Work on game playing in AI has typically ignored games of
<I>imperfect information</I> such as poker.  In this paper, we present a 
framework for dealing with such games.  We point out several important
issues that arise only in the context of imperfect information games,
particularly the insufficiency of a simple game tree model to represent
the players' information state and the need for randomization in the
players' optimal strategies.  We describe <I>Gala</I>, an implemented
system that provides the user with a very natural and expressive language
for describing games.  From a game description, Gala creates an augmented
game tree with <I>information sets</I> which can be used by various
algorithms in order to find optimal strategies for that game.  In
particular, Gala implements the first practical algorithm for finding
optimal randomized strategies in two-player imperfect information
competitive games <A HREF="stoc94.html">[KMvS94]</A>.  The running time
of this algorithm is <I>polynomial</I> in the size of the game tree,
whereas previous algorithms were exponential.  
We present experimental results showing that this algorithm is also
efficient in practice and can therefore form the basis for a game
playing system.
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