Michael Hall: How to Beat AC BJ

                      Copyright 1991, Michael Hall
----------------> Part 1: The Basics
                  Part 2: About the Strategy Charts
                  Part 3: Postscript Strategy Charts (LONG)

Help for the novice blackjack player
The basic idea of the game is to get a total less than 21 that is
higher than the dealer OR to not bust (go over 21) when the dealer
busts. With basic strategy, you reduce the house edge to about -.45% in
Atlantic City (or -.40% where late surrender is offered); it is the
*best* way to play, unless you are counting cards. All hands are dealt
face up in Atlantic City; don't touch the cards. A "soft" total means
you have an ace and can use it as 11 without going over 21; hard means
you aren't counting an ace as 11 in your total.
Insurance is a side bet for up to half of your original bet. It can
only be placed at the start of a round when the dealer has an ace
showing. A basic strategy player should never take insurance.
Insurance pays 2-1 only if the dealer has blackjack.
With early surrender, you can give up half your bet to avoid playing
your first two cards; late surrender is the same, except you still
lose you whole bet if the dealer has blackjack. To surrender, just say
Splitting can be done only on your first two cards in Atlantic City.
You push out a bet equal to your original, the dealer splits the cards
apart and deals a card to the first one, which you play normally
except that you can't resplit, and then the dealer deals a card to the
second one, which again you play normally without resplitting.
Doubling can be done on any two cards. You push out a bet equal to
your original, and you will receive exactly one more card.
Standing versus hitting is the most common and important decision. To
hit you tap the table or draw your fingers towards you. Standing is
indicated by a waving motion parallel to the table.

About Atlantic City
All Atlantic City casinos use the same rules, except when they get
special permission from the Gaming Commission to try something else.
Atlantic City rules are no resplitting, split aces get only one card
each, double down allowed after split, dealer stands on soft 17,
blackjack pays 3 to 2, insurance pays 2 to 1, and 4, 6, or 8 decks
are used, but you will find only 8 decks for less than $25 minimums.
Until recently the absolute lowest minimums were $5, but now the Taj
Mahal offers $3 tables during the day on weekdays. Late surrender was
found only at the Claridge until recently, when Trump Plaza announced
that it is offering it too. It is unlikely that early surrender will
ever be offered again, because the casinos lost so much money when it
was offered that the Gaming Commission declared a state financial
crisis (or some such) in order to get rid of it and protect this
source of New Jersey tax revenue.

Help for the aspiring card counter
I recommend Stanford Wong's book, "Professional Blackjack" as a
reference on the High-Low counting system; it is finally out as a
paperback after 9 years of being a hardback. I also recommend Humble's
"The World's Best Blackjack Book", which focuses on the Hi-Opt I
counting system but which has lots of general information that any card
counter should know, though the authors of this book are a little too
paranoid about getting cheated. Hi-Opt I and High-Low counts are very
similar, but I feel that High-Low is marginally better for most
players. More advanced counts do exist (using more numbers than -1, 0,
and +1), but they offer very little theoretical gain coupled with an
increased chance for errors. Most professional card counters use
High-Low or Hi-Opt I. An additional reference containing useful tables
of information is "Fundamentals of Blackjack" by Chambliss & Rogenski.
For example, they give a table that shows the effects of various rules
on basic strategy expectation for 1, 2, 4, 6, or 8 decks.
Here is how you do the High-Low count. Initialize running count to
zero at start. Add one for each 2, 3, 4, 5, or 6 you see and subtract
one for each 10 or Ace you see. Divide running count by estimated
number of unseen decks to get true count used in the strategy
adjustment table. The strategy adjustment table is just a minor
refinement; you get most of the benefit of counting from bet size
variation, and you should do fine if you avoid strategy adjustments at
The Kelly Criterion is a betting heuristic that minimizes your chance
of going broke while maximizing your long-run profits, and for
Atlantic City, this heuristic dictates that you should bet
approximately  (TC*0.5 - 0.5)*.0077*BR, where TC is the True Count and
BR is your BankRoll (i.e., how much money you've got on you.)
On games with large numbers of decks, it is absolutely imperative that
you abandon the table when the count goes negative. How negative?
That's a personal decision and depends on your betting spread (difference
between your lowest bet and your highest), but I would advise leaving
eight deckers when the count hits -1.
You should only take insurance if the TC is above +3 (more precisely,
+2.8 for four decks, +3.0 for six decks, and +3.1 for eight decks).
Don't be swayed by what cards you have (i.e., don't fall into the
insure-your-blackjack trap); it's a side bet, so only the count
The maximum edge that most card counters claim to attain in practice
is about 1.5%. In Atlantic City, you will need about a 1-8 spread
(i.e., highest bet is eight times your lowest) to grind out any profit
at all. My simulations show a .5% advantage (ratio of winnings to
total amount bet) for a 1-8 betting spread, 7 players, -1 to +10 strategy
adjustments, and abandoning counts of -1 or worse.  If late surrender
is available, the edge improves to .66%.
As far as risk goes, a 500 unit bankroll (e.g. $2500 for $5 minimums)
has a 81.5% chance of doubling before going broke. If late surrender
is available, this improves to 89.3%.  You are risking quite a bit
to win how much?  0.9 units is the average win per 100 hands; 1.3 units
with late surrender.  So you could make about $5 an hour or so if you
are willing to have more than a 10% chance of losing $2500 before
doubling it.
If you want to make money at blackjack, either join a blackjack team or
play the single or double deckers in Vegas.
                      Copyright 1991, Michael Hall
                  Part 1: The Basics
----------------> Part 2: About the Strategy Charts
                  Part 3: Postscript Strategy Charts (LONG)

This article describes basic and High-Low strategy tables for Atlantic
City rules with four or more decks. The strategy information was taken
from Stanford Wong's book, "Professional Blackjack". The tables tell
you the mathematically best play given a certain circumstance -
whether to surrender, split, double-down, hit, or stand.

I made these tables for myself, because I was unsatisfied with
any I could find in published books. I am very satisfied with the
result, so I thought I would share it with y'all. You may wish to
modify the tables for your particular situation (different counting
system, different casino rules, etc.) If so, you'll need to get the
troff source from me, or else you can use the "Do Your Own Strategy"
blank chart that is included.

I do not guarantee that these tables are correct. If you find any
mistakes, or have any suggestions, please let me know, and I will
repost if necessary. Also, note that Wong computed his numbers for 4
decks, and he assumes 4 decks = 6 decks = 8 decks for purposes of
strategy adjustments. If anyone has High-Low strategy numbers that have
*proved* to be more accurate for 6 or 8 decks, then let me know.

How to print the tables
In a subsequent article, you'll find the Postscript gobble-dee-gook
that hopefully can be understood by your printer. However, it's
uuencoded and compressed. Save the article to a file. "uudecode"
the file. "uncompress" the resulting file, high-low.ps.Z ("uudecode"
and "uncompress" are UNIX programs that you hopefully have. There is
no need to strip out the article header before running uudecode. If
everything works, then you should wind up with a file named high-low.ps
that has "%!PS-Adobe-1.0" as its first line.) Send high-low.ps to a
printer that understands Postscript. (This includes the popular
Apple Laserwriter II printer and many others.) There will be a few
semi-blank pages, because the original text formatter, troff, is
brain-damaged. What you want are the pages with the tables for
"High-Low", "Basic Strategy", and "Do Your Own Strategy".

How to use the Do Your Own Strategy table
Use the Do Your Own Strategy table for memory recall practice or to
devise a table with a different set of strategy adjustment numbers,
perhaps for a counting system other than High-Low.

How to read the Basic Strategy table
Cross index your hand with the dealer's face-up card. If there is an
"X", it means "yes, do the corresponding decision" - conversely,
a blank means "no, *don't* do the corresponding decision." Read from
the bottom up. First see if you should surrender (if this option is
available), then split, then double, then stand. If nothing applies,
then hit. 
For example, suppose you have two 8's, and the dealer has a 10
showing. If you are playing at the Claridge (or Trump Plaza), you
first see if you should late surrender, but cross indexing 8-8 with 10
under late surrender shows that you should not. You then check splitting
- the table shows that you always split 8's, since there are X's all the way
across. However, if you split 8's and get another hand of 8's, then
you cannot resplit. You then look up to see if you should double - of
course not - and then you look up to see if you should stand; 8-8
versus 10 is blank, so you don't stand and instead you take a hit.

How to read the High-Low Strategy table
Cross index as with the basic strategy table. Follow the basic
strategy, except in these cases:
1) If there is a positive number in the box and the true count is greater
   than it, it means "override basic strategy, so yes, do the corresponding
2) If there is a negative number in the box and the true count is lower
   than it means "override basic strategy, so no, *don't* do the corresponding
To conform to the above and to avoid confusion, zeros are noted as
positive or negative. The somewhat counterintuitive use of a "Stand"
decision as opposed to a "Hit" decision is again to conform to the
above and to avoid confusion in the long run.
This all sounds complicated, but it's simple once you get used to it.
For example, using the previous example, you would deviate from basic
strategy and surrender 8-8 against 10 if the running count were
positive (greater than +0). You would always split 8's, but you would
deviate from basic strategy and stand on hard 16 when the running
count were positive.

How to highlight the High-Low Strategy table
I highly recommended that you use a highlighting pen to indicate
basic strategy on the High-Low Strategy tables. Overlay your High-Low
printed page on top of your Basic Strategy page. Press down so you can
the X's through the High-Low page. Highlight everywhere an X shows
through. Note that there is a basic strategy X everywhere there is a
negative High-Low Strategy number, and there is a basic strategy blank
everywhere there is a positive High-Low Strategy number (this would
not be true for some ranges of counts larger than -1 to +6.)

Still confused?
You can send e-mail to hall@rocky.bellcore.com if you have any
questions on these charts.

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