Anyone know maxDTM and mzugs for KRNPKR?
Posted: Wed Nov 29, 2006 5:41 am
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.
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.