🚀 go-pugleaf

> 	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.. The tree is traversed
> by a pointer. Whenever a player makes a move, the pointer traverses to the
> corresponding node through the corresponding arc. The player than picks
> up the point value of the arc and adds it to his score. So at any given
> moment of the game, the player who has the lower score is making less
> deviation from a perfect play.
> 	The question is:
> 
> 	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??

Yes, it seems possible as follows:

The loser may be in a position at some point where there are very few
possible moves, so that a truly disasterous move may have a relatively
small point value.  Similarly, the winner could have made a slightly
inferior move at some point in the game where there were many possible
moves.  The point value of the winner's slight mistake could therefore
be larger than that of the loser's disasterous move.

It seems that the definition of perfect play needs to be better defined
than from a rank ordering of the moves in each position.  Even scaling
them so that the best move always has point value 1 and the worst move
always has point value, say, 1000 will not work because there will always
be positions where "almost anything will do" and others where "the
slightest mistake is fatal."

				Dave McCooey
				AT&T Bell Labs, Whippany
				ihnp4!whuxlk!dim