[Retros] SPGs enabled by A1.3

[Mario Richter]

Francois Labelle wrote:


> - 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.


For some special situations the following reformulation of
parts of the above might be helpful:

Each move by a king to a square on rank 3 to 6
requires one non-capturing move (either that move itself is a
non-capture or in the course of the game a piece must
have moved to the initially empty square).


and andrew buchanan wrote:


> 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.


But one can apply some kind of "stretching" to the PGs
leading to these positions.

That approach might be used to exclude from further
consideration some neighbouring KK positions that cannot
lead to a dual-free SPGs.
(Thereby supporting an idea Francois Labelle posted
 in a previous mail:
 [02.May.2004]> It might be possible to check x>=6 faster
 [02.May.2004]> by constraining the search to promising
 [02.May.2004]> king positions only. )


Example:

The position wKe2+bKe7 is the final position of the
famous K+K-massaker-SPG in 17 moves by Samuel Loyd
(http://www.softdecc.com/pdb/search.pdb?expression=PROBID='P0001931').

In one (not uniquely determined) proof game leading to
that position, after the black's 15th move the following position
is reached:

white: Kd2 Ra7 Pe2
black: Kf8 Rf2 Pe7

The original solution continues by 16.Rxe7 Rxe2+ 17.Kxe2 Kxe7,
leaving only the 2 kings on the board (wKe2+bKe7).

Now if we are interested in x=6 KK positions, we have one extra
pair of moves to reach a KK position.

So one can try now to find all continuations which after black's
18. move lead to a KK position.

(Ke2 + Kh7):  16. Rxe7 Kg8   17. Rh7 Rxe2+  18. Kxe2  Kxh7
(Ke2 + Kg7):  16. Rxe7 Rxe2+ 17. Kxe2 Kg8   18. Rg7+  Kxg7
(Kd2 + Ke8):  16. Rxe7 Rxe2+ 17. Rxe2 Kf7   18. Re8   Kxe8
(Ke2 + Ke7):  16. Kd1  Rxe2  17. Kxe2 Ke8   18. Rxe7+ Kxe7
(Ke4 + Ke7):  16. Kd3  Rxe2  17. Rxe7 Re4   18. Kxe4  Kxe7
(Ke2 + Kf7):  16. Rxe7 Kg8   17. Rf7  Rxe2+ 18. Kxe2  Kxf7
(Ke3 + Ke7):  16. Kd3  Rxe2  17. Rxe7 Re3+  18. Kxe3  Kxe7
(Kd2 + Ke6):  16. Rxe7 Rxe2+ 17. Rxe2 Kf7   18. Re6   Kxe6
(Kb2 + Ke7):  16. Kc1  Rxe2  17. Rxe7 Rb2   18. Kxb2  Kxe7
(Kd2 + Ke7):  16. Kc1  Rxe2  17. Rxe7 Rd2   18. Kxd2  Kxe7
(Kc2 + Ke7):  16. Kc1  Rxe2  17. Rxe7 Rc2+  18. Kxc2  Kxe7
(Ke1 + Ke7):  16. Kd1  Rxe2  17. Rxe7 Re1+  18. Kxe1  Kxe7

(in all cases a capture of a rook being the last move, so
 no DR arguments apply).

Because the original PG was already dualistic before move 16,
the KK positions in the above list cannot lead to dual-free
SPGs and can therefore be excluded from further investigation
for the x=6 case.

Even more 'productive' is the fascinating KK-massacre SPG
in 16.5 moves found by G.Ponzetto from Italy
(http://www.chessvariants.com/problems.dir/twokingstask.html)

where after black's 15th move we have:
white: ke1 rg7
black: kf8 rf2 pe7

and with the above approach a list of more than 40 KK positions can
be generated which can be excluded from further investigation
for the x=6 case.


greetings

   mario