Although casinos deal blackjack from a pack containing up to eight decks, analysis of the game assuming a much larger number of decks is instructive, both in the tools needed and in those readily obtainable results that are insensitive to the pack size.
Immediately following a shuffle, the first card drawn from the shoe has a 1 in 13 likelihood of having any specific value between 2 and 9, a 1 in 13 likelihood of being an ace, and a 4 in 13 likelihood of having value 10. In general, the likelihood of a specific value for any subsequently drawn card depends on which cards have previously been drawn; i.e., the composition of the remaining pack fluctuates as cards are dealt from it. However, for a shoe with a large number of decks the likelihood of drawing a specified value varies only negligibly from that of the first card. Thus, the approximation that those likelihoods are fixed and unvarying is the same as if the shoe contained an infinite number of decks. Griffin (1999) has called the shoe in this limit “nondepleting”; Epstein (1995) says that the draw is “with replacement.”
KeywordsConditional Probability Single Hand Initial Hand Stand Parameter Split Pair
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