[Retros] Massacre SPGs

[Andrew Buchanan]

Francois, I really am very impressed. Gosh.

A couple of points.
(1) In the x=5 case, it looks as if you could well exceed the 6 billion
position limit that you mentioned yesterday around before ply 25 where the
number of positions might peak, since you are at 300 million already at ply
16. But suppose you exceed 6 billion at ply n. Can't you just divide your
ply n-1 data into k batches, and process each batch separately? Then you can
just add together the data for the surviving positions when you the number
of positions starts to thin out again. The number of batches for x=5 is
probably not unwieldy, although it might become so at x=6.
(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. 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.
(3) From a DR perspective, I'm interested in *any* position you have
encountered in this quest (not necessarily a (1+1)) in which the number of
solutions is 1, but without A1.3 is greater than 1.
(4) Thanks for the 4 dead positions you showed. They are fun: please keep
tracking them. Were the 4 that you exhibited SPGs? Have you any dead SPG
positions identified so far?
(5) From an "At Home" perspective, Thierry le Gleuher & myself are
interested in the most depopulated "At Home" SPG. Thierry has a published
but C- position with only 7 units at x=6.
n°4039 Phénix 109, juillet-août 2002
1n1qk3/5p2/8/8/8/8/4P3/2B1K3
(3+4)    SPG in 15,5 moves?
1.Nf3 e5 2.Nxe5 Bd6 3.Nxd7 Bxh2 4.Nb6 axb6 5.Rxh2 Rxa2 6.Rxh7 Rxb2 7.Rxg7
Rxb1 8.Rxg8+ Rxg8 9.Rxb1 Rxg2 10.Rxb6 Rxf2 11.Rxb7 Rxf1+ 12.Kxf1 Qxd2
13.Rxc7 Qxc2 14.Rxc8+ Qxc8 15.Qd8+ Qxd8 16.Ke1

Thanks for all your efforts,
Andrew Buchanan.

Francois Labelle wrote:


>Andrew Buchanan wrote:

>

>> Francois, congratulations on your amazing Massacre SPG results

>

>Thank you! It's quite a contrast from the endless lists of easy proof

>games I've been producing so far.

>

>> > 18 SPGs without Article 1.3 of the Laws

>> > 17 SPGs with Article 1.3 (Dead Reckoning!)

>>

>> However, Dead Reckoning might in fact *enable* a massacre position to be

>> SPG.

>

>My 2nd line was meant to be taken literally. There is no "among those 18"

>implied there. I counted the number of SPGs with Dead Reckoning, period,

>without knowing a priori whether I would get more than 18 or less.

>

>I created a new web page on massacre proof games with all my results so

>you can see for yourself:

>

>http://www.cs.berkeley.edu/~flab/chess/problems-massacre.html

>

>> SPG 17.0?

>> wKc2, bKg8

>> wKe1, bKf7

>

>On my page you'll see that even with DR those two SPGs have 508 and 361122

>solutions respectively. You'll also see that the minimum is 4 solutions

>for a (1+1) SPG in 17.0 moves. Article 1.3 "enables" a 3rd example with 4

>solutions without disabling the first 2.

>

>> DR should also be borne in mind for the x=5 quest.

>

>Of course. And it's actually not very hard to do: To know what is the

>status of ply n with A3.1, I simply take ply n-1 without A3.1, remove the

>dead positions due to A3.1, and then go forward by one ply. I'm so glad

>that there is no need to run my program with dead reckoning turned on from

>the beginning. My dead reckoning code is probably correct, but it hasn't

>been tested as thoroughly as the rest.

>

>For fun, here's a sample of the "toughest" dead reckoning positions my

>program encountered: KBKB after 1 ply, KB after 2 plies, stalemate after 1

>ply in 2 ways, (same).

>

>_________________ _________________ _________________ _________________

>|                 |                 |                 |                 |

>| . . b . . . . . | . . . . k . . . | . . . . k . . . | . . . . . . . k |

>| . . . . . k . . | . . . . Q . . . | . . . R . R . . | . . . . . Q . . |

>| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

>| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

>| . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . |

>| . . . . . . . . | . . . . . b . . | . . . . . . . . | . . . . . . . . |

>| . . . q . . . . | . . . . . r . . | . . . . q . . . | . . . . q P . . |

>| . . . . K B . . | . . . . K . . . | . . . . . K N . | . . . . K B . . |

>|_________________|_________________|_________________|_________________|

>

>

>Michel Caillaud wrote:

>

>> Sorry, but Popeye found cooks :

>

>Can Popeye test (1+1) SPGs in 17.5 moves? My program thinks that 17.5 is

>about 100 times harder than 17.0, but maybe Popeye doesn't.

>

>If so, another approach for finding the "holy grail" would be to try

>promising king positions (my list of king positions in 17.0 moves could be

>helpful here) and test them with Popeye or another program. I'm sure these

>programs use the fact that the kings must go in particular directions to

>speed up the verification.