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For
security purposes, the casinos like all dealers to play
their hands by a standard set of rules. Management prefers
that dealers have no say whatsoever in how their hands are
played. This avoids possible errors in judgment and precludes
collusion between an unscrupulous dealer and player.
Because the house always plays in a fixed manner, we know
exactly what to expect from the dealer. Let's take a closer
look at the dealer's play.
In many casinos in the United States, the dealer keeps hitting
until reaching a total of 17 or more. That is, once the
dealer reaches 17, he must stop, regardless of what the
players have as their totals. Other casinos offer a variation
in which the dealer must continue to hit if holding a soft
17 (soft hands always contain an ace which counts as 1 I).
In this case, the dealer must hit until reaching a total
of 17 or more on hard hands, and 18 or more on soft hands.
In some casinos, the hitsoft-17 rule is employed in single-
or double-deck games, while the dealer stands on all 17s
in multiple-deck games (the rule in force is usually specified
on the table layout).
Since we know exactly how the dealer will play, cycling
through all the possible card sequences allows us to obtain
the dealer's theoretical distribution. Figures 1 and 2 were
generated by this type of combinatorial analysis, assuming
a pack of two freshly shuffled decks. We've chosen the 2-deck
game for our examples because it serves as an "average"
of the many games offered in casinos.
First, let's look at the theoretical final distribution
of values for the dealer's hand. Looking at Figure 1, you
can see that overall the dealer busts about 28%, of the
time, assuming we consider no information about the dealer's
upcard Additionally, the dealer will reach a pat hand (17
through 21) about 67% of the time, the remaining 5% or so
accounted for by naturals.
In reality the dealer's final outcome is heavily dependent
on the upcard. Via the same combinatorial analysis, we obtain
Figure 2 (pgs. 24 and 25), which shows the distribution
of dealer's final totals as a function of the upcard in
a 2-deck game.
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