Second Troitzky line and Syzygy.

[Martin Rattigan]

Does anyone know if the second Troitzky line result http://www.chesscafe.com/text/mueller36.pdf has been verified using Syzygy DTM50? (I think you have to interpret "securely blockaded" in the article to mean the other knight defends the blockading knight, or it obviously can't be verified).

[syzygy]

I'm guessing that "securely blockaded" means that the knight cannot easily be chased away by the enemy king. Unfortunately that is not a very clear definition.

[Martin Rattigan]

Thanks for your reply.

I agree that "securely blockaded" is unclear. I think the only good definition is "a knight blockades (stands directly in front of) the pawn and is guarded by the other knight". With other plausible definitions the positions I gave in viewtopic.php?f=6&t=8145 as well as immediate captures or forks by Black would be exceptions to the rule. This definition is implied, though unfortunately not explicitly stated, in Müller and Lamprecht Fundamental Chess Endings, with regard to the first Troitsky line. I have an email from Dr. Müller confirming that the wording in FCE was chosen to handle the possible exceptions. (See the discussion here.)

Am I right in thinking that Syzygy DTM50 tablebases are available for download or generation?

[Martin Rattigan]

I would guess from your previous reply that you know of no analysis of the "second Troitzky line" result (with a specific meaning of "securely blockaded" such as the one I suggest) using a DTM50 database. From the very limited analysis I have done myself (with the aid of the Nalimov DTM50 database) I suspect there may not be a second Troitsky line, but rather second Troitsky positions for the blockaded pawn.

[syzygy]

I agree that "securely blockaded" is unclear. I think the only good definition is "a knight blockades (stands directly in front of) the pawn and is guarded by the other knight".

But would that not greatly diminish the significance of the second Troitzky line?

For the first Troitzky line (where the 50-move rule does not count) it probably makes no difference. If the blockading knight cannot be chased away, then surely a position can be reached where the blockading knight is protected by the other knight. So "guarded by the other knight" and "cannot be chased away" most likely are equivalent. (I guess there are some exceptions, as you show on Wikipedia.)

For the second Troitzky line (where the 50-move rule does count), this equivalence is gone.

When actually playing a game and reaching a KNNvKP position, the first goal for white seems to be to block the pawn with one of its knights. If that can be done within the second Troitzky line, you still don't know if the game can be won as the blockading knight is probably not (yet) guarded by the other knight. On the other hand, even if the second Troitzky line would use "my" definition of securely blockading, it is possible that part of the 50-move counter has already elapsed at the point the blockading position is reached. So my definition is not perfect either. (Nothing beats a full KNNvKP tablebase with 50-move info .)

Am I right in thinking that Syzygy DTM50 tablebases are available for download or generation?

It is not DTM50, but DTZ50 (distance-to-zero, i.e. mate, pawn move, or capture), but that is what you need here. Available for download and for generation. Using them for verifying the Troitzky lines is a non-trivial programming exercise. The easiest approach might be to start from python-chess:
http://python-chess.readthedocs.org/en/ ... yzygy.html
https://pypi.python.org/pypi/python-chess

Computationally the most efficient way would be to hack the generator (rtbgenp) to save uncompressed WDL50 data to disk for each pawn file (a, b, c, d). Then a program could load those files into memory and quickly look at all relevant positions. But this is probably not efficient in terms of programming time.

[syzygy]

I would guess from your previous reply that you know of no analysis of the "second Troitzky line" result (with a specific meaning of "securely blockaded" such as the one I suggest) using a DTM50 database. From the very limited analysis I have done myself (with the aid of the Nalimov DTM50 database) I suspect there may not be a second Troitsky line, but rather second Troitsky positions for the blockaded pawn.

I'm indeed not aware of such analysis, except that I've learned from you that Karsten Müller has looked into this.

Note that the Nalimov tablebases are not DTM50, but DTM. They do not take into account the 50-move rule. Of course if Nalimov says a position can be won within 50 moves, then it can be won within the 50-move rule, but that's about all that can be derived easily from Nalimov. In particular, the fact that a position's optimal winning line according to DTM complies with the 50-move rule is neither sufficient nor necessary for that position to be a win within the 50-move rule.

The ChessCafe article (link, seems to be behind a paywall now) mentions that the Nalimov tables were used to solve the second Troitzky line. It might therefore be flawed.

Just discovered this very nice web interface:
https://syzygy-tables.info/?fen=8/8/8/5 ... 0-%200%201

Not usable for checking the full Troitzky line, obviously, but nice to play around with.

[Martin Rattigan]

(syzygy - I read your answers backto front, so I'm afraid my replies are also.)

Apologies again for the delayed reply.

The second Troitzky line analysis was done by Helmut Conrady, Dr. Müller asked the question in the first part of one Chess Café article and publicized Conrady's response in the second.

I've always been sceptical about the accuracy. I spent the best part of two days analysing just one of the simplest (DTM 52) endings to take into account the 50 move rule, with the aid of the Nalimov databases used along the lines you mentioned. If Helmut Conrady managed this for all endings between the two articles it seems to me to have been a superhuman effort. The 50 move rule adds an order of magnitude to the difficulty of playing this ending.

The articles are still available free online somewhere but they're hard to find and I've lost them again. This llink to my dropbox will do in the short term.

https://www.dropbox.com/sh/crrcvw1idk3a ... uSRwa?dl=0

Thank for the link. I'm actually planning to download your generation code and try a bit of programming for myself.
P.S. The list of positions I posted here (viewtopic.php?f=6&t=8189#p88851) suggests that both the Troitzky line rule and the second Troitzky line rule are incorrect however you interpret "securely blockaded".

[Martin Rattigan]

But would that not greatly diminish the significance of the second Troitzky line?

That would depend on what Helmut Conrady had in mind as the meaning of "securely blockaded".

I think Müller and Lamprecht Fundamental Chess Endings means exactly what I gave by "securely blockaded" in the case of the first Troitzky line, but whether that was Conrady's intention regarding the second is open to question. Certainly all exceptions to the first line rule are also exceptions to the second line rule with the same interpretation of "securely blockaded" being used in each. The positions I gave in viewtopic.php?f=6&t=8145#p88303 are all actually schemes and represent rather a lot of different exceptions in total to interpretations of the phrase other than the one I used. One could take the view that the significance of a rule diminishes as the number of exceptions increases.

For the second Troitzky line (where the 50-move rule does count), this equivalence is gone.

Agreed (roughly speaking, because " the knight cannot easily be chased away by the enemy king" is not a lot clearer than "securely blockaded" - is the knight chased away by the enemy king in 8/8/8/8/7p/1K5N/5N2/1k6 w - - 0 1 for example?). Hence a specific meaning of "securely blockaded" is even more important in this case. In fact it seems the second Troitzky line rule is to some extent incorrect for any plausible meaning, irrespective of whether the dots are actually in the right place. (It's not obvious to me that it should even be a line).

When actually playing a game and reaching a KNNvKP position, the first goal for white seems to be to block the pawn with one of its knights. If that can be done within the second Troitzky line, you still don't know if the game can be won as the blockading knight is probably not (yet) guarded by the other knight.

I made the same point on the Wikipedia talk page some years ago. When I looked through recorded games I found that about half became knnkp with the pawn already blockaded, I think partly because these occur after a swap of White's last pawn, as one of a pair of blocked pawns, or maybe the knnkp ending is already being played before it is reached with one eye on the second Troitsky line. If this is not the case the second Troizky line rule seems to be pretty irrelevant. More relevant would be max DTM50 values for each of the squares.

By the way when I practice these endings I find it better to think of the blocking and guarding as a single process. I just do this as far back as possible without particularly thinking of the (first) Troitzky line. I say first because I just try to hit the DTM and reset the move counter as necessary (playing against Nalimov EGTBs). Of course if the pawn is blockaded and you already have control of the black king with the other pieces you don't go back to a "Troitzky line" position.

I put a couple of pgns in the same dropbox link mentioned in the previous reply to better explain. In draw_trap the pawn can be stopped on d4, but you can't play 1. Nd3 immediately, otherwise 1. ... Ke4 draws. I played 1. Kb4 to temporarily protect the d4 square. After Black's third move the other knight has to come in to give a Troitsky line position with mutually protecting knights. In Rybka_bad_hair Nc4, Kd2-c3 will blockade the pawn on c5 and protect the blockading knight, but this is no use because the black king can attack the corner knight instead. So I had to go for a blockade with the pawn on c3 instead (this is past the Troitsky line, but ok with the black king excluded from the a1 corner). A Troitsky line position with mutually protecting knights then comes on move 5. In the second example after say move 25, a Troitsky line position with mutually protecting knights could be set up on the next move (so the position is won) but you wouldn't want to actually do that.

Nothing beats a full KNNvKP tablebase with 50-move info.

Agreed. Especially not me.

That's why I'm asking for some easy positions (viewtopic.php?f=6&t=8147) to get started.

Thanks for the technical info. I can see I'll have to get down to doing some programming again. I think the DTZ50 EGTBs will also be OK for practicing with the 50 move rule in effect.