Anyone know what the longest mates are in the 3piece set? particularly kqk, and if so what is it's fen and solution.
-Josh
Longest Mate in kqk
Re: Longest Mate in kqk
kqk (wtm) win in 10 moves - 1 only position : Ka1 Qb2 kf5jshriver wrote:Anyone know what the longest mates are in the 3piece set? particularly kqk, and if so what is it's fen and solution.
-Josh
krk (wtm) win in 16 moves - 121 positions: Ka1 Rb2 kc3 and other 120 ...
kpk (wtm) win in 28 moves - 3 positions: Ka2 Pg2 kb5, Kb2 Pg2 kb5, Ka3 Pg2 kb5
kqk (btm) loss in 10 moves - 8 positions: Ka1 Qb2 ke4 and other 7 ...
krk (btm) loss in 16 moves - 390 positions: Ka1 Rb2 kc2 and other 389 ...
kpk (btm) loss in 28 moves - 2 positions: Ka3 Pg2 ka5, Ka3 Pg2 ka6
Guido
Nulla dies sine linea
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guyhaw
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Longest mates in 3-to-5 chess
As attached ... positions and stats - both computed by Peter Karrer some years ago.
The stats can also be found at http://www.icga.org ... Game-specific info ... Western Chess ... Endgame.
I have an analogous list of maxDTC positions from Christoph Wirth of about the same vintage.
g
The stats can also be found at http://www.icga.org ... Game-specific info ... Western Chess ... Endgame.
I have an analogous list of maxDTC positions from Christoph Wirth of about the same vintage.
g
- Attachments
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- PK_maxDTM_pos.zip
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- PK_maxDTM_stats.txt
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Zvi Mendlowitz
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Contradiction!
The sources you gave contradict each other. 
From text file: "kbnk wtm: max win 33 (138)"
Spreadsheet at ICGA site says (at AT33): 144
from zipped text file you posted here: http://kd.lab.nig.ac.jp/chess/discussio ... 80ebb72348
"#DTC max info for KBBKN
#wtm 1-0: 131/32"
Spreadsheet at ICGA site says (at P49): 34[/b]
From text file: "kbnk wtm: max win 33 (138)"
Spreadsheet at ICGA site says (at AT33): 144
from zipped text file you posted here: http://kd.lab.nig.ac.jp/chess/discussio ... 80ebb72348
"#DTC max info for KBBKN
#wtm 1-0: 131/32"
Spreadsheet at ICGA site says (at P49): 34[/b]
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guyhaw
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Comparison of Nalimov and Wirth stats
[ Btw, when I said 'DTZ == DTZ' for P-less endgame (above), I meant 'DTZ == DTC' of course. ]
I forgot to mention the main difference between Wirth's EGT stats and Nalimov's. Where there are two Kings on the a1-h8 (or equivalently a8-h1) diagonal in a P-less endgame, Nalimov stores the position and the a1-h8-flip of the position. Wirth on the other hand, eliminates one of these, maybe the one with the 'higher index position'.
Thus the difference between 144 and 138 is I think that there are 12 maximal positions with the two Ks on the long diagonal, and that Wirth eliminates 6 of these because they are paired off with the other 6.
g
I forgot to mention the main difference between Wirth's EGT stats and Nalimov's. Where there are two Kings on the a1-h8 (or equivalently a8-h1) diagonal in a P-less endgame, Nalimov stores the position and the a1-h8-flip of the position. Wirth on the other hand, eliminates one of these, maybe the one with the 'higher index position'.
Thus the difference between 144 and 138 is I think that there are 12 maximal positions with the two Ks on the long diagonal, and that Wirth eliminates 6 of these because they are paired off with the other 6.
g
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Zvi Mendlowitz
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Probably correct
What you say is probably true - I just checked and saw that the 32 max KBBKN positions indeed include two positions with the kings on the same long diagonal. So probably these positions appear in Nalimov's database twich each, and that is why in his database there are 34 such positions.
I also checked and saw that the 138 max KBNK positions include exactly six positions with the kings on the same long diagonal, as you said.
I also checked and saw that the 138 max KBNK positions include exactly six positions with the kings on the same long diagonal, as you said.
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guyhaw
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Misplaced threat-components
If anyone is confused, I think the last three contributions should have been under 'DTC/DTZ-maximals' rather than under this thread.
g
g
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guyhaw
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ICGA Statistics are to the 'Nalimov norm' of counting
My spreadsheet at http://www.icga.org use to have 'Nalimov derived stats' for DTM and 'Wirth derived stats' for DTC.
When J Tamplin and M Bourzutschky made available DTC stats, mainly via MB's program GTBGEN, I standardised all ICGA stats to the norm of the Nalimov way of counting.
Thus nudges the 'DTC' %s a bit back to the 'DTM' %s of course - and note that these %s do not apply to the DTZ50 EGT which assumes the 50-move rule is invoked.
g
When J Tamplin and M Bourzutschky made available DTC stats, mainly via MB's program GTBGEN, I standardised all ICGA stats to the norm of the Nalimov way of counting.
Thus nudges the 'DTC' %s a bit back to the 'DTM' %s of course - and note that these %s do not apply to the DTZ50 EGT which assumes the 50-move rule is invoked.
g
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Zvi Mendlowitz
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Just to be sure
Just to be sure I understood everything correctly:
All the statistics in the files by Karrer are computed according to Wirth's method, right?
By Wirth's method, two pawnless positions which are related by rotation and/or reflection are always counted as one; two pawnful positions which are related by rotation and/or reflection are counted as one if and only if they are mirror images, where the mirror is vertical (columns a<->h, b<->g, c<->f, d<->e are swapped). Is all this correct?
All the statistics in the files by Karrer are computed according to Wirth's method, right?
By Wirth's method, two pawnless positions which are related by rotation and/or reflection are always counted as one; two pawnful positions which are related by rotation and/or reflection are counted as one if and only if they are mirror images, where the mirror is vertical (columns a<->h, b<->g, c<->f, d<->e are swapped). Is all this correct?
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guyhaw
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Zvi (et al): corrections
Peter Karrer did a through-review of all 3-to-5-man Nalimov DTM EGTs: his stats are therefore to the Nalimov mode of counting, which I take as 'standard' now.
Depths to Mate (DTM) are in winner's moves: Nalimov-style EGTs are being computed to other metrics but they're all in winner's moves.
Wirth's method of counting is not used today. You are right that Wirth counted just '1' for every 'equivalence class' of positions (i.e. positions that could be transformed into each other by a combination of rotations and reflections). Note that for P-ful endgames, there are no rotations and only 1 rather than 4 axes of reflection (the d/e axis).
Nalimov would get the stmK in (say) the triangle a1-d1-d4, and _then_, if the bK was in a2-a8-g7, he would flip on the a1-h8 axis. This ignored cases of the bK on the a1-h8 axes, so he ends up with (usually but not always) two equivalent positions in the EGT.
Note also that, beyond spotting obviously illegal positions (two men on one square, sntm in check), no attempt is made to eliminate unreachable positions. So you will find 'legal' positions with Ps giving check from their home square, impossible double checks, wBa1/wPb2 etc in the EGT. These may affect maxDTM, mzug counts etc. - but no attempt is made to eliminate these so that statistics from different technologies can more likely be compared.
Wirth's counting method would have been the best (in plies, so no information loss, and symmetric in counting all plies) had it not been for the flaw ignoring loser-converts to next endgame.
There are I think 6-man P-less endgames where after 101 plies in the phase, the loser is forced to capture (just after they have claimed a draw under the 50-move rule). For example, in KQNKRR, the position wKd2Qb1Ng1/bKa6ra8rg8 btm is maxDTC and maxDTM, DTC=152m and DTM=174m but in the DTC-minimaxing line I followed, Black is forced to capture. Well, I guess forced-to-capture position can be backed up and shown to lead to positions of > 100 plies DTC-depth:
1...Rad8+' 2.Ke3" Rge8+' 3.Kf4" Rd4+' 4.Kg3" Rg8+' 5.Kf2" Rf8+' 6.Ke3" Rd6' 7.Qa1+ [Qa2+] Kb6' 8.Qb2+" Kc6' 9.Qc3+' Kd7' 10.Qg7+" Ke8' 11.Qe5+" Kd7' 12.Qb5+' Ke7' 13.Qb7+" Rd7' 14.Qe4+' Kd8' 15.Qh4+' Kc8' 16.Qg4' Re8+' 17.Kf2 [Kf3] Rf8+' 18.Kg2' Kc7' 19.Sh3' Rdf7' 20.Sg5" Rf2+' 21.Kg3' Rf1' 22.Qc4+" Kb6' 23.Qd4+ [Qe6+] Kb7' 24.Qd5+' Kb6' 25.Kh4' R8f4+' 26.Kh5" Rf5' 27.Qc4' R1f2' 28.Qb3+ [Kg6/h6, Qd4+] Kc6' 29.Kg6 [Kh6] Rf6+' 30.Kg7" R6f4' 31.Qd3 [Kh7] Kb6 [Rf1] 32.Kh7' Rf1' 33.Qd6+' Kb5' 34.Se6" Rf7+' 35.Kg8' R7f2' 36.Qc5+ [Qd5+] Ka6' 37.Qc6+' Ka5' 38.Kh7 [Kh8] Rf7+' 39.Kh8' R7f2' 40.Qb7' Rf3' 41.Qd5+ [Qa7+/c7+] Kb4 [Kb6] 42.Qc5+' Ka4' 43.Qc4+' Ka5' 44.Sg5' Rf4' 45.Qb3' Rh4+ [Rf6/h1+] 46.Kg7 [Kg8] Rhf4' 47.Kh7' Rh4+ [Rh1+] 48.Kg6' Rhf4' 49.Qb2' R4f2' 50.Qb7' Rf8' 51.Kh6 [Kh7] R8f6+' 52.Kh5' R6f5' 53.Qb2 [Qb8/d7] Rf8' 54.Qc3+ [Qe5+] Kb6' 55.Qd4+' Kb5' 56.Se4 [Se6] Rh8+' 57.Kg4" Rg8+' 58.Sg5" Rgf8' 59.Kh3 [Qd5+] R8f4' 60.Qd5+" Kb6' 61.Qd7" Rh1+' 62.Kg2' Rhf1' 63.Se4' R4f3' 64.Kh2' Rf5' 65.Sd2' R1f2+' 66.Kg3' Ka6' 67.Qc7' Rf7' 68.Qc6+" Ka7' 69.Se4" Rf1' 70.Qa4+' Kb8' 71.Qb3+' Kc7 [Ka7/8] 72.Qc3+' Kb8 [Ld7] 73.Qb2+' Kc7' 74.Qe5+' Kd7' 75.Qd5+' Ke7' 76.Qd6+' Ke8° 77.Qc6+ [Qb8+] Ke7' 78.Qc7+' Kf8' 79.Qd8+' Kg7° 80.Sg5" R7f6' 81.Qd5" Kg6' 82.Se6" R6f2' 83.Qe5' Kf7' 84.Qd6' Rf3+' 85.Kh4' Rf5' 86.Kg4' R5f2' 87.Sg5+' Ke8' 88.Qb8+' Kd7' 89.Qb7+' Kd8' 90.Se6+' Ke8° 91.Qe4' Kd7' 92.Sc5+" Kd6' 93.Qd4+" Kc7' 94.Qd7+' Kb6' 95.Qd6+" Kb5' 96.Se4" {and here the DTC-minimaxing line diverges from the DTM-minimaxing line}
96...Rf8' 97.Qe6' R1f4+' 98.Kg3' Kb4' 99.Qd6+' Kc4' 100.Qd1 [Qd7] Rf3+' 101.Kh2' R3f4' 102.Qd7' Rh8+ [Rh4+] 103.Kg3' Rhh4' 104.Qc6+' Kb3 [Kb4] 105.Qb5+ [Qb6+] Ka3' 106.Qa5+' Kb3' 107.Sd2+' Kb2' 108.Sf3 [Qb5+/6+/e5+] Rhg4+' 109.Kf2' Re4' 110.Qb5+ [Qb6+] Kc3' 111.Qc5+' Kb2' 112.Se5' Rgf4+' 113.Kg3' Rh4' 114.Sd3+' Kb3' 115.Kf2 [Sc1] Rc4' 116.Qb6+' Kc3' 117.Sc5' Rcg4' 118.Ke2' Kc4' 119.Qc6' Kd4' 120.Qd6+' Kc4' 121.Sd3' Rd4' 122.Qc6+' Kb3° 123.Kd2' Rh2+' 124.Ke3' Rhh4' 125.Sc1+' Kb2' 126.Se2' Rhe4+' 127.Kf2' Rc4' 128.Qb5+ [Qb6+] Rb4 [Kc2] 129.Qg5' Rbc4' 130.Ke1' Rc7 [Kb3, Rc8] 131.Qb5+ [Qf6+] Kc2' 132.Qf5' Rcc4' 133.Qg6' Kb3' 134.Kd1' Rh4' 135.Kd2' Rce4 [Ka4] 136.Qc6 [Kd3] Kb4' 137.Kd3' Rc4' 138.Qb6+' Ka3' 139.Qb1 [Qb7] Rce4' 140.Qb5' Rc4' 141.Sc3' Rhg4' 142.Qb1' Rcd4+' 143.Ke2 [Ke3] Rc4 [Rg2] 144.Sb5+' Ka4° 145.Kd3' Rh4' 146.Qb2' Ka5' 147.Sc3' Rhd4+ [Ka6] 148.Ke3' Ka6' 149.Qb5+' Ka7° 150.Sd5' Re4+' 151.Kf3' Rh4 [Red4/g4] 152.Qb6+' Ka8° 153.Sc7+' Rxc7°
g
Depths to Mate (DTM) are in winner's moves: Nalimov-style EGTs are being computed to other metrics but they're all in winner's moves.
Wirth's method of counting is not used today. You are right that Wirth counted just '1' for every 'equivalence class' of positions (i.e. positions that could be transformed into each other by a combination of rotations and reflections). Note that for P-ful endgames, there are no rotations and only 1 rather than 4 axes of reflection (the d/e axis).
Nalimov would get the stmK in (say) the triangle a1-d1-d4, and _then_, if the bK was in a2-a8-g7, he would flip on the a1-h8 axis. This ignored cases of the bK on the a1-h8 axes, so he ends up with (usually but not always) two equivalent positions in the EGT.
Note also that, beyond spotting obviously illegal positions (two men on one square, sntm in check), no attempt is made to eliminate unreachable positions. So you will find 'legal' positions with Ps giving check from their home square, impossible double checks, wBa1/wPb2 etc in the EGT. These may affect maxDTM, mzug counts etc. - but no attempt is made to eliminate these so that statistics from different technologies can more likely be compared.
Wirth's counting method would have been the best (in plies, so no information loss, and symmetric in counting all plies) had it not been for the flaw ignoring loser-converts to next endgame.
There are I think 6-man P-less endgames where after 101 plies in the phase, the loser is forced to capture (just after they have claimed a draw under the 50-move rule). For example, in KQNKRR, the position wKd2Qb1Ng1/bKa6ra8rg8 btm is maxDTC and maxDTM, DTC=152m and DTM=174m but in the DTC-minimaxing line I followed, Black is forced to capture. Well, I guess forced-to-capture position can be backed up and shown to lead to positions of > 100 plies DTC-depth:
1...Rad8+' 2.Ke3" Rge8+' 3.Kf4" Rd4+' 4.Kg3" Rg8+' 5.Kf2" Rf8+' 6.Ke3" Rd6' 7.Qa1+ [Qa2+] Kb6' 8.Qb2+" Kc6' 9.Qc3+' Kd7' 10.Qg7+" Ke8' 11.Qe5+" Kd7' 12.Qb5+' Ke7' 13.Qb7+" Rd7' 14.Qe4+' Kd8' 15.Qh4+' Kc8' 16.Qg4' Re8+' 17.Kf2 [Kf3] Rf8+' 18.Kg2' Kc7' 19.Sh3' Rdf7' 20.Sg5" Rf2+' 21.Kg3' Rf1' 22.Qc4+" Kb6' 23.Qd4+ [Qe6+] Kb7' 24.Qd5+' Kb6' 25.Kh4' R8f4+' 26.Kh5" Rf5' 27.Qc4' R1f2' 28.Qb3+ [Kg6/h6, Qd4+] Kc6' 29.Kg6 [Kh6] Rf6+' 30.Kg7" R6f4' 31.Qd3 [Kh7] Kb6 [Rf1] 32.Kh7' Rf1' 33.Qd6+' Kb5' 34.Se6" Rf7+' 35.Kg8' R7f2' 36.Qc5+ [Qd5+] Ka6' 37.Qc6+' Ka5' 38.Kh7 [Kh8] Rf7+' 39.Kh8' R7f2' 40.Qb7' Rf3' 41.Qd5+ [Qa7+/c7+] Kb4 [Kb6] 42.Qc5+' Ka4' 43.Qc4+' Ka5' 44.Sg5' Rf4' 45.Qb3' Rh4+ [Rf6/h1+] 46.Kg7 [Kg8] Rhf4' 47.Kh7' Rh4+ [Rh1+] 48.Kg6' Rhf4' 49.Qb2' R4f2' 50.Qb7' Rf8' 51.Kh6 [Kh7] R8f6+' 52.Kh5' R6f5' 53.Qb2 [Qb8/d7] Rf8' 54.Qc3+ [Qe5+] Kb6' 55.Qd4+' Kb5' 56.Se4 [Se6] Rh8+' 57.Kg4" Rg8+' 58.Sg5" Rgf8' 59.Kh3 [Qd5+] R8f4' 60.Qd5+" Kb6' 61.Qd7" Rh1+' 62.Kg2' Rhf1' 63.Se4' R4f3' 64.Kh2' Rf5' 65.Sd2' R1f2+' 66.Kg3' Ka6' 67.Qc7' Rf7' 68.Qc6+" Ka7' 69.Se4" Rf1' 70.Qa4+' Kb8' 71.Qb3+' Kc7 [Ka7/8] 72.Qc3+' Kb8 [Ld7] 73.Qb2+' Kc7' 74.Qe5+' Kd7' 75.Qd5+' Ke7' 76.Qd6+' Ke8° 77.Qc6+ [Qb8+] Ke7' 78.Qc7+' Kf8' 79.Qd8+' Kg7° 80.Sg5" R7f6' 81.Qd5" Kg6' 82.Se6" R6f2' 83.Qe5' Kf7' 84.Qd6' Rf3+' 85.Kh4' Rf5' 86.Kg4' R5f2' 87.Sg5+' Ke8' 88.Qb8+' Kd7' 89.Qb7+' Kd8' 90.Se6+' Ke8° 91.Qe4' Kd7' 92.Sc5+" Kd6' 93.Qd4+" Kc7' 94.Qd7+' Kb6' 95.Qd6+" Kb5' 96.Se4" {and here the DTC-minimaxing line diverges from the DTM-minimaxing line}
96...Rf8' 97.Qe6' R1f4+' 98.Kg3' Kb4' 99.Qd6+' Kc4' 100.Qd1 [Qd7] Rf3+' 101.Kh2' R3f4' 102.Qd7' Rh8+ [Rh4+] 103.Kg3' Rhh4' 104.Qc6+' Kb3 [Kb4] 105.Qb5+ [Qb6+] Ka3' 106.Qa5+' Kb3' 107.Sd2+' Kb2' 108.Sf3 [Qb5+/6+/e5+] Rhg4+' 109.Kf2' Re4' 110.Qb5+ [Qb6+] Kc3' 111.Qc5+' Kb2' 112.Se5' Rgf4+' 113.Kg3' Rh4' 114.Sd3+' Kb3' 115.Kf2 [Sc1] Rc4' 116.Qb6+' Kc3' 117.Sc5' Rcg4' 118.Ke2' Kc4' 119.Qc6' Kd4' 120.Qd6+' Kc4' 121.Sd3' Rd4' 122.Qc6+' Kb3° 123.Kd2' Rh2+' 124.Ke3' Rhh4' 125.Sc1+' Kb2' 126.Se2' Rhe4+' 127.Kf2' Rc4' 128.Qb5+ [Qb6+] Rb4 [Kc2] 129.Qg5' Rbc4' 130.Ke1' Rc7 [Kb3, Rc8] 131.Qb5+ [Qf6+] Kc2' 132.Qf5' Rcc4' 133.Qg6' Kb3' 134.Kd1' Rh4' 135.Kd2' Rce4 [Ka4] 136.Qc6 [Kd3] Kb4' 137.Kd3' Rc4' 138.Qb6+' Ka3' 139.Qb1 [Qb7] Rce4' 140.Qb5' Rc4' 141.Sc3' Rhg4' 142.Qb1' Rcd4+' 143.Ke2 [Ke3] Rc4 [Rg2] 144.Sb5+' Ka4° 145.Kd3' Rh4' 146.Qb2' Ka5' 147.Sc3' Rhd4+ [Ka6] 148.Ke3' Ka6' 149.Qb5+' Ka7° 150.Sd5' Re4+' 151.Kf3' Rh4 [Red4/g4] 152.Qb6+' Ka8° 153.Sc7+' Rxc7°
g
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Zvi Mendlowitz
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Thanks
Thanks for the detailed answer.