00050	                     COMPUTER SCIENCE DEPARTMENT
00057	
00064	                         STANFORD UNIVERSITY
00071	
00078	                     Stanford, California 94305
00085	
00092	
00100	                          February 24, 1973
00200	
00300	
00400	Dear Morton Davis,
00500	
00600		Thank  you for your letter of January 30 and the copy of your
00700	paper.  It reminds me of an idea I once worked on but abandoned.   My
00800	idea  was  to  assign  a  "probability  of being a won position" as a
00900	function of position of a game.  Like your  IEF's,  it  must  obey  a
01000	consistency  criterion.  The function was to be estimated by dividing
01100	positions into a finite  number  of  classes,  classifying  a  random
01200	sample  of  positions  and their immediate successors and empirically
01300	determining  the  distribution  function  of  the  classes   of   the
01400	successors  of  positions as it depends on the class of the position.
01500	This together  with  the  consistency  condition  and  the  immediate
01600	classification  of  terminal positions will allow the "probability of
01700	win" to be estimated.  It may be that my old system reduces to  yours
01800	if the probabilities are restricted to zero and one; I'm not sure.
01900	
02000		I  gave  up the idea, because I came to believe that suitable
02100	reasonably computable classification functions probably  don't  exist
02200	for  games  like  chess  without  a  simple  mathematical  structure.
02300	Mathematically, the functions exist, but what if the simplest way  to
02400	compute  their value requires look-ahead to the end of the move tree.
02500	Then we are back to the heuristic search problem which I had hoped to
02600	avoid.
02700	
02800		Alas,  I  think  this is the case, and your success with NIM,
02900	etc. doesn't raise my hopes.
03000	
03100	
03200						Sincerely yours,	
03300		
03400		
03500		
03600						John McCarthy	
03700						Professor of Computer Science