KBBK tablebases: attempt #2
Steven J Edwards
tablebase generation run. It caused some positions to be counted
twice, and some not to be counted at all; these two effects cancelled
each other in the final totals for the summaries. I corrected the
error and so now present what I believe to be the correct KBBK
tablebase pair of summaries.
First, a few points of comparison with the original KBBK article that
appeared in the 1985.09 issue of the _ICCA Journal_.
1) The main point of the article, that the KBBK has a maximum mating
distance of 19, has been confirmed.
2) The number of distinct WTM mate in 19 positions has been confirmed
as 16 (black king rotated into the a1-d1-d4 triangle).
3) The 16 positions for the mate in 19 case have been confirmed.
These positions are:
wKa1 wBd1 wBh4 bKd2
wKa8 wBd1 wBh4 bKd2
wKa1 wBd1 wBe7 bKd2
wKa1 wBe2 wBe7 bKd2
wKa1 wBd1 wBd8 bKd2
wKa1 wBa4 wBd2 bKd3
wKh1 wBa4 wBd2 bKd3
wKa8 wBa4 wBd2 bKd3
wKh8 wBa4 wBd2 bKd3
wKa1 wBd7 wBd2 bKd3
wKh1 wBd7 wBd2 bKd3
wKh8 wBd7 wBd2 bKd3
wKa1 wBe8 wBd2 bKd3
wKh8 wBe8 wBd2 bKd3
wKa1 wBc4 wBg5 bKd4
wKa1 wBd3 wBe7 bKd4
4) The number of WTM draws (bK in triangle) has been confirmed: 112.
5) The number of WTM broken positions (bK in triangle) has also been
confirmed: 268456.
6) The number of WTM wins (bK in triangle) has been confirmed: 386792.
7) The article's claim for 1024 distinct WTM (bK in triangle) mate in
one positions has been proven FALSE. There are actually 1153 of these
(bK in triangle). I have generated a list of these and they all check
out to be mate in one. I can e-mail a copy of this position list to
anyone would like to verify Spector's claim.
Here are Spector's revised, and hopefully final, summaries:
WTM broken: 1690176 (268456)
WTM draw: 520 (112)
WTM mate in 1: 6312 (1153)
WTM mate in 2: 2608 (391)
WTM mate in 3: 14936 (3446)
WTM mate in 4: 18432 (2742)
WTM mate in 5: 30672 (5504)
WTM mate in 6: 37512 (5686)
WTM mate in 7: 56808 (8764)
WTM mate in 8: 86216 (13134)
WTM mate in 9: 124264 (19045)
WTM mate in 10: 181256 (27877)
WTM mate in 11: 249656 (37855)
WTM mate in 12: 294584 (43619)
WTM mate in 13: 354760 (53097)
WTM mate in 14: 360536 (53884)
WTM mate in 15: 316056 (49443)
WTM mate in 16: 246072 (39543)
WTM mate in 17: 109360 (19182)
WTM mate in 18: 13448 (2411)
WTM mate in 19: 120 (16)
Total symmetric: 655360
Total positions: 4194304
Tablebase summary: KBBK (BTM)
BTM broken: 724960 (113635)
BTM draw: 655304 (102866)
BTM lost in 0: 1552 (292)
BTM lost in 1: 1072 (177)
BTM lost in 2: 2344 (548)
BTM lost in 3: 3432 (573)
BTM lost in 4: 9336 (1980)
BTM lost in 5: 9320 (1525)
BTM lost in 6: 21000 (3614)
BTM lost in 7: 30408 (5134)
BTM lost in 8: 52736 (8843)
BTM lost in 9: 77632 (12517)
BTM lost in 10: 128992 (20357)
BTM lost in 11: 181592 (27839)
BTM lost in 12: 254056 (38585)
BTM lost in 13: 349712 (52645)
BTM lost in 14: 417416 (63551)
BTM lost in 15: 490368 (75226)
BTM lost in 16: 495952 (78097)
BTM lost in 17: 253800 (41565)
BTM lost in 18: 32960 (5721)
BTM lost in 19: 360 (70)
Total symmetric: 655360
Total positions: 4194304
Any comments and corrections are welcome.
-- Steven (s...@world.std.com)
Marcel van Kervinck
[on KBBK]
] Here are Spector's revised, and hopefully final, summaries:
] WTM broken: 1690176 (268456)
] WTM draw: 520 (112)
] WTM mate in 1: 6312 (1153)
] WTM mate in 2: 2608 (391)
] WTM mate in 3: 14936 (3446)
] WTM mate in 4: 18432 (2742)
] WTM mate in 5: 30672 (5504)
] WTM mate in 6: 37512 (5686)
] WTM mate in 7: 56808 (8764)
] WTM mate in 8: 86216 (13134)
] WTM mate in 9: 124264 (19045)
] WTM mate in 10: 181256 (27877)
] WTM mate in 11: 249656 (37855)
] WTM mate in 12: 294584 (43619)
] WTM mate in 13: 354760 (53097)
] WTM mate in 14: 360536 (53884)
] WTM mate in 15: 316056 (49443)
] WTM mate in 16: 246072 (39543)
] WTM mate in 17: 109360 (19182)
] WTM mate in 18: 13448 (2411)
] WTM mate in 19: 120 (16)
] Total symmetric: 655360
] Total positions: 4194304
Now these numbers exactly match Rookie's database.
] Tablebase summary: KBBK (BTM)
Again, Rookie doesn't have the BTM table yet.
Marcel
-- _ _
_| |_|_|
|_ |_ Marcel van Kervinck
|_| mar...@stack.urc.tue.nl
Ralf W. Stephan
> 7) The article's claim for 1024 distinct WTM (bK in triangle) mate in
> one positions has been proven FALSE. There are actually 1153 of these
> (bK in triangle). I have generated a list of these and they all check
> out to be mate in one. I can e-mail a copy of this position list to
> anyone would like to verify Spector's claim.
Um, a question that popped into mind when I first saw that you use
the a1-d1-d4 triangle: do you take into account that even with
one piece in the triangle, you still have some identical positions?
Example: wKa1,Qb2 bKh1 and wKa1,Qb2 bKa8 (wK in triangle)
This could be the cause of your discrepancies.
ralf
--
You are in a maze of twisty articles, all alike.
Steven J Edwards
>Steven J Edwards writes:
[In reference to _ICCA Journal_, 1985.09, pg. 144]
>> 7) The article's claim for 1024 distinct WTM (bK in triangle) mate in
>> one positions has been proven FALSE. There are actually 1153 of these
>> (bK in triangle). I have generated a list of these and they all check
>> out to be mate in one. I can e-mail a copy of this position list to
>> anyone would like to verify Spector's claim.
>Um, a question that popped into mind when I first saw that you use
>the a1-d1-d4 triangle: do you take into account that even with
>one piece in the triangle, you still have some identical positions?
>Example: wKa1,Qb2 bKh1 and wKa1,Qb2 bKa8 (wK in triangle)
>This could be the cause of your discrepancies.
The article states that the counts are made of positions with the
black king in the a1-d1-d4 triangle, and thus the total position count
at 655360 (mentioned in the article) makes sense.
For KBBK, there may be some mate in one positions with the bK on a1
and the wK on the a1-h8 diagonal; these positions have their
reflections also included in the "bK in a1-d1-d4" count. Spector is
not attempting to calculate the absolute minimum, but rather is
attempting to duplicate the counting procedure used by the article in
question. As far as I can see, all summraies for pawnless endgames in
printed articles use the same convention where one piece is rotated
with a maximum of three reflections (X, Y, X=Y). Therefore, the
article by van den Herik and Hirschfeld, the one claiming 1024 WTM
mate in one positions, is wrong.
Now, with all that said, I must admit that my implementation of
playback mode seems to have some problems with the KBBK tablebases I
genertated earier. "Playback" refers to using the chess program
interactively to probe the tablebase by playing though selected
positions. I think that this is just a minor index generation problem
peculiar to KBBK; playbacks with KRK, KQK, and KBNK all seem to work
okay. For example, I set up Spector with wBc1, wKe1, wNg1, and bKe8
and in a flash it comes back with "Mate in 29"; it then proceeds to
play out the mate in a manner far better than I could ever hope to do
manually.
-- Steven (s...@world.std.com)
Ralf W. Stephan
> ... Therefore, the
> article by van den Herik and Hirschfeld, the one claiming 1024 WTM
> mate in one positions, is wrong.
And with my building of the DB yesterday, we have the second
independent proof that you are right. Anyone to tell the
authors or the journal?
ralf
--
You are in a little maze of twisty articles, all different.