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H.G.Muller

Joined: 10 Mar 2006
Posts: 12765
Location: Amsterdam

Post subject: Re: End-game evaluation    Posted: Tue Nov 08, 2011 10:14 pm

For 4 pieces a complete retrograde analysis on 8x8, even just for the first few moves, is probably too costly. Reason is that there are usually lots of edge mates, almost all non-forcible, and even just identifying these mates takes a significant fraction of the time needed to build the entire EGT. But I guess it would be good enough for the first few iterations to only consider positions with the white King on a3,b3,c3, the black King on c2,c1,b1,a1,a2,a3, and the white pieces everywhere. That should tell you if the pieces in principle are able to perform the final mating steps. You would find that two Dababbas can do it, though:

[d]6R1/8/8/8/K7/8/8/k5R1 w
Mate in 11 with 2 Dababbas

1. Kb3 Kb1 2. De1 {closes the trap} Ka1 3. Dc1+ Kb1 4. Dc3 Ka1 5. De8 Kb1 6. Dc8 Ka1 7. Da8 Kb1 8. Da6 Ka1 9. Kb2! {triangulates} Ka2 10. Da4+ Ka1 11. Da3#

But as you can see from the complete statistics only 680 out of 2M btm positions are won:

 Code: KDD_K                  like          unlike WON.wtm   346220     371840 K capture   346220     368584 other            0       3256   0.       1823704    1881164  10.             0         16  11.             0          8  12.             0         16  13.             0         32  14.             0        176  15.             0         52  16.             0        240  17.             0         32  18.             0         96  19.             0          4  20.             0          8 WON.btm          0        680 stalemate      456        348 W check      51712      54192 LEGAL      1824160    1882192 TOTAL      1875872    1936384

The beginning of this does not really differ spectacularly from what you see with Camel + Wazir, though:

 Code: KCW_K WON.wtm    3781436 K capture   809720 other      2971716   0.        737536  10.            84  11.            18  12.            26  13.           122  14.           172  15.           396  16.           308  17.           730  18.          1048  19.          1492  20.          1121  21.          1267  22.           698  23.          1109  24.           936  25.          1001  26.          1441  27.          1231  28.          1490  29.          1500  30.          1267  31.          1178  32.          1146  33.          1232  34.           563  35.           608  36.           809  37.          1499  38.          1177  39.           560  40.           248  41.           199  42.           404  43.           440  44.           154  45.           330  46.           264  47.           210  48.           514  49.           410  50.           720  51.          1224  52.          2450  53.          2650  54.          3470  55.          4504  56.          5796  57.          9145  58.         11572  59.         14216  60.         20626  61.         32617  62.         47723  63.         63105  64.         91688  65.        127635  66.        175735  67.        225274  68.        271017  69.        301921  70.        310095  71.        285314  72.        238836  73.        177634  74.        111629  75.         64539  76.         33995  77.         16270  78.          8608  79.          5433  80.          3632  81.          2056  82.          1071  83.           473  84.           214  85.           112  86.            30  87.            10 WON.btm    2702441 stalemate     1937 W check     370342 LEGAL      3441914 TOTAL      3812256

There are still only 154 mate-in-34 positions (counting starts at 10 in my generator for technical reasons), and at that point it is not clearat all this is a generally won end-game. What you saw upto then is a lengthy and cumbersome drive of the bare King from the wrong corner into the right one. (Camel is color-bound, neither Wazir or Camel can move from c1 to a1 in 3 moves, but Camel can attack a1 and c1 at the same time in its own corner, while Wazir can move from c1 to b1 in 3 moves, so an edge-mate is possible there, and only there.) That you can drive the bare King to the edge at all turns out only later, and requires another 25 moves or so. But in the end 70% of all btm and 99% of all wtm positions is won.

Compare that to Zebra+Ferz:

 Code: KZF_K WON.wtm     832447 K capture   754740 other        77707   0.       3670601  10.            53  11.            40  12.            25  13.            48  14.            96  15.           124  16.           179  17.           272  18.           428  19.           410  20.           820  21.           832  22.           910  23.           748  24.           596  25.           876  26.          1064  27.           792  28.           592  29.           311  30.           412  31.           499  32.           294  33.           326  34.           361  35.           258  36.           148  37.           142  38.            97  39.            90  40.            90  41.           162  42.           290  43.           322  44.           704  45.           592  46.          1636  47.           661  48.          1166  49.           392  50.           596  51.           159  52.           214  53.            35  54.            81  55.             6  56.             6 WON.btm      18955 stalemate     1602 W check     121098 LEGAL      3691158 TOTAL      3812256

Here there are 159 mate-in-41 positions, and what happened until then does not seem so different from the KCWK case. But unlike the latter,it quickly peters out after that, and not even 0.5% of all btm positions is won. It is really not possible to tell the C+W can do the drive before the system becomes super-critical after 38 iterations, and that Z+F cannot do it before you reach iteration 45...

So I guess there is no shortcut for building the entire tablebase. It should be possible to do that significantly faster than the released version does it. (But the highly optimized version, which could do a 4-men in about 2 sec, was a DTM generator not supporting slider/leaper compouds.)
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
Subject Author Date/Time
H.G.Muller Tue Oct 04, 2011 11:44 am
Evert Glebbeek Tue Oct 04, 2011 1:02 pm
H.G.Muller Tue Oct 04, 2011 2:20 pm
Oliver Uwira Tue Oct 04, 2011 1:59 pm
Jon Dart Tue Oct 04, 2011 2:10 pm
Jon Dart Tue Oct 04, 2011 2:13 pm
Kevin Hearn Tue Oct 04, 2011 8:19 pm
Pawel Koziol Wed Oct 05, 2011 10:46 am
H.G.Muller Mon Oct 10, 2011 8:09 am
H.G.Muller Mon Oct 10, 2011 9:00 am
Evert Glebbeek Mon Oct 10, 2011 1:04 pm
Ed Schroder Mon Nov 07, 2011 10:15 pm
H.G.Muller Wed Oct 19, 2011 10:16 am
Michael Hoffmann Wed Oct 19, 2011 11:48 am
H.G.Muller Wed Oct 19, 2011 1:24 pm
Michael Hoffmann Wed Oct 19, 2011 2:53 pm
Volker Annuss Wed Oct 19, 2011 4:53 pm
H.G.Muller Wed Oct 19, 2011 4:54 pm
H.G.Muller Sat Oct 22, 2011 5:29 pm
H.G.Muller Mon Nov 07, 2011 7:28 pm
Evert Glebbeek Mon Nov 07, 2011 8:33 pm
Evert Glebbeek Mon Nov 07, 2011 9:02 pm
H.G.Muller Mon Nov 07, 2011 9:40 pm
H.G.Muller Tue Nov 08, 2011 11:16 am
Evert Glebbeek Tue Nov 08, 2011 5:50 pm
H.G.Muller Tue Nov 08, 2011 8:16 pm
Evert Glebbeek Tue Nov 08, 2011 8:52 pm
Re: End-game evaluation H.G.Muller Tue Nov 08, 2011 10:14 pm
Karlo Bala Jr. Mon Nov 07, 2011 11:59 pm
H.G.Muller Tue Nov 08, 2011 7:30 am
Kevin Hearn Tue Nov 08, 2011 9:58 am
H.G.Muller Tue Nov 08, 2011 12:40 pm
Evert Glebbeek Tue Nov 08, 2011 5:53 pm
Mark Lefler Mon Oct 10, 2011 4:08 pm
H.G.Muller Mon Oct 10, 2011 9:09 pm
H.G.Muller Mon Oct 10, 2011 9:58 pm
H.G.Muller Tue Oct 11, 2011 8:50 am
H.G.Muller Tue Oct 18, 2011 6:36 pm

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