[Retros] Massacre SPGs

[Francois Labelle]

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.

	Francois