Re Bubba's point here:

(i) It was the sentence that I removed that I called bogus and your OR (see (a)), not the sentence, "Black cannot be checkmated in the a8 corner because the knight on h2 is too far away – the pawn would advance.". I left the latter in because I thought a reference could be found for it. Cobblet has done that.

(ii) There are a lot of sentences in this article. Could you be more specific than just referring to "a sentence" when you discuss them please? It would simplify things.

Martin Rattigan (talk) 14:08, 13 July 2015 (UTC)[reply]

Martin, would it kill you to stop making comments that serve no purpose other than to defend views you previously expressed? This is exactly the kind of behaviour I spoke to you about earlier and if you persist I will once again stop assuming good faith from you. If you wish to make further changes to the article, discuss them succinctly (or edit boldly, though you may be reverted per BRD). Cobblet (talk) 14:24, 13 July 2015 (UTC)[reply]

Point taken.

I've formed a habit of making a point by point reply to posts because these are generally in opposition to any changes I propose, and I expected if I made a change without replying to some point I could find myself unable to log in next time I tried owing to charges of vandalism. This obviously wasn't actually necessary in this exchange because I'm not planning any changes here. Sorry.

On the other hand Bubba does appear to be already saying I acted in bad faith in his first second and seventh posts in this section, so I think it was right to reply to those. Martin Rattigan (talk) 21:25, 13 July 2015 (UTC)[reply]

You got the changes you wanted, and still you feel the need to point out how what you do is justifiable and what everyone else does isn't. Nobody here is perfect, but you are being particularly tiresome. Cobblet (talk) 21:54, 13 July 2015 (UTC)[reply]

Martin, here are just two quotes from you:

Bubba has not removed his own original research, so the material in question remains incorrect and bogusly attributed to Averbakh and Chekhover.
(i) original research, (ii) incorrect and (iii) bogusly sourced.

You accused me of giving wp:or and that the reference was bogus, which the scan of the pages from the book disprove. Bubba73 ^{You talkin' to me?} 22:21, 13 July 2015 (UTC)[reply]

And you also said (above): "(a) These are draws (with black to move in the A and B positions, mostly with either side to move in the C positions). There is no stronger side"

Quoting Yuri Averbach in Comprehensive Chess Endings, "A term which is frequently employed in this book is the 'stronger side', by which is implied the player who has either a material, or positional advantage." Bubba73 ^{You talkin' to me?} 22:52, 13 July 2015 (UTC)[reply]

Bubba, you need to stop this as well. Martin was right about the original statement in the article concerning A&C's position 251 being inaccurate. And all this fuss over what "the stronger side" means in a drawn endgame is hardly the most pressing of the many issues with the paragraph on the Troitzky line. Cobblet (talk) 00:29, 14 July 2015 (UTC)[reply]

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

(deleted unused section here) Martin Rattigan (talk) 23:02, 14 July 2015 (UTC)[reply]

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.

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Black's chances in KNNKP

I am reinstating my edit regarding Black's chances in KNNKP. This was reverted by Jasper Deng, but his reasoning is incorrect. There are many positions similar to the one I posted here where it is impossible for White to either exchange knight for pawn or draw the resulting KNNKQ ending.

@Martin Rattigan: And we don't give such attention to such positions since they should be easily avoidable. White knights on a8 and c8, black pawn on h2, kings far away from all pieces is of course a lost position for White, but so are many other positions in otherwise winning material combinations (such as white king on a1, black king on b3, black rook on c1, white queen on a4). We don't need to give them this much attention. Please don't use WP:OSE-type reasoning, it isn't really convincing.--Jasper Deng (talk) 16:14, 28 September 2017 (UTC)[reply]

@Jasper Deng: You may not give any Black won positions your attention, but they are part of the theory and as such belong in Wikipedia. There are many Black won positions that could easily occur in play (mostly with the pawn further advanced). The previous text doesn't even give any indication of how Black should go about drawing in the 70% of positions that are theoretical draws.

The KQKR position you mention appears to be illegal, but drawn positions in that endgame are certainly considered in Averbakh, and necessary for an understanding of KQKR (as indeed are the Black won positions).

@Jasper Deng: You say, "White knights on a8 and c8, black pawn on h2, kings far away from all pieces is of course a lost position for White", but if the White king on g3 were instead on g4 (arguably further away) in the position I posted then White can draw. Or with the placings you suggest:

	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 draws.

	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 loses.

For a more practical example, what would you play here as White? (Or is this also a position that you would easily avoid getting into?)

	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.

(Note: I've edited the previous position to give White a trickier task.)

@Jasper Deng: By the way, when you say, "... we don't give such attention to such positions ...", is that the royal "we" or are you referring to a group with preferential rights over the content?

Martin, there are some serious problems with your edit. For instance, twice you have "Checkmate position, but it cannot be forced from positions with the same material" - but it checkmate CAN be forced in many positions with the same material. In one case, you made that change in a sentence, and the sentence is referenced, and the reference most definitely does NOT say that. Bubba73 ^{You talkin' to me?} 23:33, 28 September 2017 (UTC)[reply]

@Bubba73: Yes, I agree that the statement in the Diagram is putting words into Sierawan's mouth, I will change it. But checkmate in KNNK cannot be forced from any position with the same material, so I think the (unattributed) sentence in text is OK. The previous text said simply "cannot be forced", which is incorrect.

@Bubba73: Changed.

There are more problems too. To start at the top, you inserted "n studies, ... " - this doesn't apply to just studies, it applies more broadly to endgames. Bubba73 ^{You talkin' to me?} 00:02, 29 September 2017 (UTC)[reply]

Next, you inserted "It can be forced from a position with extra Black material." I think this is irrelevant because the article is not about such endgames. Bubba73 ^{You talkin' to me?} 00:06, 29 September 2017 (UTC)[reply]

@Bubba73: Quite clearly, of positions where White has two knights, those where Black has just a pawn form only a tiny minority. What else did you intend by your original statement except "in studies". If not in studies in what context is the opposing material usually a pawn? I could hardly change it to, "In endgames, the material with the defending king is usually one pawn", because that is obviously nonsense. I could change it to, "In studies where there is extra material, ...", but there really aren't any studies where there is no extra material.

"Studies" are composed endgames. These occur in actual games. Bubba73 ^{You talkin' to me?} 00:53, 29 September 2017 (UTC)[reply]

@Bubba 73: The mates are in KNNK. The original statement that the mates cannot be forced is simply incorrect.

Checkmate cannot be forced with KNN vs. K. Bubba73 ^{You talkin' to me?} 00:53, 29 September 2017 (UTC)[reply]

@Bubba73: I entirely agree. But the checkmate positions with this material that you show can be forced. To say otherwise is simply incorrect.

Repeat: you cannot force checkmate with KNN vs. K. Read the references. Bubba73 ^{You talkin' to me?} 01:22, 29 September 2017 (UTC)[reply]

Are you seriously maintaining that in actual games where one side is reduced to two knights his opponent normally has exactly one pawn? Martin Rattigan (talk) 01:09, 29 September 2017 (UTC)[reply]

Not often but it DOES happen in actual games. There are some referenced in the article:

Topalov vs. Karpov, 2000
Wang vs. Anand, 2009
Pollock vs. Showalter, c. 1890
Motwani vs. I. Gurevich 1991 Bubba73 ^{You talkin' to me?} 01:28, 29 September 2017 (UTC)[reply]

The original was, "The material with the defending king is usually one pawn, ...". What was it supposed to mean? It hardly seems to mean "not often".Martin Rattigan (talk) 01:28, 29 September 2017 (UTC)[reply]

~~OK, that little bit should be expanded "in cases where the side with two knights can force checkmate.".~~ Bubba73 ^{You talkin' to me?} 01:30, 29 September 2017 (UTC)[reply]

Scratch that - the actual sentence is "In studies, the material with the defending king is usually one pawn, but some positions studied involve additional pawns or other pieces." - which is accurate. Bubba73 ^{You talkin' to me?} 01:32, 29 September 2017 (UTC)[reply]

Good - are you now happy with the edits as they stand? Martin Rattigan (talk) 01:47, 29 September 2017 (UTC)[reply]

I haven't been able to go through all of your edits yet, but with so many problems in what I've read so far, it is likely that there are more problems. Bubba73 ^{You talkin' to me?} 01:49, 29 September 2017 (UTC)[reply]

"Repeat: you cannot force checkmate with KNN vs. K. Read the references.". I don't have to read the references - I already agreed that. Read my comment. Martin Rattigan (talk) 01:53, 29 September 2017 (UTC)[reply]

The only problem you have pointed out so far is that I inserted text into a sentence that was ascribed to Sierawan. I have fixed that. The other things you have called problems are not. There were problems with the orignal page that my edits have hopefully fixed. Martin Rattigan (talk) 01:59, 29 September 2017 (UTC)[reply]

There are a lot of problems. You inserted a lot of needlessly complex and confusing material that wasn't sourced. You don't get to create a novel treatment of endgame theory in Wikipedia. Wikipedia presents the results found in the literature in much the same way that the literature does. I sense that you aren't satisfied with the way the Mednis and others present this material, but that's too bad for you. Unless you can find a reliable source that shares your peculiar approach to this, it can't go in the article (WP:NOR). Quale (talk) 08:20, 29 September 2017 (UTC)[reply]

@Quale: Ah. Mr. Quale. Nice to hear from you again. I shall insert the necessary references, but what exactly do you find needlessly complex? I shall endeavour to simplify it for you. KNNKP is in fact a complex endgame. Why, by the way, have you reverted all the edits. Are you intending to fix the inaccuracies in the original yourself? Please do so, or reinstate the edits you can understand.

Since Quale, with his customary urbanity, has failed to respond to the above question or reinstate any of the edits he reverted, I will reinstate them in stages to see which, if any, he will again delete.

I have added "[blockading]" to the text attributed to Dvoretsky in para2. Without this the phrase "other knight", used twice, refers to different knights and is confusing. I don't know whether this confusion is present in the original or introduced in the author's paraphrasing because I don't have Dvoretsky. I would be grateful if someone who has Dvoretsky can check, and if the confusion is not present remove the brackets.

Dvoretsky calls the knight that is blockading the pawn the "spare" knight. Bubba73 ^{You talkin' to me?} 01:24, 1 October 2017 (UTC)[reply]

OK. Your origianal text referred only to "other knight" twice in each case meaning different knights. In any case I'm sure you'll agree that "blockading knight" is clearer than "spare knight" also. If you're happy with the new version please remove the brackets round "blockading".

Name of the article

I have always understood the phrase "two knights endgame" to refer only to the material covered under "Two Knights cannot force checkmate". To use the name to refer also to endgames of the type two kights v other material requires a citation prior to 2 Jan 2005 where these are referred to as the "Two knights endgame". I have added the relevant "citation needed" flags.

No, that would be a one-paragraph article. It is about two knights versus possibly additional material. Bubba73 ^{You talkin' to me?} 00:51, 1 October 2017 (UTC)[reply]

Yes I know what it's about; my concern is that it's not about what the title says it's about. You can't rename an endgame via Wikipedia. If you can find a citation prior to the introduction of this article that calls two knight v other material "the two knights endgame" please insert it.

Martin, you are messing up the article in major ways. No Bubba I'm not.

Martin, you are messing up the article in major ways. For instance, you changed "On the other hand, if the weaker side ... " to "On the other hand, if the opponent of the player with the two knights ..." - which is absolutely wrong. It is if the player WITHOUT the two knights has some additional material, a forced checkmate may be possible. This, and other things, makes me think that you truly don't understand this article. Bubba73 ^{You talkin' to me?} 00:50, 1 October 2017 (UTC)[reply]

Martin, you've made such a mess of this article with many edits that are hard to follow, that I propose reverting it back to the way it was before and then discuss the changes you want to make, one by one, on the talk page. Bubba73 ^{You talkin' to me?} 01:12, 1 October 2017 (UTC)[reply]

@Bubba73:

1. In a two knights v other material endgame the side with the other material is not necessarily weaker. Even in KNNKP Black may win. In KNNKQQQ he usually would. I think it's you who do not understand the material.

In KNNKQQQ the side with two knights is NOT the weaker side. Bubba73 ^{You talkin' to me?} 23:04, 1 October 2017 (UTC)[reply]

@Bubba73:: I've just noticed this. Please post at the end.

I beg to differ. Three queens will almost invariably beat two knights.Martin Rattigan (talk) 05:05, 2 October 2017 (UTC)[reply]

2. I have not messed it up. I've improved it.

3. I am about to add a note on the changes to the problems section.

4. By all means begin discussing. (I've answered your first point.)

5. Please do not revert unless you have some valid reason.

Martin Rattigan (talk) 03:14, 1 October 2017 (UTC)[reply]

No, you have changed things that are true to things that are false. Bubba73 ^{You talkin' to me?} 21:56, 1 October 2017 (UTC)[reply]

@Bubba73: Could you please insert your comments at the end of the text in the section? That way people will notice them and, for anyone reading, the comments will be in chronological order, which makes the arguments much easier to follow. How do you expect anyone to notice something you've posted 40 lines back?Martin Rattigan (talk) 02:53, 2 October 2017 (UTC)[reply]

There are so many problems with the way you edit articles and talk pages on chess endgames that this reply is much longer than I would prefer. I don't like tl;dr walls of text on talk pages, and that's actually one of the things you do routinely. I think it rarely if ever helps to resolve anything, since the natural response to tl;dr is another tl;dr wall of text, but I don't see any other way to respond except to just let it go. Because there are many issues both this week and from when you erupted on this page in 2015, I'm going to start from the very general and work my way down to the more specific.

If you look at this talk page the one serious issue other wikipedians face when trying to work with you should jump out at you instantly. By my count, you have made 83 of the last 100 edits to this talk page. Trying to work with you on talk is absolutely exhausting. If you are trying to engage other editors and hope to begin a dialog I think you will have more success if you change your approach a bit. If instead you are not interested in dialog and you merely intend to lecture other chess editors then I suspect it is still not very effective. Few people have the time or stamina to try to plow through the text walls you dump on talk.
Generally here and at other chess endgame pages you seem to be crusading to right wrongs. This is not the best reason to edit an article, and it usually leads to trouble. You take an overly lawerly approach that disregards common sense and convention used by writers in the field. This leads to gratuitous complexity and makes it difficult for the reader to follow what you're trying to say. Experience in chess helps less than one would expect since often you approach standard topics obliquely that your presentation doesn't resemble the source material very closely. This actually applies pretty equally to you edits on the articles and to what you write on the talk pages.
This said, you do highlight some things that can be improved. For example, when you question whether it's true that the defending side is usually K P, that's a very good point. If it's true it needs a good cite, but very possibly it is not true. It does show up in endgame texts frequently, but if that is what is meant then the article should state it that way and cite it. Possibly this claim should just be removed. It isn't clear to that it's true and I don't think it's very important.
On the other hand, some of your recent edits are simply bad. The article had said "On the other hand, if the weaker side also has material, checkmate is sometimes possible." Although your concern that the side with the two knights might not be the stronger side is reasonable, your edit to try to fix this is not good. "It can be forced from a position with extra Black material" is simply not true when read naturally with "a postion" meaning "any position" or "all positions" rather than "there is one position where this is true". Sometimes it can be forced. It is just odd that someone who is so nitpicky about other people's edits would change the text to something that is just confusingly wrong. A better fix is needed. If the article notes the convention that White is the side with the two knights then "The two knights can force checkmate from some positions where Black has extra material" might work, or maybe "from some positions where the defender has extra material" instead of saying "Black".
This is another unfortunate change. You changed the text "Although there are checkmate positions with two knights against a king, they cannot be forced" to "Although there are checkmate positions with two knights against a king, they cannot be forced from positions with the same material." What is "from positions with the same material" supposed to mean? That sentence doesn't make sense in the English language, and I suspect that it is a logic issue and wouldn't make sense in any language. The original sentence was correct and makes sense, your "improvement" isn't and doesn't. It's confused thinking that muddies a simple statement about KNN vs K.

That's more than enough for now. I do appreciate your attention to technical detail and your energy to try to polish the presentation of chess endgames, but you've made 28 edits to the this article in the last 2 days and I think several of them did not improve the article. I think it's unreasonable to expect anyone else to work through that many edits to try to rescue one or two small but not really essential improvements when the edits include obvious mistakes like the two I pointed out above. That is why I reverted. Quale (talk) 07:23, 1 October 2017 (UTC)[reply]

@Quale:

Your points 1 & 2 are just lecturing. I will ignore.

I agree with your point 3. The original sentence was meaningless, I've changed it to what I suspected was meant, which Bubba eventually agreed, but if no citation is forthcoming for what it now says I will delete it.

As for point 4 you consider two different changes:

(a) I changed "On the other hand, if the weaker side also has material, checkmate is sometimes possible" to "On the other hand, if the opponent of the player with the two knights also has material, checkmate is sometimes possible". This for exactly the reasons you describe. On what grounds do you say the change is not good?

(b) I amended "Checkmate position, but it cannot be forced (Seirawan 2003:17)." to "Checkmate position, but it cannot be forced.^[3] It can be forced from a position with extra Black material.^[2]". Your suggestion that this would be taken to mean it could be forced from all positions with extra Black material (which would include the initial game position) is unlikely but I have changed the second sentence to "It can be forced from some positions with extra Black material^[2]." which can't be misinterpreted. The point is that the original was false and the replacement is true.

Point 5 is just ridiculous. The phrase "with the same material" means with the material mentioned earlier in the same sentence and would obviously be taken as such by anyone who was not just intent on preventing others from making changes to text he considered to be his personal property. Again the replaced text was false and the replacement is true.

If you have trivial quibbles about phrasing, the answer is to amend the phrasing to your liking, not to have a knee jerk reaction of reverting everything that has been changed.

You've written quite a lot of text. Can you say what the two obvious mistakes you refer to are? I've made a slight alteration to the phrasing of one sentence, which I wouldn't count as a mistake. What's the other?

Martin Rattigan (talk) 15:11, 1 October 2017 (UTC)[reply]

@Quale: You say in point 5., "The original sentence was correct and makes sense, your "improvement" isn't and doesn't.", which is quite the opposite of the truth. If you don't understand why and you don't have access to the cited reference I included, you need only look back to forced mating position? earlier in this talk page. But preferably check your facts before reverting other people's changes.

Quayle is right about #5 and other things. There is even a reference for it. I think the best thing to do is to revert it back to the way it was and discuss the changes one at a time on this page because it is too difficult to sort through your maze of edits. Bubba73 ^{You talkin' to me?} 22:03, 1 October 2017 (UTC)[reply]

@Bubba73: You yourself inserted two problems (de Musset and Sobolevsky) that finish up with a forced mate that you state is impossible to force. Please try to understand the subject matter you are writing about. If you have a reference to say the mates are impossible to force then either you have taken it out of context or the reference is incorrect. If the latter you don't need to include it in Wikipedia.Martin Rattigan (talk) 22:55, 1 October 2017 (UTC)[reply]

In both of those positions, the side with the two knights started with additional material. A king plus two knights cannot force checkmate against a lone king. Have you even read the first sentence of the article: "The two knights endgame is a chess endgame with a king and two knights versus a king, possibly with some other material." Bubba73 ^{You talkin' to me?} 23:00, 1 October 2017 (UTC)[reply]

Exactly. The positions can be forced with a king and two knights versus a king with some other material. If you say they can't be forced that is incorrect. I corrected it. Martin Rattigan (talk) 23:56, 1 October 2017 (UTC)[reply]

In both positions White loses any additional material before the checkmate occurs. The mate is then forced from a position as described in the first sentence, but that is not even relevant to whether a statement that the mate can't be forced is correct or not. If you agree that the mates can be forced, as you do, then you can't have a sentence that says they can't be forced. It needs qualification - which I inserted. Martin Rattigan (talk) 00:04, 2 October 2017 (UTC)[reply]

I've reinserted the "citation" flags you deleted. There are no citations so there can be no argument about that. I'd already checked BCE without luck. The stalemate sentence is obviously correct - it just needs a citation.Martin Rattigan (talk) 00:12, 2 October 2017 (UTC)[reply]

@Bubba73: I see you found a citation for the "stalemate" statement, but you appear to have accidentally deleted two others I inserted. I've replaced them. I take it you agree there are no citations in the relevant places. (See Name of the article.)Martin Rattigan (talk) 02:34, 2 October 2017 (UTC)[reply]

Sorry make that three. I've inserted the other one too.Martin Rattigan (talk) 03:02, 2 October 2017 (UTC)[reply]

Changes to the "Checkmate in problems" section.

I have made some changes to the "Checkmates in problems" section as follows:

1. I've changed the name to "Composed positions" to allow for editors adding "x to play and draw" problems. (There is an anchor to the old name at the same point.)

2. I've amended the introductory sentence to refer to "two knights v other material" rather than "two knights v pawn", since none of the problems shown except the one I have inserted are related to two knights v pawn.

3. I've inserted missing header for Berger's problem

4. I've moved the problems that end in a two knights mate at the edge of the board to the front to correspond with the order in the introductory sentence.

5. I've replaced the Nadanian problem with a Troitzky problem because the Nadanian problem didn't fall within the topic of the article.

6. I've changed the citations to "ref" type and moved them to the start of each problem to improve readability.

Martin Rattigan (talk) 04:13, 1 October 2017 (UTC)[reply]

I would like to include the following position as a nontrivial example of two knights winning against notionally superior forces. (There are no such examples in the article at the moment.) I have my own solution, but don't know of an acceptable reference for either the position or a solution. I would be grateful if a helpful reader of the talk pages could point me to such or suggest a similar published example.

Ottó Bláthy, 1904

	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 50

@Bubba73: I think, the Sobolovsky position needs to at least include more analysis.I don't have Nunn's book, but surely he must have given more than just this line. The reader may well wonder why Black can't simply play 1...Ke6. I can't see any particularly forcing line for White after that, though Nunn may have demonstrated one in the book. The attack on the h7 knight with the given move means nothing. If he takes he's in a lost KBNK ending. Either way he will finish up in a KBNNKN or KBNNKB ending and similarly after Nunn's suggested move 8. But these endings don't exactly fall within the article's topic. I would prefer to find a more germane example with an edge mate theme if possible. What do you think?

Your discussion doesn't seem to match the position. Also, use four tildas to sign your name on the talk page. Bubba73 ^{You talkin' to me?} 22:17, 1 October 2017 (UTC)[reply]

Sorry about the tildes - no doubt the bot will fix. Don't understand your comment - I'm talking about the Sobolevsky position in the "Composed positions" section. You inserted it in 2008. What doesn't match? Martin Rattigan (talk) 22:31, 1 October 2017 (UTC)[reply]

Sorry, I thought your comments were about the position above. Bubba73 ^{You talkin' to me?} 23:34, 1 October 2017 (UTC)[reply]

@Bubba73:: You just reverted this section again without any discussion. I was not aware of any controversy about these changes. Please say why.

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)[reply]

@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)[reply]

@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)[reply]

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)[reply]

@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)[reply]

@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)[reply]

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)[reply]

@Jasper Deng:: 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)[reply]

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

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)[reply]

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)[reply]

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)[reply]

@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)[reply]

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

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]