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%puzzle[w90,jmc]		The ``better'' heuristic and the 15-puzzle

\section{Introduction}

	The object of this note is to discuss the representation
of a class of heuristics and to illustrate it by considering the
15-puzzle.

	In most games and puzzles enjoyed by us humans, we humans
commonly do far less search than the best programs we humans know
how to write.  I think this is because we aren't very good at
introspecting and also because the programming systems we have
been able to develop aren't very good at representing heuristic
information.

	Consider the alpha-beta heuristic, used in almost all game
playing programs.  The earliest game playing programs didn't use it.
However, no human player of chess considers moves that alpha-beta
would prune.  This illustrates the fact that we aren't very good at
introspecting our own mental procedures.

	Sometimes our mathematical knowledge and habits mislead us
into formulating algorithms that are inferior to our own mental
procedures for solving a problem or playing a game.
Here's an illustration.

	It is usual to formulate our decision heuristics in games
using a numerical position evaluation function.