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Subject: Re: Solve for Mate

Author: Don Dailey

Date: 08:29:09 07/12/98

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On July 12, 1998 at 04:29:17, Shane Booth wrote:

>>>On July 11, 1998 at 19:10:59, Trefor Deane wrote:
>>>
>>>>Does anyone know of a program that can randomly generate solve for mate
>>>>problems, and not rely on a data base of previously stored problems?
>
>Danniel misread your question.  Yes, every program has an option that
>attempts to solve mate problems you give it, but I know of no program
>that will compose a valid mate problem for the user to solve.
>
>Composing a chess problem is an artistic endeavour, and getting a
>computer to generate an aesthetically pleasing problem would be an
>enormous task.  I can't see any program with this feature in the
>near future.
>
>As far as I know, the only problem ever "composed" by a computer
>was a KQN vs. KQ position by Belle, and (if I remember correctly as
>it was some years ago) Ken Thompson simply picked an interesting
>looking position from its endgame database (all pieces on the same
>file).
>
>Shane


I don't think this would be that hard.  The problems may not be
beautiful though.

Here is the algorithm:

  Generate and test random legal positions until you find a mate
  in the required depth.  I'm guessing this will not take as long
  as one might think since the kings will often be out in the
  center.  Also you could experiment with different constraints
  like number of pawns for each side.

  Once you had a mate position you could purify it by taking off
  pieces one at a time to see if they are relevant.


I didn't say it would be pretty or fast!  But it might be
interesting and fun to see what comes out.  You could have
other constraints to make the positions seem more natural
too, like having some rules or statistical tendencies for
the pawns to be on "natural" squares and other things.
Most random positions from games will have some pawns still
on their home squares and not have an unusual number of
pawn weakneses.  Things like this could be simulated.

Probably there are more elegant algorithms but this might
work.  Anybody want to take a crack at it?

I once culled games for mates.  If you do self testing
and let the games run to mate positions you are guaranteed
to be able to generate mate in N to any depth you are
capable of searching.

I also did this for tactics.  I was interested in finding
n ply tactics so ran a sequence of thousands of positions
from games looking for them.  I  ran each position
at several depths, looking for sudden jumps in score.
I required the initial scores (at shallow depths) to be
close to zero and suddenly jump to bigger scores.
The result was very surprising.  Tactics seemed to stop
dead after about 6 or 7 ply.  I found a huge number of
5 ply tactics and almost zero deep tactics (based on
how I defined a tactic.)   You would think there would
be lots of tactics at any arbitrary depth but this was
not the case.

What seemed to happen was that a mistake was made and
then a shallow tactic was possible, OR the win was
too gradual to trigger my definition of a tactical
shot.  To the best of my knowledge, I required a sudden
score jump of x to consider it a tactic, not several
small jumps from ply to ply.  But n was not very large
either, something like 3/4 pawn or so.   The difference
in number of tactics found though was enormous.  These
were games of grandmaster too, not computer generated
positions.


- Don



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