[Retros] recent improvements

andrew buchanan andrew at anselan.com
Tue Dec 19 21:50:11 EST 2006

Hi Mario,

Thanks for the further details.

>From what you say, 13 plies is really out of the question at the moment. But

I want to just understand why 12 is impossible.

If I was doing 12 ply, I would partition the work into 8 tasks, one for each
Black pawn. In each step, it would be constrained so that the particular
pawn has to move at least 5 times, not counting a single step from 2nd to
3rd rank.

This would reduce the amount of time to perhaps 12 hours per task but more
importantly would reduce the amount of space used.

Of course, at the end, any candidate PG is not *guaranteed* to be sound...
there might in principle be a sequence of moves (not necessarily even a
candidate PG) from another task which reaches the same position.

But this is easy to fix: just run through Popeye the candidate PGs in which
more than one Black pawn moved, to check for soundness.

Does this make it tractable?

Cheers for now,

-----Original Message-----
From: retros-bounces at janko.at [mailto:retros-bounces at janko.at] On Behalf Of
Mario Richter
Sent: 17 December 2006 20:08
To: andrew at anselan.com; The Retrograde Analysis Mailing List
Subject: Re: [Retros] recent improvements


Andrew wrote:

> But really they belong to Mario, if you would care to peer into your

> database and tell us what the solutions are!

My goal with providing the list without giving example games/positions
was twofold:

- helping to avoid waste of time for attempts to improve
records which are already optimal

- giving those who try to improve the current records some indications
where their efforts can be succesful

So if somebody finds an instance for a category mentioned in my
list - like Olli and Noam recently did - then he should get the
attribution as the composer, not my computer.

> 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


> access to more powerful hardware that he might run?

The way my program works, it isn't only a matter of time,
but of space too, so an exthausive search for plies > 11 might not
be the best solution or even impractical.

But I can pick out some of the current records which look like
they can be improved, and try to break them.

Noam wrote:

> Mario -- you didn't specify whether "realizable" means in a sound

> proof game or in an unrestricted game, but now I see it must have been

> the former because g7-g8Q(R)# can be easily shown in 11 ply without

> the soundness condition, e.g. 1 g4 g6 2 g6 Nh6 3 gxh6 Bg7 4 hxg7 h5

> 5 random Rh7 6 g8R#.

With realizable I meant exactly that:
- the proofgame has exactly one solution
- there is not shorter uniquely realizable game with
the same mating pattern (i.e. with e.g Pe7xd8# there is neither
a shorter correct SPG with Pe7xd8# nor one with Pe2xd1#).

> Did you keep track of how many sound proof games

> each minimally "realizable" promotion mate had?

For 9 and 10 plies I can provide them immediatly, the data for 11 plies
follow in a later posting:

9 plies:
125 Pb7xc8=R
8 Pc7xd8=R
16 Pg7xf8=R
24 Pc7-c8=Q
251 Pb7xc8=Q
42 Pc7xd8=Q
42 Pg7xf8=Q

10 plies:
6 Pg2xh1=R
54 Pd2-d1=Q
20 Pf2-f1=Q
11 Pf2xe1=Q
6 Pg2xh1=Q



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