by Douglas Zare
1 November 2005

In a mathematical approach to backgammon, we often want to convert
one set of numbers to another. In a race, we'd like to convert the pip counts
to our chance to win the race. We'd like to convert the match score to
our chance to win the match. After a late hit, we'd like to convert the number of checkers
borne off to our chances to win with one checker closed out. We can construct mathematical
models for these, and many more situations. We'd like these models to be both accurate and simple
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