H. G. Muller wrote on Sat, Mar 10, 2012 12:14 PM UTC:
I wrote a new tablebase generator, dedicated to determine mating potential,
which does not assume any symmetry, and hence can also do odd board sizes.
Not using symmetry makes it more memory hungry, but on the other hand, it
does not need the board size to be rounded up to a power of 2, like the old
one, which can save memory. As a result I can now do 4-men end-games
(mating with a pair of pieces that do not have mating potential by
themselves) on boards upto 12x12. (This takes 421MB RAM. 4-men on 14x14
would take 1.6GB, which is more than I have.)
I updated the table I had with some selected odd board sizes, mainly to
establish exactly at which board size a leaper loses mating potential. New in
the list is the (asymmetric) Charging Knight of CwDA's Nutters army.
I also added a limited version of the Cavalier, as a Knight-Camel-Giraffe
compound. This already is enough to give it mating potential on quite
large boards. In fact, the longest mate seems to increase with board size
strictly linearly, suggesting it could do it on boards of any size.
(I tried upto 25x25, which takes 84 moves.)
The largest board on which the WAN has mating potential is 20x20 (160 moves).
For KA this is 23x23 and 208 moves. KD still has it at 25x25, but can
be proven to even have it on a quarter infinite board, which is quite
exceptional for a piece with only 12 moves. ADN also has no problems yet
at 25x25 (the biggest I could go), and take 84 moves there.
Betza NR NAME Longest mate (if generally won)
8x8 10x10 11x11 12x12 14x14 15x15 16x16 17x17
F 4 Ferz color bound
W 4 Wazir pure alternator
A 4 Alfil color bound
D 4 Dabbaba color bound
N 8 Knight pure alternator
FW 8 Commoner 18 29 35 49 62 -
FA 8 modern Elephant color bound
FD 8 ? color bound
WA 8 Waffle no mates
WD 8 Woody Rook 29 52 -
AD 8 Alibaba color bound
fNbsK 9 Charging Knight 33 52 65 82 155 -
FN 12 ? 22 32 38 44 59 72 100 -
WN 12 Vicar pure alternator
AN 12 Kangaroo 35 63 78 -
DN 12 Carpenter 31 44 52 62 92 -
FWA 12 Crowned Alfil 15 22 31 41 53
FWD 12 Crowned Dabbaba 15 20 27 33 40
FAD 12 ? color bound
WAD 12 ? 26 39 -
FWN 16 Centaur 13 17 21 28 33
FAN 16 High Priestess 17 23 30 36 45
FDN 16 ? 14 19 25 31 38
WAN 16 ? 22 31 43 57 74
WDN 16 Minister 17 23 30 36 45
ADN 16 Squirrel 19 24 31 38 46
FWAD 16 Mastodon 13 19 24 29 36
FWADN 24 Lion 5 7 9 10 12
HFD 16 Half Duck 51 66 94 107 -
CZ 16 Bison 27 40 48 55 82 104 -
CNZ 24 Buffalo 18 24 31 38 45
CNG 24 Pseudo-Cavalier 18 25 28 32 39 43 46 50
4-men: B+N 33 48 64
KBN.K is the only 4-men I tried so far on larger boards. Peculiarity here
is that B is color-bound, and mate is only possible in the corner of the B
color. This makes that it is never generally won on odd-size boards,
because all corners have the same color there. To win when B is on the
right color is easier, though, because any corner will do, so the bare King
will always be comparatively close to a deadly one. While on even-sized
boards he can take shelter in the safe corner.
I wrote a new tablebase generator, dedicated to determine mating potential, which does not assume any symmetry, and hence can also do odd board sizes. Not using symmetry makes it more memory hungry, but on the other hand, it does not need the board size to be rounded up to a power of 2, like the old one, which can save memory. As a result I can now do 4-men end-games (mating with a pair of pieces that do not have mating potential by themselves) on boards upto 12x12. (This takes 421MB RAM. 4-men on 14x14 would take 1.6GB, which is more than I have.) I updated the table I had with some selected odd board sizes, mainly to establish exactly at which board size a leaper loses mating potential. New in the list is the (asymmetric) Charging Knight of CwDA's Nutters army. I also added a limited version of the Cavalier, as a Knight-Camel-Giraffe compound. This already is enough to give it mating potential on quite large boards. In fact, the longest mate seems to increase with board size strictly linearly, suggesting it could do it on boards of any size. (I tried upto 25x25, which takes 84 moves.) The largest board on which the WAN has mating potential is 20x20 (160 moves). For KA this is 23x23 and 208 moves. KD still has it at 25x25, but can be proven to even have it on a quarter infinite board, which is quite exceptional for a piece with only 12 moves. ADN also has no problems yet at 25x25 (the biggest I could go), and take 84 moves there. Betza NR NAME Longest mate (if generally won) 8x8 10x10 11x11 12x12 14x14 15x15 16x16 17x17 F 4 Ferz color bound W 4 Wazir pure alternator A 4 Alfil color bound D 4 Dabbaba color bound N 8 Knight pure alternator FW 8 Commoner 18 29 35 49 62 - FA 8 modern Elephant color bound FD 8 ? color bound WA 8 Waffle no mates WD 8 Woody Rook 29 52 - AD 8 Alibaba color bound fNbsK 9 Charging Knight 33 52 65 82 155 - FN 12 ? 22 32 38 44 59 72 100 - WN 12 Vicar pure alternator AN 12 Kangaroo 35 63 78 - DN 12 Carpenter 31 44 52 62 92 - FWA 12 Crowned Alfil 15 22 31 41 53 FWD 12 Crowned Dabbaba 15 20 27 33 40 FAD 12 ? color bound WAD 12 ? 26 39 - FWN 16 Centaur 13 17 21 28 33 FAN 16 High Priestess 17 23 30 36 45 FDN 16 ? 14 19 25 31 38 WAN 16 ? 22 31 43 57 74 WDN 16 Minister 17 23 30 36 45 ADN 16 Squirrel 19 24 31 38 46 FWAD 16 Mastodon 13 19 24 29 36 FWADN 24 Lion 5 7 9 10 12 HFD 16 Half Duck 51 66 94 107 - CZ 16 Bison 27 40 48 55 82 104 - CNZ 24 Buffalo 18 24 31 38 45 CNG 24 Pseudo-Cavalier 18 25 28 32 39 43 46 50 4-men: B+N 33 48 64 KBN.K is the only 4-men I tried so far on larger boards. Peculiarity here is that B is color-bound, and mate is only possible in the corner of the B color. This makes that it is never generally won on odd-size boards, because all corners have the same color there. To win when B is on the right color is easier, though, because any corner will do, so the bare King will always be comparatively close to a deadly one. While on even-sized boards he can take shelter in the safe corner.