[Retros] Massacre SPGs

[Gerd Wilts]

> Francois, I really am very impressed. Gosh.


I too am very impressed! Thanks to Francois' work huge progress is currently
being made in this field!


> (2) I make it that there are 3440 (1+1) positions. You have tested 92 so

> far. Does anyone have any intuition as to whether the property of being an

> SPG becomes more or less likely as x increases for the next few values?

> Presumably these correspond to positions where the kings are progressively

> further from their start squares.However, it is difficult to force

> uniqueness on king walks, unless they are strictly diagonal. My

> own feeling is that we have the best "chances" at x=5 or 6, and after

that,

> the prospect of a hit trends downwards.


I share your feeling that for x=5 and x=6 there is still a chance to find
a non-dualist (1+1) PG, although the chance is tiny. So these two cases
should in any case be tackled by an exhaustive approach, if possible.
However,
I don't think that it is very important that the kings walk strictly
diagonally,
because those PGs are all somewhat aleatory (of course, everything is
strictly
determined by the rules of the game, but the result is "chaotic"). Because
the Kings have to make some captures on appropriate squares, they might walk
quite randomly. But of course, chances are much higher the farther the Kings
are away from their initial squares.


> So we would reach a point of limiting  returns in

> using the exhaustive approach. We could use Popeye to find out

> the number of solutions for certain key (1+1) positions, and that would

give us a

> suggestion of the overall behaviour of the Massacre SPG population as x

> increases.


As far as I know the number of non-capturing moves can not be too high
in order to enable Popeye to tackle the problem. I am not sure if Popeye
can check problems with x=5 or even x=6.

Another way to get a feeling for (1+1) PGs is to compile a table of
upper limits for the number of moves for each of the 3440 possible
positions,
by extending the known PGs with 2 and 3 pieces. (On the PDB web site
28 PGs with at most 3 pieces can be found with the following query:
K='Massaker SPGs' AND APIECES<=3). Quite a high number of candidate
positions
can be ruled out in this ways for x=5, and even more for x=6.

Best,

Gerd Wilts