  Composition theory can be used to analyze and enumerate the number of ways a
dealer in Blackjack can reach any given point total. The rules of Blackjack
provide several restrictions on the number of compositions of a given number.
While theory guarantees a specific number of unrestricted compositions of any
positive integer, we must subtract the number of compositions not allowed in
Blackjack. We present a constructive approach to enumerate the number of
possible compositions for any point value by deleting those illegal
compositions from the total number of unrestricted compositions. Our results
cover all possible cases and also generalize to changes to the rules of
Blackjack, such as the point value where the dealer must stand. Using the
infinite deck assumption, we also find the approximate probability that the
dealer reaches that point total.
