Author: Roberto Waldteufel
Date: 03:21:40 04/17/99
Go up one level in this thread
On April 17, 1999 at 04:54:57, Stephen A. Boak wrote:
>On April 17, 1999 at 01:56:33, Bruce Moreland wrote:
>
>>
>>On April 16, 1999 at 22:08:56, Roberto Waldteufel wrote:
>>
>>>I am a mathematician by profession and a programmer of intelligent games (like
>>>chess, checkers etc) by hobby, and I have often contemplated the relationship
>>>between these two things. Whereas I think it is an interesting relationship, I
>>>don't think it is very useful for actually playing or programming such games.
>>>Just my opinion, for whatever it is worth,
>>
>>I agree, and I think that attempts to investigate chess using mathematics are
>>futile.
>>
>>For example, there are web sites where people try to figure out the value of
>>pieces by finding a magic formula that is a function of mobility. These
>>formulas don't take into account, among many other things, the interaction
>>between the pieces and pawn structure.
>>
>>bruce
>
>Whoa! "using mathematics" is a broad phrase. Every chess program uses some sort
>of mathematical evaluation/scoring routine ('magic formula'), even ferret. Few
>people would conclude that such formulas are 'perfect' or 'magically correct'.
>
>Seems to me that mathematical modeling is the art of using mathematics to
>describe the real world, measure it, and to forecast or predict. To create
>chess evaluation formulas with piece values based on 'whatever' is one
>mathematical method applied to a real chess board. It may not work perfectly to
>describe reality on the board (who is winning and by how much or what means).
>It may not work perfectly to predict best moves and steer the position toward an
>actual winning position. But it works, moreland or less (pun intended, sorry).
>
>I have contemplated using a type of math (this is my abstract notion--not
>implemented) in chess programs that leads to calculating winning combinations
>very quickly (compared to exhaustive searches, no matter how selective). Many
>sets of moves from a given chess position will transpose into each other at some
>point. I visualize these varying lines of play as lines or ropes that
>intertwine and join or separate. I wonder if knot theory (a type of
>mathematics) or some variant or parallel mathematical theory can figure out if
>you can get from here (current position) to there (winning position) based on
>current position and the threads of play that can result therefrom.
>
>Part of the Jeremy Silman, IM, teaching is to envision an improved or winning
>position that you would like to achieve, based first on analysis of strengths &
>weaknesses of both sides, plus an assessment of the right plan (or type of plan)
>called for in the position. The next step is to see if you can achieve such a
>position by some logical series of moves (forcing).
>
>I believe that a 'smarter' program will someday be able to use the Silman method
>to 'dream' potential winning plans and positions, then quickly determine if they
>can be achieved by force from the current position. If not, then the program
>would then be able to 'build up' its position according to the 'right plan'
>until it could effect such a forcing series of moves.
>
>For this method to have some success (admittedly not perfect), the planning and
>combination calculation would have to be mathematically modeled in the chess
>program. If this 'smart method' succeeded, it would be a program that made the
>right plans for the current position, and then spent its time only on evaluating
>logical move sequences that achieve (if forcing) its plans, or make progress (in
>non-forcing situations) toward its plans. Even the 'mere progress' itself is
>part of an overall trying to do the right thing in the given position.
>
>This 'mimicry' of the master's mind might allow the speed of the microprocessor
>to be harnessed in a focused manner, considering for example the relations
>between the pawn structure and the piece placements in the creation of good
>plans, and concentrated on making moves that are not just tactically accurate,
>but that drive the position toward the ones where the winning plans become
>forcing.
>
>Just some ideas for discussion.
>
>--Steve Boak
Hi Steve,
There was a program called Paradise which worked loosely on these principles. If
you are not already familiar with it, I strongly recommend you read up on this
program. Somewhere I have a copy of a paper about it, but I can't find it at
present. I think it is reproduced in David Levy's "Computer Chess Compendium".
Paradise could solve forcing combination problems that were far too deep for
brute force programs running on the hardware (very slow by today's standards)
available at that time. However, it could not play a whole game, only solve
tactical positions. Nonetheless, parts of your "abstract notion" could almost be
a description of the program. I'm sure you will find it interesting, and maybe
you can extend the method further in the light of improved hardware. If you do,
be sure to let us know: I would be very interested to hear if you can make it
work for more general positions. Endgames might be fertile ground.
Best wishes,
Roberto
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.