Raplh Betza posted this game after I stopped haunting the Chess Variant
Pages around 2000, and so I didn't become aware of it until recently. And
having become aware of it, I am (like some of the previous posters)
intrigued by the extreme challenge (apparently yet unmet) of writing a ZRF
for it.

In response to Robert Price's post of 2004-01-17, it seems to me that the
nonsimultaneous shout of the Go Away is actually a more interesting problem
than multiple occupancy. As far as I know, Mr. Price's proposal to treat
this as a 3-dimensional game with visually overlapping cells is, although
a pain to code, the appropriate solution for Zillions. However, I believe
it is infeasible to code a Go Away shout as a single Zillions move. As Mr.
Price implies, using add-partial to code a shout as a series of all legal
submoves is likely to result in a very weak computer opponent, because
Zillions will be able to look ahead only a very short distance when a
complicated shout is available. Nonetheless, I think you have to do just
that.

The reason why the shout is so troublesome is that in the worst case, a Go
Away can be surrounded by a large number of pieces, including both
Basilisks. As I understand it, the order in which a Go Away pushes pieces
does not matter unless it pushes Basilisks; but if does push Basilisks,
then it matters which pieces are pushed before and which after each
Basilisk.

That means that when a Go Away is surrounding by n non-Basilisk pieces
subject to petrification (that is, n pieces that are not Basilisks, and
not statues or otherwise immune to the Basilisk's glare), the number of
distinct moves a Go Away can make is equal to the number of ways to
partition a set into b + 1 parts, where b is the number of Basilisks among
the n pieces.

For a large n (say, 8 or so, but multiple occupancy can result in an even
larger n than 8), this is a big enough number for one Basilisk (256 for n
= 8), and an even bigger one for two (6561 for n = 8). Certainly the
number could be big enough that the menu of move choices Zillions would
display for a single-move Go Away shout would be substantially larger than
the average computer screen. I know such menus are broken into multiple
columns when longer than the height of  the screen, but a big shout could
easily fill the entire width of the screen with such columns, and still
not be done. What happens then? I've never seen a program display such a
long list of choices, but my experience with Microsoft products leads to
me fear that Windows does not handle the situation gracefully.

However, I think there is a solution involving add-partial that is near
optimal. Code it as follows: first move all the non-Basilisk
petrification-immune pieces simultaneously, and then move each of the
remaining pieces in a partial move. I think the result in terms of
lookahead difficulty is the same for Zillions as for a single-move shout,
but the menus should be manageable for a human player.

If someone who understands the implications of the rules of Nemoroth
better than I do figures out that there is actually a tight enough
constraint on the number of nonpetrifiable pieces that can be adjacent to
a Go Away that the unitary Go Away move actually is feasible, I'd welcome
the news.

In any case, Nemoroth is an extremely deep game, much more so than any
other pure strategy game I know of, and computers are likely to play it
very badly for the foreseeable future.

An alternative to implementing the full rules might be to nerf the Go
Away, and code its shout as simultaneous (move all the pieces first, and
only then calculate the Basilisks' effects). This would not really be
Nemoroth, of course; it would be a less deep variant (you might call it
Nemoroth Lite), but computers might play it better.

As an aside, I'm grateful for John Lawson's comment of 2008-10-30, where
he says it's difficult to play Nemoroth legally. When I first read the
rules, I thought, there's no way I'd be able to figure out what was a
legal move in this game without a computer to help me. I'm glad it's not
just my own thickheadedness.