10X10 draughts endgame databases
Jonathan Schaeffer
Following are some of the numbers for 2-5-piece endgame databases
for 10X10 draughts. I am missing some of the 5-piece numbers. We
also have a few of the 6-piece databases computed.
In the following, the database number is interpreted as follows:
ABCD: A = # Black kings; C = #Black checkers;
B = # White kings; D = #White checkers;
Thus the database 2001 is 2 Black kings against one White checker.
In our database format the 5-piece databases take 36 MB of space.
Number of W/L/D in each subdatabase (all positions).
__________________________________________________________________
Pieces Database Wins Losses Draws Positions
__________________________________________________________________
2 1100 424 2 2024 2450
1001 4410 3434 121 855
0011 736 450 799 1985
__________________________________________________________________
1:1 5570 3886 2944 5290
__________________________________________________________________
__________________________________________________________________
3 2100 19970 3240 94390 117600
2001 95071 245 10524 105840
1110 24879 16369 170432 211680
1011 154624 1746 34190 190560
0120 5346 38119 51575 95040
0021 48613 3915 33052 85580
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2:1 348503 63634 394163 806300
__________________________________________________________________
__________________________________________________________________
4 2200 146610 3432 1231758 1381800
2101 821492 150701 4002287 4974480
2002 1628882 11260 593298 2233440
1111 882645 26562 3568953 4478160
1012 2326580 125586 1570094 4022260
0022 276206 96419 530815 903440
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2:2 6082415 413960 11497205 17993580
__________________________________________________________________
3100 527030 16812 1298558 1842400
3001 1559744 460 97956 1658160
2110 1096484 122349 3755647 4974480
2011 4093813 3864 380483 4478160
1120 694767 252885 3519228 4466880
1021 3410526 8520 603214 4022260
0130 120365 189857 1023638 1333860
0031 826633 8043 366744 1201420
__________________________________________________________________
3:1 12329362 602790 11045468 23977620
__________________________________________________________________
__________________________________________________________________
5 3200 3894824 747242 37733134 42375200
3101 20182194 689968 55403198 76275360
3002 28893108 23338 5329634 34246080
2210 7164041 6039894 101209105 114413040
2111 41353162 5713833 158928365 205995360
2012 72793251 294458 19424271 92511980
1220
1121
1022
0230
0131
__________________________________________________________________
0032
__________________________________________________________________
3:2 174280580 13508733 378027707 565817020
__________________________________________________________________
4100 16688244 87330 4412026 21187600
4001 18949720 766 118354 19068840
3110 58703305 681528 16890527 76275360
3011 68068370 7803 588947 68665120
2120 76198146 1924149 24615945 102738240
2021 91287019 22815 1202146 92511980
1130 41668796 2199700 17489064 61357560
1031 53958077 27137 1280106 55265320
0140 6011801 886306 6809433 13707540
0041 11530987 12566 806477 12350030
__________________________________________________________________
4:1 443064465 5850100 74213025 523127590
__________________________________________________________________
Number of W/L/D in each subdatabase (no captures included).
____________________________________________________
Pieces Database Wins Losses Draws
____________________________________________________
2 1100 16 2 2024
1001 3026 1 855
0011 616 450 799
____________________________________________________
1:1 3658 453 3678
____________________________________________________
____________________________________________________
3 2100 2566 0 80322
2001 73575 0 9686
1110 3119 17 153820
1011 127476 1 31241
0120 344 25340 48748
0021 42333 2430 30958
____________________________________________________
2:1 249413 27788 354775
____________________________________________________
____________________________________________________
4 2200 10519 11 697448
2101 87162 11253 2720548
2002 994879 1308 427819
1111 66781 1537 2734001
1012 1569146 6799 1249967
0022 170641 88695 451336
____________________________________________________
2:2 2899128 109603 8281119
____________________________________________________
3100 152014 0 963746
3001 1096605 0 85928
2110 276321 0 2879224
2011 3022663 0 332578
1120 147006 15 2833025
1021 2649695 2 527378
0130 17737 43833 877755
0031 673446 2981 327104
____________________________________________________
3:1 8035487 46831 8826738
____________________________________________________
____________________________________________________
5 3200 478392 33564 15788664
3101 868990 33918 30082468
3002 14690326 4569 3653084
2210 1000286 392683 46881860
2111 7027516 400093 92463325
2012 40256732 47386 13206160
1220
1121
1022
0230
0131
0032
____________________________________________________
3:2 64322242 912213 202075561
____________________________________________________
4100 11189948 0 22384
4001 12489105 0 2831
3110 41713112 0 376270
3011 46886110 0 33214
2120 57300544 22 2048816
2021 66040247 2 120218
1130 32886046 7 4357345
1031 41270750 1 225463
0140 4632362 16831 4122565
0041 9366528 1212 396037
____________________________________________________
4:1 323774752 18075 11705143
____________________________________________________
Rein Halbersma
Jonathan Schaeffer wrote:
>
> Following are some of the numbers for 2-5-piece endgame databases
> for 10X10 draughts. I am missing some of the 5-piece numbers. We
> also have a few of the 6-piece databases computed.
>
> In the following, the database number is interpreted as follows:
> ABCD: A = # Black kings; C = #Black checkers;
> B = # White kings; D = #White checkers;
> Thus the database 2001 is 2 Black kings against one White checker.
>
> In our database format the 5-piece databases take 36 MB of space.
>
> Number of W/L/D in each subdatabase (all positions).
> __________________________________________________________________
> Pieces Database Wins Losses Draws Positions
> __________________________________________________________________
> 2 1100 424 2 2024 2450
> 1001 4410 3434 121 855
Shouldn't this be 3434 wins, 121 losses, 855 draws and 4410 positions?
[snip]
In the 1993 May issue of the Dutch Draughts Magazine 'Hoofdlijn', Bert
van Oortmarssen published a similar list for all 2,3 and 4 piece
endgames. For the endgames with only kings present, he used symmetry to
reduce the size by a factor of approximately four.
His article contained a list of all the endgames and their conjugates
(the conjugate of ABCD is BADC). He gave #positions, #positions with
white to move and win and #positions with black to move and lose. Adding
these numbers should give #winning positions, as should adding these
numbers for the conjugate databases give #losing positions.
I did this check on all the 2,3 and 4 piece databases numbers and found
that *all* the results agreed exactly! There weren't any publications on
5 piece databases to compare with. So either both databases are correct
or they're having the same bug :)
Van Oortmarssen also gave the longest distance to win (with as metric
the distance to mate, not to conversion), e.g. the longest possible win
in the king against three men endgame is 43 plies. It would be nice to
have some comparison on these figures as well.
In rec.games.chess.computer, you wrote:
[snip]
> Completing the 6-piece and doing the 7-piece databases is doable, but > I have found no reason to do so. There is a suggestion that we
> complete the 10X10 draughts databases and make them available on a CD, > complete with the 7-piece 8X8 checkers databases and the 8X8 pool
> checkers databases.
[snip]
There are some reasons for computing 6 and 7 piece databases for 10x10
draughts. From a scientific viewpoint, computing 8x8 or 10x10 databases
isn't that different.
But in 10x10 draughts there is a huge amount of literature on the so
called 'powerplay' endgames ('overmachtseindspelen' in Dutch). These are
endgames in which at least one of the players has 4 or more pieces. A
typical example is the 2121 endgame.
There are a lot of these 4 vs 2 endgames analysed and it would be of
great (game-)theoretical importance to compare those analyses with
optimal play from a database.
As a draughts player, I can only look forward to the day when the 6 and
7 piece engames come available on CD.
--
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| Rein S. Halbersma |
| |
| e-mail: R.S.Ha...@cpedu.rug.nl |
| URL: www.cpedu.rug.nl/~N0769940/ |
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