Lex Luther / LOG: How to Hack BJ

Editor Note: This article is circa 1998 or earlier.  Original formatting has been kept intact.

==Phrack Magazine==

                 Volume Four, Issue Forty-Three, File 9 of 27

                            How to "Hack" BlackJack
                                  Lex Luthor
                         The Legion of Gamblerz!! (LOG)
                 [email protected] (or) [email protected]

                               Part 1 of 2 (50K)

"I learned a lot of things I didn't know from Lex's File" ---Bruce Sterling


   With the DEF CON 1 hacker/cyberpunk/law enforcement/security/etc convention
coming up in Las Vegas, Nevada on July 9-12 1993, I felt that now would be a
good time to write a "phile" on something the attendants could put to use to
help legally defray the costs of going. The thought of a bunch of ex-hackers
running around Las Vegas without shirts (having 'lost' them in the various
Casinos) frightened me into immediate action. Besides, I don't write articles
on 'Underground' topics anymore and since I have done a lot of research and
playing of Casino BlackJack, the CON in Vegas provided me the perfect excuse
to finally write an article for PHRACK (not withstanding the pro-phile in
Issue 40 which doesn't really count).

   Regardless of whether you go to this DEF CON 1 thing, if you ever plan to
hit a casino with the purpose of MAKING MONEY, then you really should
concentrate on ONE game of chance: BlackJack. Why? Because BlackJack is the
*ONLY* casino game that affords the educated and skilled player a long-term
mathematical advantage over the house. All the other casino games: Craps,
Roulette, Slots, etc. have the long-term mathematical advantage over the
player (see table below). BlackJack is also the only casino game for which the
odds are always changing. Don't be fooled by all the glitter, a casino is a
business and must make a profit to survive. The profit is ensured by using a
set of rules which provides them with an edge. Now you say: wait a sec, how do
they make money if BlackJack can be beaten? There are a couple of reasons. One
reason is that there are very few good players who make it their profession to
beat casinos at BlackJack day in and day out. There are many more who THINK
they are good, THINK they know how to play the game, and lose more money than
the really good players win. Notwithstanding the throngs of vacationers who
admit to not being well versed in the game and consequently are doomed to
lose...plenty. Another reason is that if a casino thinks you are a "counter"
(a term just as nasty as "phreaker" to the phone company) there is a good
chance that they will ask you to leave. See the section on Social Engineering
the Casino to avoid being spotted as a counter. Also, the house secures its
advantage in BlackJack from the fact that the player has to act first. If you
bust, the dealer wins your bet regardless of whether the dealer busts later.

   The following table illustrates my point regarding house advantages for the
various casino games and BlackJack strategies. The data is available in most
books on casino gambling. Note that negative percentages denote player
disadvantages and are therefore house advantages.

   GAME                             Your Advantage (over the long run)
   Craps                            -1.4 % overall average
   Baccarat                         -1.1 % to -5.0 %
   Roulette                         -2.7 % to -5.26 %
   Slots                            -2.5 to -25 % depending on machine setting
   Keno                             -25 % more or less

   BlackJack (WAG Player)           -2 % to -15 %
   BlackJack (Mirror Dealer)        -5.7 %
   BlackJack (Basic Strategy)       -0.2 % to +0.3 %
   BlackJack (Basic Strategy &      Up to +3.1 % depending on card counting
              Card Counting)        system and betting range.

   A -2 % player advantage (2 percent disadvantage) means that if you play a
hundred hands at a dollar each, then ON AVERAGE, you will lose two dollars.
Note that the typical "pick three" State Lottery game is a disaster as your
advantage is -50 %. If you make 1000 $1 bets, you will lose $500 on average.
Some people say that state lotteries are taxation on the stupid...

   This article contains thirteen sections. It was written in a fairly modular
fashion so if there are sections which do not interest you, you may omit them
without much loss in continuity however, all the sections are networked to
some degree. For the sake of completeness, a fairly comprehensive list of
topics has been presented. Due to email file size restrictions, I had to
divide this article into two parts. Note that I am NOT a Professional
BlackJack player, the definition being someone whose livelihood is derived
solely from his/her winnings. I did however, dedicate a summer to gambling 5
evenings a week or so, keeping meticulous records of wins, losses and expenses
incurred. I averaged 1-2 nights a week playing BlackJack with the other nights
divided among 3 different forms of Pari-Mutual gambling. At the end of the
summer I tallied the wins/losses/expenses and am proud to say the result was a
positive net earnings. Unfortunately it was instantly apparent that the net
money when divided up by the number of weeks gambling was not enough to
warrant me to quit school and become a professional gambler. Besides that
one summer, I have played BlackJack off and on for 7 years or so. In case you
were wondering, no, I have never been a member of GA [Gamblers Anonymous]
contrary to what one of those Bell Security "Hit-Lists" circulated many years
ago would have you believe. The topics contained herein are:

     o    Historical Background of the BlackJack Card Game
     o    Useful Gambling, Casino, and BlackJack Definitions
     o    Review of BlackJack Rules of Play
     o    Betting, Money Management, and the Psychology of Gambling
     o    Basic Strategy (End of Part 1)
     o    Card Counting (Beginning of Part 2)
     o    Shuffle Tracking
     o    Casino Security and Surveillance
     o    "Social Engineering" the Casino
     o    Casino Cheating and Player Cheating
     o    Some Comments Regarding Computer BlackJack Games for PC's
     o    A VERY Brief Description of Other Casino Games
     o    Selected Bibliography and Reference List


     a) I made extensive use of my many books, articles, and magazines on
gambling and BlackJack along with actual playing experience. References are
denoted by square brackets [REF#] and are listed in the Selected Bibliography
and Reference List section.

     b) It's hard to win at something you don't understand. If you want to win
consistently at anything, learn every thing you can about it. BlackJack is no

History of BlackJack:

   I provide this historical background information because I find it rather
fascinating and it also provides some insight into contemporary rules and
play. I think it is worth reading for the sole reason that you might some day
use one of the historical tid-bits to answer a question on Jeopardy!#@%!
Seriously, the first couple of paragraphs may read a bit like a book report,
but bear with it if you can as I did all of the following research
specifically for this file.

   First, a brief history of cards: Playing cards are believed to have been
invented in China and/or India sometime around 900 A.D. The Chinese are
thought to have originated card games when they began shuffling paper money
(another Chinese invention) into various combinations. In China today, the
general term for playing cards means "paper tickets". The contemporary 52 card
deck used in the U.S. was originally referred to as the "French Pack" (circa
1600's) which was later adopted by the English and subsequently the Americans.

   The first accounts of gambling were in 2300 B.C. or so, and yes, the
Chinese again get the credit. Gambling was very popular in Ancient Greece even
though it was illegal and has been a part of the human experience ever since.
Today, with the all too common manipulation of language to suit one's own
purposes, gambling is no longer a term used by casinos....they prefer to use
the word GAMING instead. Just as Post Traumatic Stress Disorder has replaced
the term Shell Shock in military jargon. Since this manipulation of language
is all the rage these days, why don't we water down the name Computer Hacker
and replace it with Misguided Information Junky or someone who is afflicted
with a Compulsive Curiosity Disorder?

   The history of the BlackJack card game itself is still disputed but was
probably spawned from other French games such as "chemin de fer and French
Ferme", both of which I am completely unfamiliar with. BlackJack originated in
French Casino's around 1700 where it was called "vingt-et-un" ("twenty-and-
one" in French) and has been played in the U.S. since the 1800's. BlackJack is
called Black-Jack because if a player got a Jack of Spades and an Ace of
Spades as the first two cards (Spade being the color black of course), the
player was additionally remunerated.

   Gambling was legal out West from the 1850's to 1910 at which time Nevada
made it a felony to operate a gambling game. In 1931, Nevada re-legalized
casino gambling where BlackJack became one of the primary games of chance
offered to gamblers. As some of you may recall, 1978 was the year casino
gambling was legalized in Atlantic City, New Jersey. As of 1989, only two
states had legalized casino gambling. Since then, about 20 states have a
number of small time casinos (compared to Vegas) which have sprouted up in
places such as Black Hawk and Cripple Creek Colorado and in river boats on the
Mississippi. Also as of this writing, roughly 70 Native American Indian
reservations operate or are building casinos, some of which are in New York
and Connecticut. In addition to the U.S., some of the countries (there are
many) operating casinos are: France, England, Monaco (Monte Carlo of course)
and quite a few in the Caribbean islands (Puerto Rico, Bahamas, Aruba, etc.).

   Now: The first recognized effort to apply mathematics to BlackJack began in
1953 and culminated in 1956 with a published paper [6]. Roger Baldwin et al
(see Bibliography) wrote a paper in the Journal of the American Statistical
Association titled "The Optimum Strategy in BlackJack". These pioneers used
calculators, and probability and statistics theory to substantially reduce the
house advantage. Although the title of their paper was 'optimum strategy', it
wasn't really the best strategy because they really needed a computer to
refine their system. I dug up a copy of their paper from the library, it is
ten pages long and fairly mathematical. To give you an idea of its importance,
the Baldwin article did for BlackJack playing what the November 1960 issue of
The Bell System Technical Journal entitled, "Signalling Systems for Control of
Telephone Switching", did for Blue Boxing.

   To continue with the analogy, one can consider Professor Edward O. Thorp to
be the Captain Crunch of BlackJack. Dr. Thorp, then a mathematics teacher,
picked up where Baldwin and company left off. In 1962, Thorp refined their
basic strategy and developed the first card counting techniques. He published
his results in "Beat the Dealer" [3], a book that became so popular that for a
week in 1963 it was on the New York Time's best seller list. The book also
scared the hell out of the Casino's. Thorp wrote "Beat the Market" in 1967, in
which he used mathematics and computer algorithms to find pricing
inefficiencies between stocks and related securities. Currently he is using an
arbitrage formula to exploit undervalued warrants in the Japanese stock

   The Casinos were so scared after Beat the Dealer, that they even changed
the rules of the game to make if more difficult for the players to win. This
didn't last long as people protested by not playing the new pseudo-BlackJack.
The unfavorable rules resulted in a loss of income for the casinos. Not making
money is a sin for a casino, so they quickly reverted back to the original
rules. Because Thorp's "Ten-Count" method wasn't easy to master and many
people didn't really understand it anyway, the casinos made a bundle from the
game's newly gained popularity thanks to Thorp's book and all the media
attention it generated.

   Beat the Dealer is rather difficult to find these days, I picked up a copy
at the library recently and checked the card in the back to see how popular
it is today. I was surprised as hell to find that it was checked out over 20
times in the past year and a half or so! How many books from 1962 can claim
that? I do not recommend reading the book for anything other than posterity
purposes though, the reason being that newer books contain better, and easier
to learn strategies.

   Another major contributor in the history of winning BlackJack play is
Julian Braun who worked at IBM. His thousands of lines of computer code and
hours of BlackJack simulation on IBM mainframes resulted in THE Basic
Strategy, and a number of card counting techniques. His conclusions were used
in a 2nd edition of Beat the Dealer, and later in Lawrence Revere's 1977 book
"Playing BlackJack as a Business".

   Lastly, let me mention Ken Uston, who used five computers that were built
into the shoes of members of his playing team in 1977. They won over a hundred
thousand dollars in a very short time but one of the computers was
confiscated and sent to the FBI. The fedz decided that the computer used
public information on BlackJack playing and was not a cheating device. You may
have seen this story in a movie made about his BlackJack exploits detailed in
his book "The Big Player". Ken was also featured on a 1981 Sixty Minutes show
and helped lead a successful legal challenge to prevent Atlantic City casinos
from barring card counters.

Useful Definitions:

   Just as in Social Engineering the Phone Company, an essential element for
success is knowing the right buzzwords and acronyms. Therefore, I list some
relevant definitions now, even though the reader will probably skip over them
to get to the good stuff. The definitions merely serve as a reference for
those who are uninitiated with the terminology of gambling, casinos, and
BlackJack. If you encounter a term you don't understand in the article, look
back here. The definitions are not in alphabetical order on purpose. I grouped
them in what I feel is a logical and easy to remember fashion.

Action: This is a general gambling term which refers to the total amount of
        money bet in a specific period of time. Ten bets of ten dollars each
        is $100 of action.

Burn Card: A single card taken from the top of the deck or the first card in
           a shoe which the dealer slides across the table from his/her left
           to the right, and is placed into the discard tray. The card may or
           may not be shown face up (which can affect the count if you are
           counting cards). A card is burned after each shuffle. I have
           not been able to find out how this started nor the purpose for
           burning a card. If you know, drop me some email.

Cut Card: A solid colored card typically a piece of plastic which is given to
          a player by the dealer for the purpose of cutting the deck(s) after
          a shuffle. Cutting the cards in the 'right' location is part of
          the 'shuffle tracking' strategy mentioned later in Part 2.

Hole Card: Any face down card. The definition most often refers to the
           dealer's single face down card however.

Shoe: A device that can hold up to eight decks of cards which allows the
      dealer to slide out the cards one at a time.

Hard Hand: A hand in which any Ace is counted as a 1 and not as an 11.

Soft Hand: A hand in which any Ace is counted as an 11 and not as a 1.

Pat Hand: A hand with a total of 17 to 21.

Stand: To decline another card.

Hit: To request another card.

Bust: When a hand's value exceeds 21....a losing hand.

Push: A player-dealer tie.

Pair: When a player's first two cards are numerically identical (ie, 7,7).

Point Count: The net value of the card count at the end of a hand.

Running Count: The count from the beginning of the deck or shoe. The running
               count is updated by the value of the point count after each

True Count: The running count adjusted to account for the number of cards left
            in the deck or shoe to be played.

Bankroll: The stake (available money) a player plans to bet with.

Flat Bet: A bet which you do not vary ie, if you are flat betting ten dollars,
          you are betting $10 each and every hand without changing the betting
          amount from one hand to the next.

Black Chip: A $100. chip.

Green Chip: A $25.00 chip.

Red Chip: A $5.00 chip.

Foreign Chip: A chip that is issued by one casino and is honored by another
              as cash. A casino is not necessarily obligated to accept them.

Settlement: The resolving of the bet. Either the dealer takes your chips,
            pays you, or in the case of a push, no exchange of chips occurs.

Toke: Its not what some of you may think...to "toke" the dealer is just
      another word for tipping the dealer.

Marker: An IOU. A line of credit provided by the casino to a player.

Junket: An organized group of gamblers that travel to a casino together.
        Junkets are usually subsidized by a casino to attract players.

Comp: Short for complimentary. If you wave lots of money around, the casino
      (hotel) may give you things like a free room or free f00d hoping you'll
      keep losing money at the tables in their casino.

Heat: The pressure a casino puts on a winning player, typically someone who
      is suspected of being a card counter.

Shuffle Up: Prematurely shuffling the cards to harass a player who is usually
            suspected of being a counter.

Nut: The overhead costs of running the casino.

Pit: The area inside a group of gaming tables. The tables are arranged in
     an elliptical manner, the space inside the perimeter is the pit.

House: The Casino of course.

Cage: Short for cashier's cage. This is where chips are redeemed for cash,
      checks cashed, credit arranged, etc.

House Percentage: The casino's advantage in a particular game of chance.

Drop Percentage: That portion of the player's money that the casino will win
                 because of the house percentage. It is a measure of the
                 amount of a player's initial stake that he or she will
                 eventually lose. On average this number is around 20 percent.
                 That is, on average, Joe Gambler will lose $20 of every $100
                 he begins with.

Head-On: To play alone at a BlackJack table with the dealer.

WAG Player: Wild Assed Guessing player.

SWAG Player: Scientific Wild Assed Guessing player.

Tough Player: What the casino labels an '3L33T' player who can hurt the casino
              monetarily with his or her intelligent play.

Counter: Someone who counts cards.

High Roller: A big bettor.

Mechanic: Someone who is elite in regards to manipulating cards, typically for
          illicit purposes.

Shill: A house employee who bets money and pretends to be a player to attract
       customers. Shills typically follow the same rules as the dealer which
       makes them somewhat easy to spot (ie, they don't Double Down or Split).

Pit Boss: An employee of the casino whose job is to supervise BlackJack
          players, dealers, and other floor personnel.

Review of BlackJack Rules of Play:

   The rules of BlackJack differ slightly from area to area and/or from casino
to casino. For example, a casino in downtown Vegas may have different rules
than one of the Vegas Strip casinos which may have different rules from a
casino up in Reno or Tahoe (Nevada). The rules in a casino in Freeport Bahamas
may differ from those in Atlantic City, etc. Therefore, it is important to
research, a priori, what the rules are for the area/casino(s) you plan on
playing in. For Nevada casinos you can order a copy of [1] which contains
rules info on all the licensed casinos in the state. Later in this article,
you will see that each set of rule variations has a corresponding Basic
Strategy chart that must be memorized. Memorizing all the charts can be too
confusing and is not recommended.

   The BlackJack table seats a dealer and one to seven players. The first seat
on the dealer's left is referred to as First Base, the first seat on the
dealer's right is referred to as Third Base. A betting square is printed on
the felt table in front of each player seat. Immediately in front of the
dealer is the chip tray. On the dealer's left is the deck or shoe and beside
that should be the minimum bet sign--something that you ought to read before
sitting down to play. On the dealer's immediate right is the money drop slot
where all currency and tips (chips) are deposited. Next to the drop slot is
the discard tray. Play begins after the following ritual is completed: the
dealer shuffles the cards, the deck(s) is "cut" by a player using the marker
card, and the dealer "burns" a card.

   Before any cards are dealt, the players may make a wager by placing the
desired chips (value and number) into the betting box. I used the word "may"
because you are not forced to bet every hand. Occasionally a player may sit
out a hand or two for various reasons. I have sat out a couple of hands at
times when the dealer was getting extremely lucky and everyone was losing. If
you attempt to sit out too many hands especially if there are people waiting
to play at your table, you may be asked to leave the table until you are ready
to play. If you don't have any chips, put some cash on the table and the
dealer will exchange them for chips.

   Once all the bets are down, two cards (one at a time) are dealt from left
to right. In many Vegas casinos, players get both cards face down. In Atlantic
City and most every where else the player's cards are dealt face up. Should
the cards be dealt face up, don't make the faux pas of touching them! They are
dealt face up for a reason, primarily to prevent a few types of player
cheating (see section on cheating in Part 2) and the dealer will sternly but
nicely tell you not to touch the cards. As most of you know the dealer receives
one card down and one card up. The numerical values of the cards are:
(10, J, Q, K) = 10 ; (Ace) = 1 or 11 ; (other cards) = face value (3 = 3).

   Since a casino can be as noisy as an old Step-by-Step Switch with all those
slot machines going, marbles jumping around on roulette wheels, demoniacal
shrieks of "YO-LEVEN" at the craps table, people screaming that they hit the
big one and so on, hand signals are usually the preferred method of signalling
hit, stand, etc.

   If the cards were dealt face down and you want a hit, lightly flick the
cards across the felt two times. If the cards were dealt face up, point at the
cards with a quick stabbing motion. You may also want to nod your head yes
while saying "hit".  The best way to indicate to the dealer that you want to
stand regardless of how the cards were dealt is to move your hand from left
to right in a level attitude with your palm down. Your hand should be a few
inches or so above the table. Nodding your head no at the same time helps,
while saying "stay" or "stand".

   Permit me to interject a comment on the number of decks used in a game.
Single deck games are pretty much restricted to Nevada casinos. In the casinos
that have one-deck games, the tables are usually full. Multiple deck games
typically consist of an even number of decks (2, 4, 6, 8) although a few
casinos use 5 or 7 decks. The two main reasons many casinos use multiple decks
      1) They allow the dealer to deal more hands per hour thereby increasing
         the casino take.

      2) They reduce but in no way eliminate the player advantage gained
         from card counting.

   Dealer Rules - The rules the dealer must play by are very simple. If the
dealer's hand is 16 or less, he/she must take a card. If the dealer's hand is
17 or more, he/she must stand. Note that some casinos allow the dealer to hit
on soft 17 which gives the house a very small additional advantage. The
dealer's strategy is fixed and what you and the other players have is
immaterial to him/her as far as hitting and standing is concerned.

   Player rules - The player can do whatever he/she wants as far as hitting and
standing goes with the exception of the following special circumstances. See
the section on Basic Strategy for the appropriate times to hit, stand, split,
and double down. The aim is to have a hand which is higher than the dealers'.
If there is a tie (push), neither you nor the dealer wins. Should a player get
a BlackJack (first 2 cards are an Ace and a ten) the payoff is 150% more than
the original bet ie, bet $10.00 and the payoff is $15.00.

DOUBLE DOWN: Doubling down is restricted to 2-card hands usually totalling
9, 10, or 11 although some casinos allow doubling down on any 2-card hand. If
your first two cards provide you with the appropriate total and your cards
were dealt face down, turn them over and put them on the dealer's side of the
betting square. If your first two cards provide you with the appropriate total
and your cards were dealt face up, point to them and say "double" when the
dealer prompts you for a card and simultaneously put an equal amount of chips
NEXT TO (not on top of) those already in the betting box. The dealer will give
you one more card only, then he/she will move on to the next hand.

SPLITTING PAIRS: If you have a pair that you want to split and your cards are
dealt face down, turn them over and place them a few inches apart. If your
cards were dealt face up, point to your cards and say "split" when the dealer
prompts you for a card. The original bet will go with one card and you will
have to place an equal amount of chips in the betting box near the other card.
You are now playing two hands, each as though they were regular hands with the
exception being that if you have just split two aces. In that case, you only
get one card which will hopefully be a 10. If it is a ten, that hand's total
is now 21 but the hand isn't considered a BlackJack. That is, you are paid 1:1
and not 1:1.5 as for a natural (BlackJack).

Combined example of above two plays: Say you are dealt two fives. You split
them (you dummy!). The next card is another 5 and you re-split them (you
chucklehead!!). Three hands have grown out of one AND you are now in for
three times your original bet. But wait. Say the next card is a six. So one
hand is a 5,6 which gives you eleven; another just has a 5 and the other hand
has a 5. You decide to double down on the first hand. You are dealt a 7 giving
18 which you stand on. Now a ten is dealt for the second hand and you decide
to stay at 15. The last hand is the lonely third 5, which is dealt a four for
a total of nine. You decide to double down and get an eight giving that hand a
total of 17. Shit you say, you started with a twenty dollar bet and now you
are in for a hundred! Better hope the dealer doesn't end up with a hand more
than 18 lest you lose a C-note. The moral of this example is to not get caught
up in the excitement and make rash decisions. However, there have been a
couple of times where Basic Strategy dictated that certain split and double
down plays should be made and I was very low on chips (and cash). Unless you
are *really* psychic, don't go against Basic Strategy! I didn't and usually
came out the better for it although I was really sweating the outcome of the
hand due to my low cash status. The reason it was stupid to split two fives is
that you are replacing a hand that is great for drawing on or doubling down
on, by what will probably be two shitty hands.

INSURANCE: This option comes into play when the dealer's up card is an Ace. At
this point all the players have two cards. The dealer does not check his/her
hole card before asking the players if they want insurance. The reason being
evident as the dealer can't give away the value of the hole card if the dealer
doesn't know what the hole card is. If a player wants insurance, half the
original amount bet is placed on the semicircle labeled "insurance" which is
printed on the table. If the dealer has a BlackJack the player wins the side
bet (the insurance bet) but loses the original bet, thus providing no net loss
or gain since insurance pays 2 to 1. If the dealer does not have a BlackJack,
the side bet is lost and the hand is played normally. If you are not counting
cards DO NOT TAKE INSURANCE! The proper Basic Strategy play is to decline. The
time to take insurance is when the number of non-tens to tens drops below a
2 to 1 margin since insurance pays 2 to 1. It's simple math check it yourself.

SURRENDER: This is a fairly obscure option that originated in Manila
(Philippines) in 1958 and isn't available in many casinos. There are two
versions, "early surrender" and "late surrender". Early surrender  allows
players to quit two-card hands after seeing the up card of the dealer. This
option provides the player an additional 0.62 percent favorable advantage
(significant) and therefore the obvious reason why many Atlantic City casinos
abandoned the option in 1982. Late surrender is the same as early except that
the player must wait until the dealer checks for a BlackJack. If the dealer
does not have a BlackJack then the player may surrender. The following table
was taken verbatim from [5] and is valid for games with 4+ decks. It details
the best strategy regarding late surrender as determined from intensive
computer simulation:

        TWO-CARD HAND           TOTAL           DEALER'S UP-CARD
        -------------           -----           ----------------
             9,7                 16                    ACE
             10,6 *              16 *                  ACE
             9,7 *               16 *                  10
             10,6 *              16 *                  10
             9,7 *               16 *                  10
             10,5 *              15 *                  10
             9,7                 16                     9
             10,5                16                     9

        "In a single-deck game, you would surrender only the above hands
         marked with an asterisk, as well as 7,7 against a dealer's 10
         up-card." [5]

Casino variations - Note that some casinos do not permit doubling down on
split pairs, and/or re-splitting pairs. These options provide the player with
a slight additional advantage.

Betting, Money Management, and the Psychology of Gambling:

   Let me begin this section with the following statement: SCARED MONEY RARELY
WINS. Most gambling books devote quite a bit of time to the psychology of
gambling and rightfully so. There is a fine line to responsible gambling. On
one hand you shouldn't bet money that you cannot afford to lose. On the other
hand, if you are betting with money you expect to lose, where is your
confidence? When I used to gamble, it was small time. I define small time as
bringing $250.00 of 'losable' money. I've lost that much in one night. I
didn't like it, but I still ate that week. One pitfall you can easily fall
into happens AFTER you lose. You scold yourself for losing money you could
have done something productive with. "DAMN, I could have bought a 200 MB hard
drive with that!#&!". You should think about these things BEFORE you play.

   Scared money is more in the mind than real. What I mean by that is even if
you gamble with your last $10.00 in the world, it is important to play as
though you have thousands of dollars in front of you. I don't mean piss the
ten bucks away. I mean that there are certain plays you should make according
to your chosen strategy which are the optimum mathematically. Don't make
changes to it out of fear. Fear is not your friend.

   The "risk of ruin" is the percent chance that you will lose your entire
bankroll. This percentage should not exceed 5% if you plan on playing multiple
sessions to make money. The risk of ruin is dependent on the sizes of your
bets during a session. The "Kelly Criterion" provides a zero percent risk of
ruin. The system requires that you bet according to the percent advantage you
have at any one time. For example, if you are counting cards and your
advantage for a certain hand is 2% then you may bet 2% of your total bankroll.
If your total is $1000. then you can bet $20. Note that if you won the hand
your bankroll is now $1020 and if your advantage dropped to 1.5%, taking .015
times 1020 (which will determine your next bet size) in your head isn't all
that easy. The literature provides more reasonable systems, but do yourself a
favor and stay away from "betting progressions". See Reference [16] (available
on the Internet) for more information regarding risk of ruin & optimal wagers.

   If you are gambling to make money, it is important to define how much cash
you can lose before quitting. This number is called the "stop-loss limit". My
stop-loss limit was my entire session bankroll which was $250 (50 betting
units of $5.00 or 25 betting units of $10.00). This concept is especially
important if you expect to play in the casinos for more than one session. Most
books recommend that your session bankroll be about a fifth of your trip
bankroll. Unfortunately, most people who have $500 in their wallet with a self
imposed stop-loss limit is $200 will violate that limit should they lose the
two hundred. Discipline is what separates the great players from the ordinary

   Obviously you don't want to put a limit on how much you want to win.
However, if you are keeping with a structured system there are certain limits
to what your minimum and maximum bets should be. I am not going to go into
that here though.

   In my gambling experience, there has been one non-scientific concept that
has proven itself over and over again. NEVER BUCK A TREND! If you have just
won three hands in a row, don't think that you are now 'due' for a loss and
drastically scale back your bet. If you are winning go with it. A good friend
of mine who was my 'gambling mentor' won $30,000 in a 24 hour period with a
$200 beginning bankroll. This was not accomplished by scaling back bets. By
the same token, if you see that the players at a certain table are losing
consistently, don't sit down at that table. One problem that I've seen is when
someone has won a lot and starts to lose. Mentally, they keep saying, "if I
lose another $100 I will stop". They lose the hundred and say "no, really, the
NEXT $100 I lose, I will stop", etc. When they go broke, that's when they stop.
Live by the following graph typically designated as The Quitting Curve and you
won't fall into that trap:

                    |             *                  <-+
                    |            *  *                  |   Loss
                 ^  |           *    *                 |   Limit
                 |  |          *      * <----QUIT!   <-+
                 |  |         *
                 W  |        *
                 i  |       *
                 n  |      *
                 n  |     *
                 i  |    *
                 n  |   *
                 g  |  *
                              Time ---------------->

   Determine your loss limit and stay with it. Obviously the loss limit will
change as you keep winning. Standard loss limits are 10 to 20 percent of the
current bankroll. Note that this philosophy is also used in stock market

Basic Strategy:

    If you only read one section of this file, and you don't already know what
Basic Strategy is, then this is the section you should read. Knowing Basic
Strategy is CRITICAL to you gaining an advantage over the house. The Basic
Strategy for a particular set of rules was developed by intensive computer
simulation which performed a complete combinatorial analysis. The computer
"played" tens of thousands of hands for each BlackJack situation possible and
statistically decided as to which play decision favored the player. The
following 3 charts should be duplicated or cut out from a hardcopy of this
file. You don't want to wave them around at a BlackJack table but its nice to
have them on hand in case you fail to recall some plays, at which time you can
run to the rest room to refresh your memory.

   I hope you don't think this is weird but I keep a copy of a certain Basic
Strategy chart in my wallet at ALL times...just in case. Just in case of what
you ask? Permit me to go off on a slight(?) tangent. The following story really
happened. In 1984 I was visiting LOD BBS co-sysop, Paul Muad'dib up in New York
City. After about a week we were very low on cash despite the Pay Phone
windfall mentioned in my Phrack Pro-Phile ;->. I contacted a friend of mine
who was working in New Jersey and he offered us a job for a couple of days. I
spent just about the last of my cash on bus fair for me and Paul figuring that
I would be getting more money soon. Some how, the destination was
miscommunicated and we ended up in Atlantic City, which was not the location of
the job. We were stuck. Our only recourse was to attempt to win some money to
get us back on track. First we needed a little more capital. Paul, being known
to physically impersonate phone company workers, and a Department of Motor
Vehicles computer technician among others, decided to impersonate a casino
employee so he could "look around". Look around he did, found a storage closet
with a portable cooler and a case of warm soda, not exactly a gold mine but
hey. He proceeded to walk that stuff right out of the casino. We commandeered
some ice and walked around the beach for an hour selling sodas. It wasn't all
that bad as scantily clad women seemed to be the ones buying them. To cut the
story short, Paul knew ESS but he didn't know BlackJack. He lost and we
resorted to calling up Sharp Razor, a fellow Legion member residing in NJ, who
gave us (or is it lent?) the cash to continue our journey. For the record, I
was fairly clueless about BlackJack at the time which really means that I
thought I knew how to play but really didn't because I didn't even know Basic
Strategy. The same goes for Paul. Had we had a chart on hand, we would at least
have made the correct plays.

   Here are the charts, memorize the one that is appropriate:

                    Las Vegas Single Deck Basic Strategy Table

                                Dealer's Up-Card
               Your  +---+---+---+---+---+---+---+---+----+---+
               Hand  | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A |
               |  8  | H | H | H | D | D | H | H | H |  H | H |
               |  9  | D | D | D | D | D | H | H | H |  H | H |
               | 10  | D | D | D | D | D | D | D | D |  H | H |
               | 11  | D | D | D | D | D | D | D | D |  D | D |
               | 12  | H | H | S | S | S | H | H | H |  H | H |
               | 13  | S | S | S | S | S | H | H | H |  H | H |
               | 14  | S | S | S | S | S | H | H | H |  H | H |
               | 15  | S | S | S | S | S | H | H | H |  H | H |
               | 16  | S | S | S | S | S | H | H | H |  H | H |
               | 17  | S | S | S | S | S | S | S | S |  S | S |
               | A,2 | H | H | D | D | D | H | H | H |  H | H |
               | A,3 | H | H | D | D | D | H | H | H |  H | H |
               | A,4 | H | H | D | D | D | H | H | H |  H | H |
               | A,5 | H | H | D | D | D | H | H | H |  H | H |
               | A,6 | D | D | D | D | D | H | H | H |  H | H |
               | A,7 | S | D | D | D | D | S | S | H |  H | S |
               | A,8 | S | S | S | S | D | S | S | S |  S | S |
               | A,9 | S | S | S | S | S | S | S | S |  S | S |
               | A,A | P | P | P | P | P | P | P | P |  P | P |
               | 2,2 | H | P | P | P | P | P | H | H |  H | H |
               | 3,3 | H | H | P | P | P | P | H | H |  H | H |
               | 4,4 | H | H | H | D | D | H | H | H |  H | H |
               | 6,6 | P | P | P | P | P | H | H | H |  H | H |
               | 7,7 | P | P | P | P | P | P | H | H |  S | H |
               | 8,8 | P | P | P | P | P | P | P | P |  P | P |
               | 9,9 | P | P | P | P | P | S | P | P |  S | S |
               |10,10| S | S | S | S | S | S | S | S |  S | S |
               H = Hit  S = Stand   D = Double Down   P = Split

                  Las Vegas Multiple Deck Basic Strategy Table

                                Dealer's Up-Card
               Your  +---+---+---+---+---+---+---+---+----+---+
               Hand  | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A |
               |  8  | H | H | H | H | H | H | H | H |  H | H |
               |  9  | H | D | D | D | D | H | H | H |  H | H |
               | 10  | D | D | D | D | D | D | D | D |  H | H |
               | 11  | D | D | D | D | D | D | D | D |  D | H |
               | 12  | H | H | S | S | S | H | H | H |  H | H |
               | 13  | S | S | S | S | S | H | H | H |  H | H |
               | 14  | S | S | S | S | S | H | H | H |  H | H |
               | 15  | S | S | S | S | S | H | H | H |  H | H |
               | 16  | S | S | S | S | S | H | H | H |  H | H |
               | 17  | S | S | S | S | S | S | S | S |  S | S |
               | A,2 | H | H | H | D | D | H | H | H |  H | H |
               | A,3 | H | H | H | D | D | H | H | H |  H | H |
               | A,4 | H | H | D | D | D | H | H | H |  H | H |
               | A,5 | H | H | D | D | D | H | H | H |  H | H |
               | A,6 | H | D | D | D | D | H | H | H |  H | H |
               | A,7 | S | D | D | D | D | S | S | H |  H | H |
               | A,8 | S | S | S | S | S | S | S | S |  S | S |
               | A,9 | S | S | S | S | S | S | S | S |  S | S |
               | A,A | P | P | P | P | P | P | P | P |  P | P |
               | 2,2 | H | H | P | P | P | P | H | H |  H | H |
               | 3,3 | H | H | P | P | P | P | H | H |  H | H |
               | 4,4 | H | H | H | H | H | H | H | H |  H | H |
               | 6,6 | H | P | P | P | P | H | H | H |  H | H |
               | 7,7 | P | P | P | P | P | P | H | H |  H | H |
               | 8,8 | P | P | P | P | P | P | P | P |  P | P |
               | 9,9 | P | P | P | P | P | S | P | P |  S | S |
               |10,10| S | S | S | S | S | S | S | S |  S | S |
               H = Hit  S = Stand   D = Double Down   P = Split

                   Atlantic City Multiple Deck Basic Strategy Table

                                 Dealer's Up-Card
                Your +---+---+---+---+---+---+---+---+----+---+
                Hand | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A |
               |  8  | H | H | H | H | H | H | H | H |  H | H |
               |  9  | H | D | D | D | D | H | H | H |  H | H |
               | 10  | D | D | D | D | D | D | D | D |  H | H |
               | 11  | D | D | D | D | D | D | D | D |  D | H |
               | 12  | H | H | S | S | S | H | H | H |  H | H |
               | 13  | S | S | S | S | S | H | H | H |  H | H |
               | 14  | S | S | S | S | S | H | H | H |  H | H |
               | 15  | S | S | S | S | S | H | H | H |  H | H |
               | 16  | S | S | S | S | S | H | H | H |  H | H |
               | 17  | S | S | S | S | S | S | S |  S | S | S |
               | A,2 | H | H | H | D | D | H | H | H |  H | H |
               | A,3 | H | H | H | D | D | H | H | H |  H | H |
               | A,4 | H | H | D | D | D | H | H | H |  H | H |
               | A,5 | H | H | D | D | D | H | H | H |  H | H |
               | A,6 | H | D | D | D | D | H | H | H |  H | H |
               | A,7 | S | D | D | D | D | S | S | H |  H | H |
               | A,8 | S | S | S | S | S | S | S | S |  S | S |
               | A,9 | S | S | S | S | S | S | S | S |  S | S |
               | A,A | P | P | P | P | P | P | P | P |  P | P |
               | 2,2 | P | P | P | P | P | P | H | H |  H | H |
               | 3,3 | P | P | P | P | P | P | H | H |  H | H |
               | 4,4 | H | H | H | P | P | H | H | H |  H | H |
               | 6,6 | P | P | P | P | P | H | H | H |  H | H |
               | 7,7 | P | P | P | P | P | P | H | H |  H | H |
               | 8,8 | P | P | P | P | P | P | P | P |  P | P |
               | 9,9 | P | P | P | P | P | S | P | P |  S | S |
               |10,10| S | S | S | S | S | S | S | S |  S | S |
               H = Hit  S = Stand   D = Double Down   P = Split

                 End of "How To Hack BlackJack": File 1 of 2

                                ==Phrack Magazine==

                 Volume Four, Issue Forty-Three, File 10 of 27

                            How to "Hack" BlackJack
                                  Lex Luthor
                            [email protected]

                               Part 2 of 2 (50K)

Card Counting:

   Card Counting? Don't you have to be some sort of mathematical genius or
have a photographic memory to count cards? No, these are as mythical as that
415-BUG-1111 "trace detector" number posted on all those old hacker BBSes.
Well, you may now say, what if the casino is using 4, 6, or even 8 decks?
Surely you can't keep track of 300+ cards! Don't sweat these details. Probably
the hardest part about learning to play successful BlackJack has already been
accomplished in the previous section. That is: memorizing the appropriate
basic strategy chart. All you really need to count cards is the ability to
count up to plus or minus twelve or so...by ONES! Of course there are more
complicated systems but that is all you need to do for the simplest ones.

   The first card counting systems were developed by our old friend Dr. Thorp.
He determined through mathematical computation that the card that has the most
influence on the deck being in a favorable condition (for the player) was the
five. When the deck is low in fives, the player has a higher advantage than if
it's sparse in any other card. Logic dictated that for a very simple card
counting strategy, simply keep track of the abundance (or lack thereof) of
fives. This is the basis of his "Five Count" system which was later improved
to include tens and renamed the "Ten Count" system.

   Today, there are many different card counting systems. Typically, the more
complex a system is, the better your advantage should you master it. However,
the difference between card counting System X and System Y is usually so small
that ease of using the system becomes more important than gaining an
additional .15 % advantage or whatever it is. I am going to restrict the
discussion to a single card counting system: the high/low (also called the
plus/minus) point count. This strategy is very easy to master. Two other
methods that I recommend if you're serious are the Advanced Plus/Minus and the
"Hi-Opt I" systems. The former being similar to the high/low but assigns
fractional values to certain cards as opposed to integer values which are
easier to add in your head. The latter method is considered one of the most
powerful yet reasonable (with respect to complexity) counting systems of all
time and is detailed extensively on pages 213 to 277 of [7].

   The quick and dirty reason why card counting works is this: The player
gains an advantage when a deck has a SHORTAGE of cards valued 2, 3, 4, 5, 6,
7, 8. When a deck has a SHORTAGE of cards valued 9, 10, Ace; the player has a
DISadvantage. If you can tell when the deck is rich in 9's, 10's, and Aces
(ie, when you hold the advantage) you can do one of the following things:

      1) Bet more money when the deck is favorable to you.
      2) Alter your Basic Strategy play to account for the favorability
         thereby increasing the odds of winning a particular hand.
      3) Combine 1 & 2 by betting more AND altering Basic Strategy.

   Now lets discuss the +/- Point Count. As you can see from the small chart
below, a plus value is given to low cards, and a minus value is given to high
cards. Notice that 7, 8, and 9 have a value of zero. This is because their
overall effect is negligible as compared to the others. Some systems use a
value of -2 for the Ace instead of -1 and give a value of +1 to the seven
instead of zero. If you are using a BlackJack computer game for practice,
check to see what card counting system(s) it uses. They should offer one of
the above two variations. Learn that one, since it will allow you to prepare
well for actual casino play. See the "Some Comments Regarding Computer
BlackJack Programs for the PC" section for more on this. Now the chart:

                   |    PLUS (+1)      ||     MINUS (-1)     |
                   | 2 | 3 | 4 | 5 | 6 || 7 | 8 | 9 | 10 | A |
                   | 1 | 1 | 1 | 1 | 1 || 0 | 0 | 0 | 1  | 1 |

   As you may notice, this is a balanced system. There are 20 cards in a deck
that are valued +1: two through six. There are 16 ten value cards and 4 Aces
in a deck (20 total) that are valued -1. The remaining 12 cards (7, 8, 9) have
a value of zero. At the end of a deck the count should be zero. A good drill
to practice is to get a deck of cards, turn them over one by one, and keep
track of the count. If you enter a game mid-way between the deck or shoe, flat
bet until the cards are shuffled. Once the cards are shuffled commence
counting from zero.

   Lets do a quick example using ten cards. The following ten cards are shown
in the course of a hand: A, 4, 7, 10, 10, 9, 10, 2, 10, 5. Just so no one gets
lost, we will do one card at a time and then keep the running total: the first
value is -1 (the Ace) & the second is +1 (the 4) = 0 (the current total hand
count). The next card is the 7 which is zero so disregard it. The next card is
a ten so the total count is now -1. The next card is another ten, giving a
total count of -2. The next card is a nine which has a value of zero so ignore
it, total count is still at -2. Next is a ten, total count is at -3. Next is
a two which adds +1 to the minus three yielding a total of -2. A quick look at
the next two cards shows that the two will cancel each other out (-1+1=0). So
at the end of a hand of ten cards dealt to 2 players and the dealer, the point
count is minus two. This provides you with the knowledge that your are at a
slight disadvantage. Your next bet should either be the same or a unit or two

   From this example you see that it would be easier to count cards if you
play in a "cards-up" game. That way you can see all the cards as they are
dealt and count them as they go by. When the dealer deals fast, just count
every two cards. You still count each card but you only add to your total
count after every two cards since many times the two values will cancel each
other out to give a net value of zero, which doesn't need to be added to your
total. If you play in a cards-down game, you may want to consider playing at
third base. The reason being is that in a cards-down game you only see the
other players' cards:

 a) if you peek at their hand (not polite but it's not cheating like in poker)
 b) if a player busts
 c) when the dealer settles each players' hand.

   When there are other people at a table, all this happens rather quickly and
you may miss a few cards here and there which essentially invalidates your
count. You can't control how fast the dealer deals, but you can slow things
down when the dealer prompts you for a play decision.

   I am not going to discuss changing basic strategy here. The chart you
memorize in Basic Strategy section of this file will be fine for now. If you
are already adept at the plus/minus count then find a book that has a complete
system including the appropriate changes to Basic Strategy that reflect the
current running and/or true count.

   For one deck, alter your wager according to the following table:

                        BET UNITS   +/- Running Count
                            1            +1 or less
                            2            +2 or +3
                            3            +4 or +5
                            4            +6 or +7
                            5            +8 or more

   Example: After the first hand of a one deck game, the point count is plus
four and you just bet a $5.00 chip. Before the next hand is dealt, wager
$15.00 (three units of $5.00) as the above table mandates.

   What if there are four, six, or more decks instead of just one? I recommend
that you perform a "true-count" rather than trying to remember different
betting strategies for different number of deck games. By doing a true count,
the above table can still be used.

   The True Count is found by the ensuing equation. I provide an example along
with it for the case of having a running count of +9 with one and a half decks
left unplayed. It doesn't matter how many decks are used, you just have to have
a good eye at guesstimating the number of decks that are left in the shoe. I
just measured the thickness of a deck of cards to be 5/8 (10/16) of an inch.
Hence the thickness of a half deck is 5/16 of an inch. One and a half decks
would be 10/16 + 10/16 + 5/16 = 25/16 or a little over an inch and a half. You
probably see a relationship here. The number of decks is approximately equal
to the height of the cards in inches. Easy.

                             Running Count           +9
            True Count = ----------------------  =  ----- = +6
                          # of Decks Remaining       1.5

   Looking at the table of betting units above, the proper wager would be four

   If you have trouble keeping the count straight in your head, you can use
your chips as a memory storage device. After every hand tally up the net count
and update the running or true count by rearranging your chips. This is
somewhat conspicuous however, and if done blatantly, may get you labeled a

   If for some reason you despise the notion of counting cards, you may want
to pick up Reference [11], "Winning Without Counting". The author writes about
using kinesics (body language) to help determine what the dealers' hole card
is after checking for a Natural. He claims that certain dealers have certain
habits as far as body language is concerned, especially when they check to see
if they have a BlackJack. The dealer will check the hole card if he/she has a
ten value card or an Ace as the up-card. When the hand is over you will see
what the hole card really was. You may be able to discern a certain
characteristic about the dealer, such as a raising of the eyebrows whenever
the hole card is a 2-9 or perhaps a slight frown, etc. There is some
usefulness to this method but I wouldn't rely on it very much at all. I have
only used it for one particular situation. That being when the dealer has a
ten up card and checks to see if the hole card is an Ace. Note that many
dealers check the hole card very quickly and turn up just the corner of the
card so as to prevent any of the players from seeing the card. If the hole
card is an Ace, the dealer will turn over the card and declare a BlackJack.
However, if the hole card is a 4, many times the dealer will double check it.
The reason for this double take is simply that a 4 looks like an Ace from the
corner, get a deck of cards and see for yourself. A 4 really looks like an Ace
and vice-versa when the corner is checked in a QUICK motion. So, if you see
the dealer double check the hole card and NOT declare a BlackJack, you can be
fairly sure the hold card is a four, giving the dealer a total of 14. You can
now adjust your basic strategy play accordingly. This situation has only come
up a few times in my case, but once was when I had a $50.00 bet riding on the
hand and I won the hand by using that additional information. Dr. Julian Braun
has previously calculated that the player has about a 10% advantage over the
house should he/she know what the dealer's hole card is. This is quite
substantial. Of course you have to memorize a specific Basic Strategy chart
for the case of knowing what the dealers' total is in order to obtain the
maximum benefit. I haven't bothered memorizing this chart simply because it is
a rare occurrence to know what the dealers' hole card is. If you sit down at a
table with an inexperienced dealer, you might catch a couple more than usual,
but I don't think it is enough to warrant the extra work unless you want to
turn pro.

   Another thing Winning Without Counting mentions is to pay attention to the
arches and warps in the cards. Perhaps a lot of the ten value cards have a
particular warp in them due to all those times the dealer checked for a
BlackJack. The author claims that he has used this to his advantage. Maybe so,
but I don't put much stock in this technique. I have enough things to worry
about while playing.

   One last thing. There is no law or rule that says a dealer cannot count
cards. A dealer may count cards because he or she is bored but more likely is
that the casino may encourage counting. The reason being that if the deck is
favorable to the player, the house can know this and "shuffle up". This is
also called preferential shuffling (a game control measure) and it vaporizes
your advantage.

Shuffle Tracking:

  Shuffle What? Shuffle Tracking. This is a fairly new (15 years +/-)
technique that has not been publicized very much. One problem with many of the
BlackJack books out there is that they are not hip to the current game. The
obvious reason for this is that many are old or simply re-formulate strategies
that were invented decades ago. It's just like reading "How to Hack the Primos
Version 18 Operating System" today. The file may be interesting, many of the
commands may be the same, but it doesn't detail how to take advantage of, and
subvert the CURRENT version of the OS.

   The best definition I have seen is this one quoted from Reference [5]:
"'Shuffle-tracking' is the science of following specific cards through the
shuffling process for the purpose of either keeping them in play or cutting
them out of play." The concept of Shuffle tracking appears to have resulted
from bored mathematician's research and computer simulation of shuffling
cards, a familiar theme to BlackJack you say. The main thing that I hope every
reader gets from this section is that just because someone shuffles a deck (or
decks) of cards does not in any way mean that the cards are "randomized". The
methods mentioned in the two previous sections (Basic Strategy and Card
Counting) ASSUME A RANDOM DISTRIBUTION OF CARDS! That is an important point.
According to some authors, a single deck of cards must be shuffled twenty to
thirty times to ensure a truly random dispersion. If a Casino is using a 6
deck shoe, that's 120 to 180 shuffles! Obviously they aren't going to shuffle
anywhere near that many times. But don't despair, there are some types of
shuffles which are good, and some that are bad. In fact, if the cards were
always randomly disbursed, then you would not be reading this section due to
it's lack of relevance. As in the Card Counting section, I am going to
restrict the discussion to the basics of shuffle tracking as the combination
of references listed at the end of this section provide a complete discourse of
the topic.

   A beneficial (to the player) shuffle for a one deck game is executed by
dividing the deck equally into 26 cards and shuffling them together a minimum
of three times. This allows the cards to be sufficiently intermixed to yield a
fairly random distribution. An adverse shuffle prevents the cards from mixing

   The simplest example is the Unbalanced Shuffle. As its name implies, the
dealer breaks the deck into two unequal stacks. As an example, lets say you
are playing two hands head on with the dealer and the last 10 cards in the
deck are dealt. The result of the hand was that both your hands lost to the
dealer primarily due to the high percentage of low value cards in the clump.
Note that if you were counting, you would have bet a single unit since the
deck was unfavorable. The dealer is now ready to shuffle the deck, and
separates the deck into 31 cards in one stack and 21 in the other stack. The
dealer shuffles the two stacks. If the shuffle is done from the bottom of each
stack on up, the top ten cards of the larger stack will remain intact without
mixing with any of the other cards. Those ten cards can remain in the order
they were just dealt throughout the shuffle if the process of bottom to top
shuffling is not altered. You are now asked to cut the deck. If you don't cut
the deck, the 10 cards that were dealt last hand will be dealt as your first
two hands. The result will be the same as your last and you will lose the two
hands. However, if you cut the deck exactly at the end of those ten cards, you
have just altered the future to your benefit. Those cards will now be placed at
the bottom of the deck. Should the dealer shuffle up early, you will avoid them
altogether. In addition, if you were keeping count, you would know that the
deck was favorable during the first 3-4 hands since there would be an abundance
of tens in the portion of the deck that will be played. You would accordingly
increase you bet size to maximize your winnings.

   Some dealers will unknowingly split the deck into unequal stacks. However,
more often than not, they are REQUIRED to split the deck into unequal stacks.
If they are required to do this, they are performing the House Shuffle. The
casino has trained the dealer to shuffle a particular way...on purpose! Why?
Because in the long run, the house will benefit from this because most players
will not cut any bad clumps out of play. If you have played BlackJack in a
casino, how much did you pay attention to the way they shuffled? Like most
people you were probably oblivious to it, perhaps you figured that during the
shuffle would be a good time to ask that hot waitress for another drink.
Regardless, you now see that it may be a good idea to pay attention during the
shuffle instead of that set of "big breastseses" as David Allen Grier says on
the "In Living Color" TV show ;)-8-<

   There are a number of shuffle methods, some of which have been labeled as:
the "Zone Shuffle", the "Strip Shuffle", and the "Stutter Shuffle". The Zone
Shuffle is particular to shoe games (multiple deck games) and is probably one
of the most common shuffle methods which is why I mention it here. It is
accomplished by splitting the shoe into 4 to 8 piles depending on the number
of decks in the shoe. Prescribed picks from each pile are made in a very exact
way with intermittent shuffles of each pair of half deck sized stacks. The net
effect is a simple regrouping of the cards pretty much in the same region of
the shoe as they were before, thereby preventing clumps of cards from being
randomly mixed. If the dealer won 40 hands and you won 20, this trend is
likely to continue until you are broke or until the unfavorable bias is
removed through many shuffles.

   What if the players are winning the 40 hands and the dealer only 20? If the
dealer has been mentally keeping track of how many hands each side has won in
the shoe, the dealer will probably do one of two things. One is to keep the
shuffle the same, but 'strip' the deck. When a dealer strips a deck, he/she
strips off one card at a time from the shoe letting them fall on top of one
another onto the table. This action causes the order of the cards to be
reversed. The main consequence is to dissipate any clumping advantages (a bunch
of tens in a clump) that the players may have. The second thing the dealer may
do is simply change the way they shuffle to help randomize the cards.

   I personally believe that casinos use certain shuffles on purpose for the
sole reason that they gain some sort of advantage. A BlackJack dealer friend
of mine disputes the whole theory of card clumping and shuffle tracking
though. The mathematics and simulation prove the non-random nature of certain
shuffles under controlled conditions. Perhaps in an actual casino environment
the effect isn't as high. Regardless, next time you are playing in a casino
and its time to shuffle a shoe, ask the dealer to CHANGE they WAY he/she
shuffles. The answer will nearly always be NO. Try to appeal to the pit boss
and he/she will probably mumble something about casino policy. Why are they
afraid to change the shuffle?

Relevant Reading: [4], [5] Chapters 5 and 6 pages 71 to 98, [14] pages 463
to 466, and [15] which is very detailed and accessible via Internet FTP.

Casino Security and Surveillance:

   I figured this section might get some people's attention. It is important
to know what the casino is capable of as far as detecting cheating (by
employees and customers) and spotting card counters.

EYE IN THE SKY: A two way mirror in the ceiling of the casino. It's not hard
to spot in older casinos as it usually is very long. Before 1973 or so,
employees traversed catwalks in the ceiling and it was easy for dealers and
players to hear when they were being watched. Sometimes dust from the ceiling
would settle down onto a table when someone was above it. Newer casinos use
those big dark plexiglass bubbles with video camera's which should be watched
constantly. These cameras have awesome Z00M capabilities and according to
Reference [9], the cameras can read the word "liberty" on a penny placed on a
BlackJack table. I am sure the resolution is better than that for the latest
equipment. The video images are also taped for use as evidence should anything
that is suspect be detected. Just like computer security audit logs, if no one
pays attention to them, they don't do much good. If you want a job monitoring
gamblers and casino employees, you need to train for about 500 hours (about
twenty 40 hour weeks) to learn all the tricks people try to pull on you.
Pretty intensive program wouldn't you say?

CASINO EMPLOYEES: Then there are the casino employees. The dealers watch the
players, the floor men watch the dealers and the players, the pitbosses watch
the dealers, the floormen, and the players, etc. There may be plain clothes
detectives roaming about. In a casino, everyone is suspect.

BLACK BOOK: A company that you will see mentioned in a lot of casino books is
Griffin Investigations. They periodically update a book that casino's
subscribe to that have pictures and related info on barred card counters and
known casino cheats.....I suppose the "black book" as it is called, is
analogous to the "Bell security hit-lists", that had (have?) files on known
phreaks and hackers.

Social Engineering the Casino:

   If you are good at getting an ESS operator to enter NET-LINE on DN COE-XXXX,
and at getting those "Engineering Resistant Hard Asses up at SNET (Southern
New England Telephone)" [as The Marauder affectionately calls them] to give
you the new CRSAB number; then this section will be a piece of cake for you
to master.

   References [3], [7], and [8] have many stories regarding playing in
casinos, getting barred, and various exploits. I am not going to repeat any of
them here. In each of those books, the authors talk about their first
experiences getting barred. In each case they were fairly bewildered as to why
they were kicked out, at least until some casino employee or owner told them
things like "you're just too good" and the ever diplomatic: "we know your
kind, get the hell out!".

   As you probably have gathered thus far, card counters are as undesirable in
a casino as a phone phreak is in a central office. There are a number of
behavioral characteristics which have been attributed to the 'typical' card
counter. Probably the most obvious act of a counter is a large increase in bet
size. If you recall in the Card Counting section, when the deck is favorable,
you bet more. When the deck is unfavorable, you bet less. Dr. Thorp's original
system required a variation in bet size from one to ten units. When the deck
is favorable the system may dictate that you go from a ten dollar bet to a
hundred dollar bet. Kind of gets the attention of the dealer and the pit boss.
However, this type of wild wagering is typical of big money hunch bettors.
Hunch betters will just plop down a bunch of chips at random due to 'hunches'.
Therefore, a large increase in bet size won't necessarily cause you to be
pegged as a counter.

   Intense concentration, never taking your eyes off the cards, lack of
emotion...ie, playing like a computer, is pretty much a give away that you are
counting. Other things such as 'acting suspicious', meticulously stacking your
chips, betting in discernable patterns, and a devout abstention from alcohol
may also attract unwanted attention.

   Another criteria used for spotting counters is if there are two or more
people playing in concert with one another. Ken Uston is famous for his
BlackJack teams. They have literally won millions of dollars collectively.
When the "Team-LOD" gets together to play, we have to pretend we don't know
each other so as not to attract undue attention ;-)

   What I mean by Social Engineering the casino is to list ways that trick the
casino into thinking you are just a dumb tourist who is throwing money away.
Look around, smile, act unconcerned about your bet, don't be afraid to talk to
the dealer, floorperson, or pit boss. Don't play 8 hours straight. Perhaps
order a drink. Things of this nature will help deflect suspicion.

   I only recall attracting attention once. The casino wasn't very busy, there
were 3 people at the table including myself. I only had about an hour to play
so I bet aggressively. I started with $5 and $10 but made some $50.00 bets
whenever I got a feeling that I was going to win the next hand (quite the
scientific strategy I know). A woman next to me who seemed to be a fairly
seasoned player made a comment that I was a little too aggressive. The pit boss
hovered about the table. My hour was nearly up, I bet $10.00 for the dealer and
$50.00 for myself. I lost the hand leaving me only $100.00 ahead, and left. The
only thing I could think of besides the betting spread which really wasn't a
big deal was that the casino was FREEZING inside. I was shivering like hell,
it probably looked like I was shaking out of fear of being spotted as a
counter or worse...a cheater.

   So what if a casino thinks you are counter? To be honest, there have
probably been less than 1000 people who have been permanently barred from play
(ie, they have their mugs in the black book). A far greater number have been
asked to leave but were not prevented from returning in the future.

   Tipping the dealer may not necessarily get the casino off your back but
certainly doesn't hurt. When you toke the dealer, place the chip in the corner
of your betting box a few inches from your bet. You may want to say "we are in
this one together" or some such to make sure they are aware of the tip. This
approach is better than just giving them the chip because their 'fate' is tied
in with yours. If your hand wins, 99 out of 100 times they will take the tip
and the tip's winnings off the table.

   The 1 out of 100 that the dealer let the tip+win ride happened to me over
and over again for the better part of a day. It was a week before I had to go
back to college and I was broke, with no money to pay the deposits for rent
and utilities. Basically, if I didn't come up with some money in 7 days, I was
not going back to school. This was 4 years ago BTW. I took out $150 on my
credit card (stupid but hey, I was desperate) and started playing and winning
immediately. I pressed my bets time and time again and in an hour or two had
$500 in front of me (+$350). I started losing a bit so I took a break for a
short while. I went back to a different table with a different dealer. As soon
as I sat down I started winning. I started to tip red chips ($5.00) for the
dealer. The first couple of times he took the $10.00 right away. I kept
winning steadily and continued to toke him. Then he started to let the $10.00
ride! I was amazed because I had never seen that before. That is when I knew I
was HOT. If the dealer is betting on you to win, that says something. When I
stopped playing I cashed in eight black chips. I left with eight one hundred
dollar bills, a net profit of $650.00, just enough to cover everything. Whew!
I probably tipped close to $100.00 that day, and the dealer must have made
double to triple that due to him betting with me. There were a number of times
when the pit boss wasn't close that the dealer would IGNORE my hit or stand
signal. The first time he did this I repeated myself and he did what I asked
but gave me a 'look'. Needless to say, I lost the hand. After that, if he
'thought' I said stand, I didn't argue. This occurred when he had a ten as the
up-card so he knew his total from peeking at the hole card. I am not sure if
this is considered cheating because I did not ask him to do this, nor did we
conspire. It just happened a few times, usually when I had $25-$50 bets on the
line which is when I made sure to throw in a red chip for him.

Casino Cheating and Player Cheating:

   Cheating by the house is rare in the major casinos ie, those located in
Nevada and Atlantic City. The Nevada Gaming Commission may revoke a casino's
gambling license if a casino is caught cheating players. Granted, there may be
a few employees (dealers, boxmen, whomever) that may cheat players, but it is
extremely doubtful any casino in Nevada or Atlantic City does so on a
casino-wide scale. You definitely should be wary of any casino that is not
regulated such as those found on many cruise ships. Because a casino does not
have to answer to any regulatory agency does not mean it is cheating players.
The fact is that casino's make plenty of money legitimately with the built-in
house advantages and don't really need to cheat players to survive. I provide
some cheating methods here merely to make you aware of the scams. These
techniques are still carried out in crooked underground casinos and private

   The single deck hand-held BlackJack game is quite a bit more susceptible to
cheating by both the dealer and the player than games dealt from a shoe. The
preferred method of dealer cheating is called the "second deal". As you may
infer, this technique requires the card mechanic to pretend to deal the top
card but instead deals the card that is immediately under the top card.
Imagine if you could draw a low card when you need a low card, and a high card
when you need a high card. You could win large sums of money in a very short
period. Well, a dealer who has the ability to execute the demanding sleight of
hand movements for second dealing can drain even the best BlackJack player's
bankroll in short order.

   If someone is going to deal seconds, they must know what the second card is
if he or she is to benefit. One way to determine the second card is by
peeking. A mechanic will distract you by pointing or gesticulating with the
hand that is holding the deck. "Look! There's Gail Thackeray!". While you are
busy looking, the dealer is covertly peeking at the second card. A more risky
method is pegging. A device called a pegger is used to put small indentations
in the cards that the dealer can feel. Pegging all the ten value cards has
obvious benefits.

   Another method is the "high-low pickup". I like this one because it's easy
for a novice to do especially in a place where there are a lot of distractions
for the players. After every hand, the dealer picks up the cards in a high-low
alternating order. The mechanic then proceeds with the "false shuffle" in
which the deck is thought to have been shuffled but in reality the cards
remain in the same order as before the shuffle. As you well know by now, a
high-low-high-low arrangement of the cards would be death to the BlackJack
player. Get dealt a ten and then a 5, you have to hit, so get another ten.
Busted. Since the dealer doesn't lose until he/she busts, all the players who
bust before lose. Bottom dealing and switching hole cards are other techniques
that may be used to cheat players.

   For shoe games, there is a device called a "holdout shoe" that essentially
second deals for the dealer. Discreet mirrors and prisms may be contained in
the holdout shoe which only allow the dealer to see what card is next.
Shorting a regular shoe of ten cards will obviously have a detrimental effect
on the BlackJack player.

   Player cheating isn't recommended. However, I'll quickly list some of the
methods for awareness purposes. The old stand-by of going up to a table,
grabbing some chips, and running like hell is still done but certainly lacks
originality. Marking cards while you play is another popular method. "The
Daub" technique is done by clandestinely applying a substance that leaves an
almost invisible smudge on the card. High value cards like tens are usually
the targets. One scam mentioned in one of the references was the use of a
special paint that was only visible to specially made contact lenses. The
"hold out" method requires the palming of a card and substituting a better
one. This is usually done when there is big money bet on the hand. One of the
risks to these methods is when the deck is changed since the pit boss always
scrutinizes the decks after they are taken out of play.

   Other methods entail playing two hands and switching cards from one hand to
the other, counterfeiting cards and/or casino chips, adding chips after a
winning hand (I have seen this done twice, couldn't believe my eyes but
certainly wasn't going to RAT the thieves out). Some dealers may be careless
when looking at their hole card for a BlackJack. A person behind the dealer on
the other side of the pit may be able to discern the card. The value is then
signalled to a player at the table. Astute pit bosses may notice someone who
is not playing that scratches their head too much though. Wireless signalling
devices have been used for various purposes but some casinos have new
electronic detection systems that monitor certain frequencies for activity.

Some Comments Regarding Computer BlackJack Software for PC's:

   I strongly recommend that you practice using a BlackJack program of some
kind before going out to play with real cash. The first program I used for
'training' some years ago was "Ken Uston's BlackJack" on my old Apple ][+.
Later I acquired "Beat The House" for the same machine. I recently bought a
program for my IBM and have been using it to refresh my memory regarding basic
strategy, card counting, and money management techniques. I assume you will
recognize the guy's name in the title now that you have read most of this
article. I bought: "Dr. Thorp's Mini BlackJack" by Villa Crespo Software at a
Wal-Mart of all places for a measly $7.88. This is an abridged version
however. Villa Crespo charges $12.95 for it if you order via mail. They also
offer an unabridged version for $29.95 via mail. Villa Crespo (don't ask me
where they got that name) offers other programs for Craps, Video Poker, and
7-Card Stud in case you are interested in those games of chance. By the way,
on the order form I also noticed "FAILSAFE Computer Guardian (Complete
protection and security for your system)" for $59.95. For some reason any time
a piece of paper has the word 'security' on it, my eyes zero in on it....

   Some features that I liked about this scaled down version of their
BlackJack program were the TUTOR, which advises you on whether to hit, stand,
take insurance (no way), etc. as per Basic Strategy. The Tutor for the
abridged version does NOT take into consideration the card count when making
recommendations though. If you are counting the cards, the program keeps count
also, so if you lose count you can check it by pressing a function key. The
STATS option is neat since it keeps track of things such as how many hands
were dealt, how many you won/lost, etc. and can be printed out so you can
track your progress. The program allows you to save your current session in
case you get the urge to dial up the Internet to check your email, something
that should be done every hour on the hour....

   One thing I did not like about the program was that it allowed you to bet
over your bankroll. I accidentally pushed [F2] (standardized at $500.00 a
bet instead of [F1] (standardized at $5.00 a bet) ---- a slight difference in
wager I'd say. Having only $272.00 in my bankroll didn't stop the program from
executing the command and in my opinion it should have prevented the overdraft.

   The first time I played Dr. Thorp's Mini BlackJack, it took me about 95
hands to double my money. I started with $200.00, bet from $5.00 to $25.00,
never dropped below $180.00 which surprised me, and received 3 BlackJacks. I
won 63 hands, and lost 32. I played head on against the dealer, although the
program allows for up to 6 players. I consider that lucky since I had my fair
share of going broke in later sessions.

   My advice when using a BlackJack computer program is: do not start with a
bizzillion dollars or anything like that. Start with the amount that you truly
plan to use when you sit down at an actual table. If you play in a crowded
casino, all the low minimum bet tables (ie: $1.00 to $5.00) will most likely be
filled to capacity and only $10.00 or $15.00 tables will have openings. Keep
this in mind because when you make bets with the computer program, you should
wager no less than whatever the minimum will be at the table you sit down at.
If your bankroll is only $200.00 playing at anything more than a $5.00 minimum
table is pushing it.

   Another thing to note is that playing at home is kind of like watching
Jeopardy on TV while you are sitting on the couch. People who have been on the
show always say it was much harder than when they blurted out answers during
dinner with their mouths full (the Heimlich maneuver--a real lifesaver!). The
same thing goes for BlackJack. When you are sitting at an actual table, your
adrenaline is flowing, your heart starts to pump faster, you make irrational
plays especially when you start losing, and odds are you will forget things
that were memorized perfectly. There is no substitute for the real thing and
real experience.

Quick Comments on Other Casino Games:

   A few people suggested I briefly mention some of the other casino games so
I added this section. I don't go into much detail at all as this file is too
unwieldy already. Besides, if you want to know more, I am sure you'll pick up
the appropriate reference. Hundreds of books have been published on gambling
and they are available by contacting [2]. My aim here was to mention details
that most people may not be aware of.

BACCARAT: This is the game you see in movies a lot. See [12]'s FAQ for a good
explanation of this game.

CRAPS: Craps is probably the most complicated casino game as far as the
different ways to bet things are concerned but its really not that hard to
learn. I just want to throw one table at you adapted from Reference [13]. The
table won't make much sense unless you are already familiar with craps. In
case you have forgotten or didn't know, craps is 'that dice game'. The purpose
of presenting it is to save you $$$$$ <-- Still love that dollar sign key! hehe

                         Lamest Bets at the Craps Table

                BET            PAYS     SHOULD PAY   YOUR ADVANTAGE
              Any-7            4  to 1     5 to 1         -16.7 %
              2 (or 12)        30 to 1    35 to 1         -13.9 %
              Hard 10 (or 4)   7  to 1     8 to 1         -11.1 %
              3 (or 11)        15 to 1    17 to 1         -11.1 %
              Any Craps        37 to 1     8 to 1         -11.1 %
              Hard 6 (or 8)    9  to 1    10 to 1         -9.1  %

SLOTS: Playing slots is a gamble. Obviously you say. No, I mean its a gamble
to play them. House advantages are almost never displayed on a particular slot
machine. Different machines and different locations may have different casino
win percentages. When you go up to a slot machine, you have no idea if its'
advantage over you is 5% or 25%. Unless you have been watching it, you don't
know if it just paid off a big jackpot either. I don't play slots as a matter
of principle. If you do play I think there are still some $.05 slots in Vegas.
Play the nickel slots and keep your shirt, especially if its an LOD T-shirt.

VIDEO POKER: Reference [13] gives the following advice regarding video poker:
"...don't expect to win. Manage your money so that you limit your losses." I
think its a bit negative but I can't argue with the logic. Also, as with
slots, you may want to play at a machine that is networked with others which
has a progressive payoff. This way at least you have a chance of making the
big bucks in addition to those periodic small payoffs.

VIDEO BLACKJACK: If you like to avoid people and like BlackJack, you may be
thinking that this is a great way for you to "hack two systems with one
password" and make a little money on the side. Before you start putting
quarter or dollar tokens into video BlackJack machines there are a couple of
things to know. First, you can't use card counting techniques because
every hand is essentially dealt from a new deck. When the computer deals a
hand it is just providing 'random' cards. Perhaps if you saw the source code,
you may be able to determine some sort of bias but I suspect it would be
minuscule at best. The rules vary from machine to machine and the maximum
allowable bet varies also. As with the video poker and video slot machines,
the owner of the machine may set the options to their taste (amount of profit).

Selected Bibliography:

The following are some references you may want to check out and some of my
sources of information for this article. They are not in any particular order
and the format is far from standard as opposed to my thesis bibliography :)

[1] "BlackJack Forum Newsletter" by RGE Publishing in Oakland California. This
is a quarterly publication which has the location and rule variations info
(among other things) for casinos in the state of Nevada.

[2] The Gamblers Book Club (its really a store) can sell you a sample of the
BlackJack Forum Newsletter for $10.00. They have all kinds of new and out of
print books, used magazines, etc. They are located in Vegas (630 S. 11th St.)
so stop by in person or call 1-800-634-6243 which was valid as of 6/1/93 since
I just gave them a ring...the guy I spoke to was very nice and helpful so I
thought I'd give them a plug here.

[3] "Beat The Dealer" by Dr. Edward O. Thorp. Make sure you get the SECOND
edition (1966) since it has Dr. Julian Braun's additions to the original 1962

[4] "Gambling Times Magazine" (now defunct), 'BlackJack Bias Part 1 and 2' July
and August 1987 Issues by Mason Malmuth. This magazine was great because it
kept you up to date on the latest in gambling systems and what casinos are up
to. The article is about the author using his PC to perform simulations
regarding the effects of non-random card distribution on BlackJack.

[5] "Break The Dealer" by Jerry L. Patterson and Eddie Olsen, 1986 Perigee
Books. Worth the money for the chapters on Shuffle Tracking alone.

[6] "The Optimum Strategy in BlackJack" by Roger R. Baldwin, Wilbert E.
Cantey, Herbert Maisel, James P. McDermott. Journal of the American
Statistical Association, September 1956. Eight of ten pages are mathematics.

[7] "The World's Greatest BlackJack Book" revised edition (1987) by Dr. Lance
Humble and Dr. Carl Cooper, Doubleday. I am not sure it is THE world's
greatest, but it is an excellent book. It is 400 pages and provides more
details than you probably care to know about the Hi-Opt I counting system.

[8] "Turning the Tables on Las Vegas" by Ian Anderson, 1978. This is an
excellent book if you were interested in The Social Engineering the Casino
section. The author shares a lot of interesting and funny stories that can
keep you from getting barred. Note that 'Ian Anderson' is the authors' handle.

[9] "Las Vegas, Behind the Tables" by Barney Vinson, 1986, Gollehon Press.
Written by a casino executive, I found it to be quite illuminating.

[10] "Gambling Scams" by Darwin Ortiz, 1990, Carrol Publishing. If you play in
any private games, be sure to read this one to avoid getting screwed. It even
has a section on crooked carnival games.

[11] "Winning Without Counting" by Stanford Wong. This book has an interesting
section on 'Dealer Tells' and how to exploit them.

[12] "Rec.Gambling" Internet USENET Newsgroup. The rec.gambling newsgroup is
an excellent free source of current information on BlackJack and other games.
People who have just gotten back from various casinos post about their playing
results and the treatment from casinos. One person just posted that he was
barred from playing BlackJack (a casino employee told him he could play any
game in the casino EXCEPT BlackJack) after he was ahead only $40.00. The
reason apparently was due to his fairly mechanical play and betting. The
rec.gambling FAQ was message #15912 when I read the newsgroup on 6/8/93. They
plan on posting the FAQ every month or so. I found the FAQ to be very
informative. There is an alt.gambling newsgroup but it is dead with 0

[13] "The Winner's Guide to Casino Gambling", revised edition by Edwin
Silberstang, 1989 Plume printing. This book covers a wide range of casino
games and has a large list of gambling terms in the back.

[14] "Gambling and Society" edited by William R. Eadington, 1976. This book
provides plenty of information on the psychology of gambling. I found the
section on 'Who Wants to be a Professional Gambler?' interesting as the study
indicates the types of vocations that show high correlations with being a
professional gambler. One of those vocations with an 'extremely high
correlation' was being a Secret Service agent. Maybe Agent Foley will change
jobs.....he can't do much worse, ahem. Chapter 24 by James N. Hanson is
entitled "Nonlinear Programming Simulation and Gambling Theory Applied to
BlackJack" which some of you programmers might be interested in.

[15] "The BlackJack Shuffle-Tracking Treatise" by Michael R. Hall accessible
via the Internet by anonymous FTP: soda.berkeley.edu in the
pub/rec.gambling/blackjack directory. This is a very detailed 78K file that
was well done. It provides plenty of the nitty-gritty details that I did not
have the space to mention in this article. I highly recommend it.

[16] "Risk of Ruin" by Michael R. Hall available from same source as [15]
above. This paper provides some mathematical formulas for helping you
determine the likelihood of losing portions of your starting bankroll.
Although the equations look complicated, anyone with a $10. scientific
calculator can use them. The author provides source code for a program written
in C that calculates the risk formula. Also get his "Optimal Wagering" file
which helps you determine your bet size.

[17] The movie: "Fever Pitch" starring Ryan 'O Niel. This is the most realistic
movie I have seen regarding the psychology of a gambler. If I recall correctly,
it was made in 1985 and is in most video rental stores.

Final Comments:

   Let me quickly thank those who took the hour to read my article, recommended
corrections and offered their insightful comments: The Marauder, Mark Tabas,
Professor Falken, Al Capone, Jester Sluggo, and Bruce Sterling. Also, I would
like to thank JLE, my 'gambling mentor' mentioned earlier even though he
doesn't know me as 'lex' and probably will never see this file.

   If anyone has comments, corrections, etc. feel free to email me. Kindly
note that I have no interest in receiving flames from any self professed
BlackJack experts out there as I do not claim to be an expert and due to size
restrictions, I couldn't get all that complicated regarding counting
techniques and such. Besides, anyone who wants to get serious will take the
time to thoroughly read the references listed in the previous section. My main
purpose was to familiarize you with the game of BlackJack and provide a
resource which can point you in the right direction for more in-depth
information. Thank you for your time and I hope you learned something from
this article even if you don't put any of the information to use.

   If you have something really SEKRET to tell me, here is my PGP Public Key:

Version: 2.2


                 End of "How To Hack BlackJack": File 2 of 2 
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