Newsgroups: comp.ai.games
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!howland.reston.ans.net!Germany.EU.net!EU.net!sun4nl!cs.vu.nl!victor
From: victor@cs.vu.nl (Victor Allis)
Subject: Re: Solving Chess
Nntp-Posting-Host: fluit.cs.vu.nl
References: <D6HpH3.6sJ@mv.mv.com>
Sender: news@cs.vu.nl
Organization: Fac. Wiskunde & Informatica, VU, Amsterdam
Date: Sat, 8 Apr 1995 07:17:15 GMT
Message-ID: <D6pG8s.2p0@cs.vu.nl>
Lines: 38

sje@mv.mv.com (Steven J. Edwards) writes:

>Using old style formalism, I interpret the phrase "solving chess" to
>mean the determination of the game theoretic value of chess.  That is,
>to determine if the game is a win, loss, or draw for the first player
>assuming optimal play for both sides.

That is only ONE definition of solving the game. Like with complexity of
a game, there is no clear definition of what it means to solve a game.

In my thesis, I have given three definitions:
1. ultra-weakly solved: For the initial position(s), the game-theoretic
   value has been determined.

2. weakly solved: For the initial position(s), as strategy has been determined
   to obtain at least the game-theoretic value of the game, for both players,
   under reasonable resources.

3. strongly solved: For all legal positions, a strategy has been determined to
   obtain the game-theoretic value of the position, for both players, under
   reasonable resources.

(The size of the resources is meant only to give an approximate indication
 of the time and computing equipment allowed for reproducing a solving
 strategy. The reasonable resources mentioned should typically allow
 the use of a state-of-the-art computer and several minutes of computation
 time per move.).

Personally, I call a game solved when it is at least weakly solved, since it
guarantees that in each match against any competition you will at least
draw the match (given that you play both sides equally often).

Having only ultra-weakly solved a game does not guarantee anything: Hex
is ultra-weakly solved, but we have no optimal strategies.

For more details, see http://www.cs.vu.nl/~victor/thesis.html

Victor Allis.
