From: Peter Marko <pmarko@bnr.ca>
Subject: Re: When Deep Thought Beats Kasparov...
Organization: Northern Telecom Canada Ltd.
X-Useragent: Nuntius v1.1
     <1992Oct8.202021.15709@midway.uchicago.edu>
Date: Fri, 9 Oct 1992 15:28:02 GMT

In article <1992Oct8.211647.28522@cis.uab.edu> Kenneth Sloan,
sloan@cis.uab.edu writes:

  >In article <1992Oct8.170109.16988@bnr.ca> Peter Marko <pmarko@bnr.ca>
writes:
  >
  >[a very cogent presentation of the trends in computer chess strength -
  >with which I entirely agree]

Thanks for the kind words...

  >Except:
  >
  >The plot of data points giving rating vs. time has data points
separated
  >by an average of 6 years apart.  If development can be characterized by
  >"punctuated equilibrium", it is dangerous to then produce a set of
  >predictions at 1-year intervals.  I would be more comfortable with
  >extrapolations separated at least 12 years apart.

I agree.  We are talking about discrete achievements here.

  >Actually - this correlates well with the claim that "just knowing the
  >rules" corresponds to a rating of about 900.

According to Mr. Elo, this figure is about 945 (USCF, in 1978) if the
distribution of the proficiencies of chessplayers follows the
Maxwell-Boltzmann function (paragraph 9.15 in his book).  There is some
evidence that it does (better than the normal, anyway).

  >>Would the absolute maximum [Elo rating] be about 12500?  Is it
significantly lower,
  >>higher?  Why?  Is it infinite? 
  >
  >Yes (theoretically) - as long as you can construct a series of players
  >(machine or otherwise) such that player A plays at, say, the 3000 level
  >but always loses to player B, who always loses to player C, who...
  >
  >As long as winning a game guarantees that you gain rating points - a
  >player who wins all games will (eventually...) achieve any finite
rating
  >- which is as good an operational definition of "infinity" as we need
  >here.
  >
  >[...]
  >
  >The question really is: how close is a 3000 player to perfection? 
  >On the one hand, a 3000 player may have solved the game, but
  >nevertheless draws occasionally with 2800 players.  This would connect
  >"perfection" to the current rating scale, and prevent the construction
  >of my infinite series of players.
  >
  >If, on the other hand, it turns out that the value of chess is 1/2 -
but
  >no 2800 player could ever draw against perfect play - then we have the
  >possibility of an infinite top rating.

Like I said before, I do not advocate the number 12500 or the approach
used to derive this figure.  All I wanted to do is provide an example for
the discussion.

I will try to tackle this problem seriously now.  First of all, let us
assume the following:

  1. Chess is solvable;
  2. The normal distribution applies to chessplayers' performance.

Then, consider the following facts:

  1. The numer of possible moves in each position is finite
  2. The length of each game is finite

From fact number 1 it follows that, for any chessplayer, the probability
of finding the best (perfect) move in each position is finite.  From this
and fact number 2 follow that, for any chessplayer, the probability to
conduct a perfect game (i.e., to find the best moves for the entire
length of the game) is finite.

This means that there is a finite chance that any chessplayer will score
against a perfectly playing opponent.  In other words, the strength
(rating) of the perfect machine is finite.  The big question is, of
course, what this number is.

As I do not have the answer to this question right now, let me finish
here.  I will post again after a brainstorm.

   ...Peter

---------------------------------------------------------------
Peter Marko    .....    (613)763-5344    .....    pmarko@bnr.ca
Northern Telecom Canada Ltd.   .....    Ottawa, Ontario, Canada
Newsgroups: rec.games.chess