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H. G. Muller wrote on 2012-03-10 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.