[Retros] recent improvements

andrew buchanan andrew at anselan.com
Sun Dec 17 12:55:22 EST 2006

Hi Mario,

Thanks for this. It was with some trepidation that I checked your results
against the list of positions we had assembled - I was worried that our work
might all be undercut.

It turns out that in *5* cases, our homespun results can be improved upon:
Piece Line Ours Actual
N cxd 13 11
N exd 12 11
R e 13 11
R dxe 12 11
Q dxe 12 11 (presumably similar to R dxe).

I will have a think to see whether I can come up with the actual results.
But really they belong to Mario, if you would care to peer into your
database and tell us what the solutions are!

There are now however *40* of our solutions (including some 12 ply cases)
which were already best possible. This means that there are 43 cases where
we don't know whether our solutions are optimal.

I presume that none of the solutions so far includes any double/discovered
mates? It might *just* be possible...?

Extrapolating the values you gave, the 12 ply case might take of the order
of 100 hours. Is this possible for you to run? Or does Francois Labelle have
access to more powerful hardware that he might run?

Thanks again,

-----Original Message-----
From: Mario Richter [mailto:mri_two at t-online.de]
Sent: 17 December 2006 13:42
To: andrew at anselan.com; The Retrograde Analysis Mailing List
Subject: Re: [Retros] recent improvements

Andrew wrote:

> However, Francois Labelle's (& Mario Richter's?) programs have not spoken


> this discussion. Tasks of this kind ought to be tractable in the same way

> that massacre positions proved to be. Basically, ignore any move where a

> promotion cannot be achieved in the number of moves remaining.

The problem is, that the more degrees of freedom (in the case of
MPGs non-capturing moves, in the case of 'mate by promotion' moves
that do not advance the thematical pawn) you have,
the longer the search will take.

This could be observed in the case of K+K-MPGs, were the 33 plies
case could be completely investigated in less than 10s, while the
next step, 34 plies, already required approx. 10min.

Nevertheless, at least up to 10 plies Francois Labelle surely
knows the answer.
(s. www.cs.berkeley.edu/~flab/chess/statistics-positions.html )

Just out of curiosity (and because Andrew asked for it) I let my own
program run.

Computing all games, that end with mate by pawn promotion,
required for:
- 9 plies 2s
- 10 plies 42s
- 11 plies 1h 50min

The way my program works there is some extra time needed for
post-processing the result sets to find the the uniquely
realizable games.

Here my results:

Realizable in 9 plies
- Pb7xc8=R
- Pc7xd8=R
- Pg7xf8=R
- Pc7-c8=Q
- Pb7xc8=Q
- Pc7xd8=Q
- Pg7xf8=Q

Realizable in 10 plies
- Pg2xh1=R
- Pd2-d1=Q
- Pf2-f1=Q
- Pf2xe1=Q
- Pg2xh1=Q

Realizable in 11 plies
- Pc7xd8=N
- Pe7xd8=N
- Pe7xf8=N
- Pg7xf8=N

- Pe7-e8=B
- Pe7xf8=B

- Pc7-c8=R
- Pd7-d8=R
- Pe7-e8=R

- Pb7xa8=R
- Pd7xc8=R
- Pd7xe8=R
- Pe7xd8=R
- Pe7xf8=R
- Ph7xg8=R

- Pe7-e8=Q
- Pb7xa8=Q
- Pd7xc8=Q
- Pd7xe8=Q
- Pe7xd8=Q
- Pe7xf8=Q
- Pf7xe8=Q
- Ph7xg8=Q



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