Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 ggr 10/10/85; site bentley.UUCP
Path: utzoo!watmath!clyde!burl!ulysses!mhuxr!mhuxn!ihnp4!bentley!kwh
From: kwh@bentley.UUCP (KW Heuer)
Newsgroups: net.games.chess
Subject: Re: Perfect Play?
Message-ID: <628@bentley.UUCP>
Date: Tue, 11-Mar-86 18:19:47 EST
Article-I.D.: bentley.628
Posted: Tue Mar 11 18:19:47 1986
Date-Received: Thu, 13-Mar-86 07:25:46 EST
References: <2916@sunybcs.UUCP>
Organization: AT&T Bell Laboratories, Liberty Corner
Lines: 42

In article <2916@sunybcs.UUCP> sunybcs!ugfailau (Fai Lau) writes:
>Therefore, it seems that the one who wins is the one who makes the fewer
>mistakes during the couse of the game.

I've heard it said that the winner is the one who makes the second-to-
last mistake.

>	Now let's consider a game tree is available for SCORING ONLY for
>the game of chess. Every arc of the tree is assigned a point value denoting
>the quality of the move comparing to other moves branching from a common
>node. That is, the best move following every node carries the point value
>of one, second best two, third best three, etc..

Who decides which move is "best", "second best", etc.?  Let's take a
specific example: suppose I have three ways (a,b,c) to mate on the move,
one (d) which will throw away the mate threat but leave sufficient
material advantage for a clear win, one (e) which will stalemate, and one
(f) which is a losing blunder.  How would you assign numerical values
to these?  I think the only fair system is to compare against perfect
play; i.e. (a-d) are equally good, since they all win (although (a-c)
are "faster" wins); I'd assign them a score of zero.  (e) is a mistake,
since it converts a won game into a draw; I'd assign it a score of one
(along with any other move whose outcome is a draw after subsequent
perfect play).  (f) is a double-mistake, equivalent to a win->draw and
a draw->lose at the same time; I'd assign it a two.  These are the only
possible values in my scheme.  At the end of the game, your total score
is the number of mistakes you've made.

>	IS IT POSSIBLE FOR THE LOSER OF THE GAME TO ACTUALLY HAVE
>ACQUIRED LOWER SCORE? IN OTHER WORD, IS IT POSSIBLE FOR THE LOSER TO HAVE
>MADE FEWER DEVIATION FROM A PERFECT PLAY EVEN THOUGH HE LOST THE GAME??

With my counting scheme, assuming the initial position is a draw under
perfect play (which seems extremely likely), each mistake changes the
game value by one, so if one player wins, he has made one less mistake
than his opponent.  The game ends in a draw iff both players have made
the same number of mistakes.

I realize that the "mistake-score" of a move cannot, in general, be
computed.  But how else are you going to assign a score?

Karl W. Z. Heuer (ihnp4!bentley!kwh), The Walking Lint.