Anyone know maxDTM and mzugs for KRNPKR?

[yrobinso]

I have been using tablebases to analyze some endings, and I have found that although all 6-men tablebases are available (except for 5 vs. 1), the data-mining results are not available for the newer tablebases. Specifically, I cannot find maxDTM and/or maxDTC wins, a list of mutual zugzwangs, and the longest DTM/DTC mutual zugzwang for the 6-men pawnful endgames.

Data for 3-5 endings and pawnless six-men endings has been published, both in the ICGA journal and more extensively on the web. I have placed links to separate sites dealing with maxDTM for 3-5 men and John Tamplin's mutual zugzwang list at the Wikipedia article on endgame tablebases: http://en.wikipedia.org/wiki/Endgame_tablebase.

I am wondering if such data is readily available for pawnful six-men endings. Perhaps that's what Wilhelm and eMule are for, but I don't know the first thing about those programs.

In particular, I have taken an interest in the KRNPKR endgame. Somewhat by accident, I discovered an incredible series of mzugs, and that discovery raised more questions, which I have begun to analyze. I want to know what is the maxDTM and if there are any mzugs other than the ones I have found.

The longest DTM win I have found so far is 75 moves, as shown in the first diagram below. (Note that the longest DTM for KRPKR is 74 moves.) At first it seems remarkable that White can win this at all, until you realize that the knight on a8 is close enough to threaten a check on f4 in only three moves. Exclamation points stand for only-winning moves.

N7/8/8/8/r7/3R3P/3K2k1/8


1. Nc7! Ra2+
2. Kd1! Ra1+
3. Kc2 Re1
4. Nd5! Re2+
5. Kc3 Re4
6. Kd2!!

This is mutual zugzwang: wtm draws; btm loses with DTM = 69

8/8/8/3N4/4r3/3R3P/3K2k1/8


6...Ra4
7. Ne7 Rf4
8. Kc3!!

A second mutual zugzwang, DTM = 67.

8/4N3/8/8/5r2/2KR3P/6k1/8


8...Ra4
9. Kb3 Rf4
10. Rc3

A third mutual zugzwang, DTM = 65.

8/4N3/8/8/5r2/1KR4P/6k1/8


10...Kh2
11. Ng6! Rf6
12. Ne5! Rh6
13. h4! Kg2
14. Nf3 etc.

I have produced extensive analysis of this endgame, starting from a slightly different position, but I do not intend to publish it in this forum for now. The other six zugzwangs are as follows. They are all similar in form to the three for which I have posted diagrams already.

8/4N3/8/8/5r2/3KR2P/6k1/8, DTM = 44
4N3/8/8/5r2/3KR2P/6k1/8/8, DTM = 40
4N3/8/8/5r2/2KR3P/6k1/8/8, DTM = 71
4N3/8/8/5r2/1KR4P/6k1/8/8, DTM = 69
4N3/8/8/5r2/KR5P/6k1/8/8, DTM = 70
8/8/8/N7/1r6/R3P3/K2k4/8, DTM = 38

It is noteworthy that 8/4N3/8/8/5r2/KR5P/6k1/8 is a draw even with Black to move, even though all similar positions are zugzwang. The reasons for this are very interesting. Once again, I will not provide the analysis here because it would take too much time to write it out.

Can anyone tell me if there are other mzugs in KRNPKR besides these nine, and if there is a maxDTM longer than 75 moves? I am curious, and I suspect that somebody (Guy Haworth, perhaps?) either knows already or is capable of finding out.

Thank you to anyone who is willing to answer this question.

[Kirill Kryukov]

Hi Yechiel,

I am collecting longest direct checkmate positions (wtm maxDTM) on this page. Simple result of search with Wilhelm.

The longest wtm DTM in KRNPKR is 85 moves:

Code: Select all

8/7N/8/8/8/2k5/4r2P/K2R4 w - -

8/7N/8/8/8/2k5/4r2P/K2R4 w - -


I did not check how many mzugs the line has.

[guyhaw]

I believe that Marc Bourzutschky has computed KRNPKR DTC EGTs, and I hope to have the maxDTC results to hand shortly. There is no DTZ EGT yet.
For DTM, the maxDTM wtm/btm 1-0 and 0-1 statistics are: (wtm 1-0 win) 4 @ 85, (btm 1-0 loss) 2 @ 85, (wtm 0-1 loss) 1 @ 64, (btm 0-1 win) 122 @ 67.
wtm 1-0 wins and btm 1-0 losses here, courtesy of Eiko Bleicher:
8/7N/8/8/8/2k5/4r2P/K2R4 w - -
8/7N/8/8/8/2k5/6rP/K2R4 w - -
8/7N/8/8/8/2k4P/K3r3/3R4 w - -
8/7N/8/8/8/2k4P/K5r1/3R4 w - -
8/7N/8/8/3k4/8/4r2P/K2R4 b - -
8/7N/8/8/3k4/8/6rP/K2R4 b - -
maxDTM 0-1 positions (wtm/btm) expected shortly.
The mzug statistics are as follows, given that there are no 'e.p.-capture available' positions:
Type 1 (draw/win/draw from point of view of 1st player to play): 3,933 positions
Type 2 (lost/drawn/lost from ....) 1 position: RK5N/6r1/P1k5/8/8/8/8/8 w, DTM=4
Type 3 (full-point zug: lost/won/lost ... ) none
No data available yet on the maxDTM of the Type 1 zugs, but file attached here.
g

[yrobinso]

Thanks for the reply to Kirill Kryukov and Guy Haworth. These are interesting data.

I am surprised by the large number of btm/1-0 zugzwangs. If there are indeed 3,934 of them, that would mean only four endgames on John Tamplin's list (http://chess.jaet.org/cgi-bin/mzugs?sort=count) have more mzugs than the 6-men KRNPKR. These are KRNKNN, KRNKBN, KPPKP, and KNPKN. I would like to see a couple more examples so that I can get an idea of what mzugs in this ending looks like.

I have another unrelated question. I was looking through Kirill Kryukov's list of maxDTM wins for a variety of 3-6 men endings. One thing I noticed is that many times, a pawnful ending will have a maxDTM when the pawn shortly promotes, sometimes an underpromotion. One typical example: KBPKN has maxDTM in this position, where White's first move must be 1. d8=N!

1n6/3P4/8/8/1K6/7B/8/k7


I understand that there are two reasons for people to compile maxDTX lists: practical and theoretical. The practical purpose, as I understand, is to design a compression technique that takes advantage of the maxDTX so that the minimum number of bits is used in the data storage. The theoretical purpose, of course, is the chess curiosity.

Toward that second end, I would be interested in seeing a second list of maxDTM positions for pawnful endgames. This list would make the restriction that all pawns must be no farther advanced than the fourth (or possibly fifth) rank. Thus, this list would give the longest path toward promoting the pawn: i.e., the maxDTC. I suppose that's not an original idea. My point is that a KBPKN ending as above is not really that at all; it is a KBNKN ending in a pawnful ending's clothing. That would explain the value of maxDTC lists for endings where the winning side has a pawn, more than for other endings where maxDTC is of somewhat less intrinsic importance.

[guyhaw]

It seems that the large file of Type 1 ('dwd' = draw/win/draw) mzugs did not get attached - a combination of my clumsiness and its size.
Some KRNPKR Type 1 mzugs, taken at random from the list, here:'

8/8/8/8/4r3/7P/R1N5/K1k5 w - -
RN6/1r6/7P/8/8/8/8/K1k5 w - -
8/5R2/8/8/8/7P/2r1k3/KN6 w - -
8/8/8/8/8/1k1P4/1N2r3/KR6 w -
8/8/8/8/4k3/8/2r1P1N1/K3R3 w - -
8/1R1P4/5k2/8/5N2/8/3r4/K7 w - -
8/8/8/8/8/1k1r2NR/3P4/1K6 w - -
2K5/k4rNR/8/2P5/8/8/8/8 w - -
R2K4/6r1/5N2/P7/k7/8/8/8 w - -
3K3k/3N1R2/3r2P1/8/8/8/8/8 w - -

The presence of Ns and Ps tends to increase the number of mzugs. Full-point mzugs without Ns and Ps have long been on the agenda, and a 7-man one has now been found by Marc B.

If you look at the DTM stats, you can see where maxDTMs are not 'adjacent' (the same or 1-out) for wtm and btm. This indicates an immediate conversion out of the endgame, and because it is at the maxDTM end, it is quite likely to be an underpromotion.

I think there are several reasons for taking an interest in the maxDTM positions:
a) the 'Everest' one - they are there,
b) they define the outposts or extremities of that endgame
c) something strange and fascinating is likely to be going on, and
d) there may be a long trail of unique or effectively-unique winner's moves from them

maxDTx defines whether one wants an 8-bit or 16-bit cell to hold the depth information. Nalimov tended to guess, sometimes wrongly, in which case he had to generate the endgame again - unless he'd done it in 16-bit mode (in which case it could be converted to 8-bit mode).
The compression method for Nalimov EGTs is by Andrew Kadatch, maybe based on LZW-compression [though I could have got that well wrong] and doesn't rely on maxDTM. However, DTZ produces more compact compressed EGTs as it involves a smaller ranges of depths.

I hope to have 6-man P-ful endgame DTC data shortly. I think Yakov K intended to send it to me but left the file off.
g