Blackjack First Base Penalty
For some time, we have been aware that it is better to sit at third
base in single deck, face down games. (That is the seat to the far left
at a Blackjack table.) Common sense tells us that we get to see more cards
and can make better playing decisions. In an extreme case (seven players),
the advantage difference between seats 6 and 7 is about 0.05%. You lose
another .05% per seat as you move toward first base. However, the difference
in advantages for a card counter between first and second seat is much
worse. First seat can be as much as .16% worse than second seat. As this
is a severe penalty, I decided to take a look. First, I looked at the
winnings by true count. I created a chart which shows the winnings for
first seat and second seat by true count. [link]
The chart shows that the winnings are identical for all counts below 4.
But, at a TC of 4, second seat does better. At 58, better and better.
After that,. It evens out. OK, we now know that there is something about
these particular counts that we should examine. I then decided to look
at hand types. I took the winnings for the second seat and broke them
up into an array of all possible two card hands vs. dealer up cards. This
is an array of 330 values. I also created the same array for the second
seat. I subtracted the second array from the first array and charted the
remainders. The result is a combination surface area/contour chart that
indicates the hands where the first seat has a problem. [link]
Eureka! First seat has a serious problem with two tens against a 3, 4,
5 and 6. Tens vs. 6 is particularly severe. All other hand results are
about the same. Common thinking would have expected many differences along
the lines of the Illustrious 18.
So, we have a problem with 10’s against 36 at TC’s of 48. Guess
what, the indexes for splitting tens at 36 are 48 (HiLo.) So, why is
there a major problem with splitting tens in seat one? Well, if you think
about it, there is a quirk in seat one. Remember, we are playing SD, face
down, seven seats. That means, two rounds. Only round two is important
as that is where you are betting. To split tens, you must have two tens
and the dealer must have a low card. If you are sitting at seat one, the
only cards that you can see after the start of the round are two high
cards and one low card. This means that the playing count will now be
the count at the start of the round minus 1. If the round starts at a
TC of +3, any seat has the possibility of splitting tens against a 3.
That is, any seat except for seat one. Seat one cannot because the count
will always be one less than the count at the start of the round or +2.
9% of the time, you will start round two at a true count of +3. 2.74%
of the time, you will start at a true count of +4. This means that 6.26%
of the time, every player has the possibility of splitting tens against
a 6 in the second round, except for the player in seat one. (26% of all
gain is in round two at a starting TC of +3 in this example.) The same
holds for the other ten split opportunities, at reduced percentages. Therefore,
seat one, and only seat one, has an automatic reduction in opportunity.
By the way, if you go through the same process between other seat
pairs, you get the charts that you would expect. That is, the tens peak
is muted and the other Illustrious 18 decisions start to poke out from
the plane.
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