I often read the
column of my friend and colleague John Brokopp, who also writes for
this site. John recently had a series of columns devoted to interviews
with a successful Blackjack player identified only as Mr. Aces. In John's
February 8, 2006 article he asked Mr. Aces if he used Basic Strategy
all the time. The answer was that it is important to use Basic Strategy
all the time. He went on to say that on rare occasions he does deviate
from it and that "quite frankly it is one of my downfalls."
The specific example he gave is the situation wherein the player has
a total of 15 or 16 and the dealer shows a 7. Here are his exact words.
"...I have
a tendency to hesitate, especially if I have a large bet on the table.
Basic strategy tells you to hit the hand, but when I see that dealer's
seven I think that if there is anything but a ten or ace in the hole
he's going to have to hit the hand."
It is interesting
to me that this guy, who obviously knows better, would admit to hesitating
in this situation and perhaps even intentionally misplaying the hand.
It is also understandable. After all, the seven is not a very good card
for the dealer and one's gut reaction is to sit back and let the dealer
draw, this being the most probable scenario. Gut reaction or not, standing
is the wrong play and I'd like to show you why.
I'm going to do
this analysis two ways. One is anecdotal and the other is to show you
the exact numbers involved. I will use an infinite deck analysis for
simplicity. As Peter Griffin points out in his book Theory of Blackjack,
an infinite deck is not infinite at all but rather is a deck used in
a game where one draws with replacement. This means that the probabilities
don't change as the game progresses. This is a good approximation for
multiple-deck games. The more decks the less the probabilities are affected
by the removal of a card and thus the reason for the infinite deck terminology.
The probability
of a ten is 4/13 and the probability of any other card is 1/13. Thus
there is a 5/13 probability that by standing you will be beaten. But
there is also a 3/13 probability that the dealer will draw a two, three,
or four, which would result in a good drawing hand for the dealer --
that is, a nine, ten or eleven. This means that 8/13 of the draws are
favorable for the dealer, only 5/13 of them are not. Of course, some
of the good draws for the dealer may result in busts but some of the
bad draws may result in good hands; it takes a more refined analysis
to sort these out. Thus the above argument is not definitive but it
sure is enough to make me doubt the wisdom of standing.
A precise argument
would have to look at all of the possible situations and look at the
expected returns by either standing or hitting and compare the two.
I am going to assume an infinite deck game with the dealer hitting the
soft seventeen (which is actually good for the player in the situation
we're discussing). I wrote a program that calculates these expected
returns and here are the results. If the player holds a sixteen versus
the dealer's seven, the player has an expected return of approximately
-0.4754 units if he stands and an expected return of -0.4148 if he hits.
The difference is 0.0606. This means that the player is losing about
six cents per dollar in this situation if he stands. If the player hits
on 15 his expected return is -0.3698 and so standing in this situation
costs the player about ten and a half cents per dollar.
So, grit your teeth
and hit that sixteen versus the seven; in the long run you'll be glad
you did. See you next month.