If you did this stochastically, i.e. by sampling randomly, you could
concentrate on the playing algorithm and trade off space for time to achieve
as much precision you need.  Also, a stochastic version is easily
parallelizable - see
http://www.jsoftware.com/jwiki/DevonMcCormick/ParallelizedJCodeExamples for
an example of how you could do this.
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