Author: Stephen A. Boak
Date: 01:54:57 04/17/99
Go up one level in this thread
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
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.