# [Retros] SPGs enabled by A1.3

Francois Labelle flab at EECS.Berkeley.EDU
Fri May 7 02:36:14 EDT 2004

andrew buchanan wrote:

> I am interested in how francois plans to prune the

> search for x=6 KK positions.

I can prune the search each time I can guarantee that a KK position cannot
be reached from the current position.

- Right now I'm only pruning if the number of non-captures exceeds x.

- As you mentioned, in a quest for KK, the non-capturing moves must be
split equally (3+3 if x=6, 4+3 if x=7, etc.), so I can prune the search if
the number of non-captures of a particular side exceeds its limit.

- My other idea is to make a list of KK positions that have the potential
to lead to a dual-free SPG (kings are far enough from wKe1, bKe8), and
prune the search if the kings can't possibly make it to one of them
(they're too close to wKe1, bKe8). If the kings are close to wKe1, bKe8,
there must be a path of pieces (white or black) that the kings can use to
get away, otherwise prune. I still haven't formulated the pruning strategy
in detail. It looks complicated, and I must not forget about castling and
en passant.

- (Any other reason why I can prune the search is welcome.)

> DR does ensure that the exactly 7200 legal KK

> positions don't interfere with one another. I.e. if

> one such position has been achieved (presumably

> non-uniquely) in n ply, then this will not spoil the

> chance of achieving a neighbouring KK in n+1.

Didn't we decide that there were 64^2 - 36*9 - 24*6 - 4*4 = 3612 legal KK
positions? Anyway, I may have to cut corners and remove some KK positions
from consideration based on heuristics rather than absolute impossibility.
But ideally I'd like to know how many moves are required for all 3612
positions, even wKa8, bKa1.

> PS: What do you plan to do with the other 8 DR SPGs? I

> would be very happy to find them a home on my website

> at your convenience. In any case a private email to

> one person does not constitute publication :-)

Since they look similar I thought that 2 DR SPGs were enough, and that
only a DR nut like Andrew Buchanan would be interested in all 10. Oh
wait... you *are* Andrew Buchanan :) I can send you the SPGs for your
website (I have the diagrams, but I'm not sure I have the solutions, I
have to do extra work to get them).

Francois