Millions of players have heard
the message that of all the casino table games, blackjack is the one that it is
possible to beat. A practical system for counting cards in blackjack to gain an
edge over the casino was made available to the public in the early 1960s. As it
happened, few players ever really learned to beat the dealer. Furthermore,
playing conditions have changed since then. Some tables use more than one deck
at a time or cut a percentage of the cards out of play so that a card counter
never sees them.
Even though most players don't have the skill to win
consistently, the belief that blackjack can be beaten was enough to spark a boom
in the game. Blackjack is by far the most popular casino table game in the
United States, with more players than craps, roulette, and baccarat
combined.
A lot of people don't have either the patience, persistence,
and concentration necessary for card counting or the bankroll to make it
effective. But they can still narrow the house advantage to less than 1 percent
in blackjack. The secret is to learn basic strategy for hitting, standing,
doubling down, and splitting pairs. A little time spent learning to play well
can make your money go a lot farther in the casino. In this article, you will
learn the fundamentals of blackjack, as well as some strategies to increase your
odds of winning. Let's get started by learning how to play the
game:
Rules
Blackjack is played with one or more standard
52-card decks, with each denomination assigned a point value. The cards 2
through 10 are worth their face value. Kings, queens, and jacks are each worth
10, and aces may be used as either 1 or 11. The object for the player is to draw
cards totaling closer to 21, without going over, than the dealer's
cards.
The best total of all is a two-card 21, or a blackjack. Blackjack
pays 3-2--that is, a two-card 21 on a $5 bet will win $7.50 instead of the usual
$5 even-money payoff on other winning hands. However, if the dealer also has a
two-card 21, the hand pushes, or ties, and you just get your original bet back.
But if the dealer goes on to draw 21 in three or more cards, your blackjack is
still a winner with its 3-2 payoff.
The game is usually played at an
arc-shaped table with places for up to seven players on the outside and for the
dealer on the inside. At one corner of the table is a rectangular placard that
tells the minimum and maximum bets at that table, as well as giving variations
in common rules. For example, the sign might say, "BLACKJACK. $5 to $2,000.
Split any pair three times. Double on any two cards." That means the minimum bet
at this table is $5 and the maximum is $2,000. Pairs may be split according to
the rules described below, and if more matching cards are dealt, the pairs may
be split up to three times for a total of four hands. The player may double the
original bet (double down) and receive just one more card on any two-card
total.
 ?006 Publications International, Ltd. The
standard table layout for
blackjack.
| Most games today
use four, six, or eight decks. After being shuffled, the cards are placed in a
receptacle called a shoe, from which the dealer can slide out one card at a
time. Single- or double-deck games, most common in Nevada, but also popular in
Mississippi and some other markets, may be dealt from the dealer's
hand.
Play begins when you place a bet by stacking a chip or chips in the
betting square on the table directly in front of you. After all bets have been
placed, each player and the dealer are given two cards. In a shoe game, all
player cards are dealt faceup, and the players are not permitted to touch their
cards. In a single- or double-deck game dealt from the hand, cards are dealt
facedown and players may pick them up with one hand. Either way, one of the
dealer's cards is turned faceup so the players can see it.
Once the cards
have been dealt, players decide in turn how to play out their hands. After all
players have finished, the dealer plays according to set rules: The dealer must
draw more cards to any total of 16 or less and must stand on any total of 17 or
more. In some casinos, the dealer will also draw to "soft" 17 -- a 17 including
an ace or aces that could also be counted as a 7. The most common soft 17 is
ace-6, but several other totals, such as ace-3-3 or ace-4-2, on up to
ace-ace-ace-ace-ace-ace-ace in a multiple deck game, are soft 17s.
Hit: If you hit, you take another card or cards
in hopes of getting closer to 21. If the player's total exceeds 21 after
hitting, the player is said to "bust" and loses the bet. In shoe games, the
player signals a hit by pointing to his cards or scratching or waving toward
himself. In facedown games, the player signals a hit by scratching the table
with the cards. Verbal calls to hit are not accepted -- signals are used for the
benefit of the security cameras above the table, so a taped record is on hand to
settle any potential disputes.
Stand: If you stand, you elect to draw no more
cards in hopes that the current total will beat the dealer. Signal a stand by
holding a flattened palm over your cards in a faceup game or by sliding your
cards under your bet in a facedown game.
Double down: You may elect to double your
original bet and receive only one more card regardless of its denomination. Some
casinos restrict doubling down to hands in which your first two cards total 10
or 11. Others allow you to double on any two cards. Double down by taking a chip
or chips equal to the amount of your original bet and placing them next to your
bet. In a facedown game, at this point you also need to turn your original two
cards faceup.
Split: If your first two cards are of the same
denomination, you may elect to make a second bet equal to your first and split
the pair, using each card as the first card in a separate hand. For example, if
you are dealt two 8s, you may slide a second bet equal to the first to your
betting box. The dealer will separate the 8s, then put a second card on the
first 8. You play that hand out in normal fashion until you either stand or
bust; then the dealer puts a second card on the second 8, and you play that hand
out.
Insurance: If the dealer's
faceup card is an ace, you may take "insurance," which essentially is a bet that
the dealer has a 10-value card down to complete a blackjack. Insurance, which
may be taken for half the original bet, pays 2-1 if the dealer has blackjack.
The net effect is that if you win the insurance bet and lose the hand, you come
out even. For example, the player has 18 with a $10 bet down. The dealer has an
ace up. The player takes a $5 insurance bet. If the dealer has blackjack, the
player loses the $10 bet on the hand but wins $10 with the 2-1 payoff on the $5
insurance bet.
Many dealers will advise players to take insurance if the
player has a blackjack. This can be done by simply calling out, "Even money" --
because if the dealer does have blackjack, the player gets a payoff equal to the
player's bet instead of the 3-2 normally paid on blackjack.
These are the
steps involved: Player bets $10 and draws a blackjack. Dealer has an ace up.
Player makes a $5 insurance bet. Dealer has blackjack. The player's blackjack
ties the dealer's, so no money changes hands on the original bet. But the $5
insurance bet wins $10 on the 2-1 payoff -- the same as if the original $10 bet
had won an even-money payoff.
As it happens, dealers who suggest this
play are giving bad advice. Insurance would be an even bet if the dealer showing
an ace completed a blackjack one-third (33.3 percent) of the time. But only 30.8
percent of cards have 10-values. Taking insurance is a bad percentage play, no
matter what the player total, unless the player is a card counter who knows that
an unusually large concentration of 10-value cards remains to be played.
Variations
Not all blackjack games are
created equal. Some variations in the rules are good for the player, and some
are bad. The shifts in the house edge may look small, but they make large
differences in a game in which the total house edge is less than 1 percent
against a basic strategy player. Here are some common variations and their
effect on the house advantage:
Double
downs after splitting pairs permitted: A very good rule for the player,
it cuts the house advantage by .13 percent. In areas where several casinos are
within reasonable distance, the player should choose games in which doubling
after splits is allowed.
Resplitting of aces permitted: At most casinos,
the player who splits aces receives only one more card on each ace. But if the
player receives another ace, some casinos allow the resulting pair to be
resplit. This option cuts the house edge by .03 percent. It is rare to find a
game that goes even further by allowing the player to draw more than one card to
a split ace, an option that cuts the house edge by .14 percent.
Early surrender: When the dealer's faceup card
is an ace, the dealer checks to see if the down-card is a 10 to complete a
blackjack before proceeding with play. If the house allows the player to
surrender half the original bet instead of playing the hand before the dealer
checks for blackjack, that is early surrender. A great rule for the player, and
one that is rarely found, early surrender cuts the house edge by .624 percent.
Surrender can easily be misused by beginners who haven't mastered basic
strategy.
Late surrender: Found
more often than early surrender, but still not commonplace, late surrender
allows the player to give up half the bet rather than playing the hand after the
dealer checks for blackjack. This decreases the house edge by .07 percent in a
multiple-deck game, .02 percent in a single-deck game.
Double-downs limited to hard 11 and hard 10:
Some casinos do not allow the player to double on totals of less than 10
or on soft hands. The net is a .28-percent increase in the house
edge.
Dealer hits soft 17: If,
instead of standing on all 17s, the dealer hits hands including an ace or aces
that can be totaled as either 7 or 17, the house edge is increased by .2
percent.
Blackjack pays 6-5:
Common on single-deck games on the Las Vegas Strip, this game is a bankroll
breaker for players. For example, a two-card 21 pays only $6 for a $5 bet
instead of the usual $7.50, which adds 1.4 percent edge to the house--more than
the usual house edge against the basic strategy of seasoned players in nearly
all games with the normal 3-2 return.
Now that you know how to play, let's explore
some of the finer points of the game. In the next section, you will learn the
etiquete and strategy of blackjack.
Blackjack Etiquette and
Strategy There's more to mastering any
game than a fundamental understanding of how to play. You must also know the
customs of the game and how to finnesse the rules.
Etiquette
When you sit down at a table,
wait for the dealer to finish the hand in progress. Then you may buy chips by
placing currency on the layout, pushing it toward the dealer, and saying,
"Change, please."
Do not leave currency in the betting box on the table.
In most newer gaming jurisdictions, casinos are not allowed to accept cash bets.
However, casinos in some places allow cash bets with the call "Money plays."
Don't leave the dealer wondering if that $100 bill is a request for change or a
bet on the next hand.
Once you make a bet, keep your hands off the chips
in the betting box until the hand is over.
If you are betting chips of
different denominations, stack them with the smallest denomination on top. If
you put a larger denomination on top, the dealer will rearrange them before
going on with the hand. It's one way the casino guards against someone
attempting to add a large-denomination chip to their bet after the outcome is
known.
In multiple-deck games, give playing decisions with hand signals.
In single- or double-deck games dealt facedown, pick up the cards with one hand,
scratch the table with the cards for a hit, and slide the cards under your chips
to stand. Turn the cards faceup if you bust or if you wish to split pairs or
double down. At the conclusion of play, let the dealer turn faceup any cards
under your chips.
If you are a novice, you might want to avoid the last
seat at the table, the one all the way to the players' left. This is called
"third base," and the player here is the last to play before the dealer.
Although in the long run bad plays will help other players as much as they hurt
them, in the short term other players will notice if a mistake by the third
baseman costs them money. For example, the dealer shows a 6, the third baseman
has 12 and hits a 10 to bust. The dealer turns up a 10 for 16, then draws a 5
for 21, beating all players at the table. The third baseman is likely to take
heat from other players for taking the dealer's bust card instead of standing.
If you don't want the heat, sit elsewhere.
If you wish to use the rest
room and return to the same seat, you may ask the dealer to mark your place. A
clear plastic disk will be placed in your betting box as a sign that the seat is
occupied.
The House Edge
Because the player hands are completed first, the
players have the chance to bust before the dealer plays. And the house wins
whenever the player busts, regardless of how the dealer's hand winds up. That is
the entire source of the casino's advantage in blackjack. Because of this one
edge, the casino will win more hands than the player, no matter how
expert.
The casino gives back some of this advantage by paying 3-2 on
blackjack, allowing players to see one of the dealer's cards, and by allowing
the player to double down and split pairs. To take advantage of these options,
the player must learn proper strategy.
Basic Strategy
Played well, blackjack becomes a game of skill in
a casino full of games of chance. Studies of millions of computer-generated
hands have yielded a strategy for when to hit, when to stand, when to double,
when to split. This strategy can take the house edge down to about .5 percent in
a six-deck game -- and lower in games with fewer decks. In a single-deck game in
which the dealer stands on all 17s and the player is allowed to double down
after splits, a basic strategy player can even gain an edge of .1 percent over
the house. Needless to say, such single-deck games are not commonly
dealt.
Compare those percentages with players who adopt a never-bust
strategy, standing on all hands of 12 or more so that drawing a 10 will not
cause them to lose before the dealer's hand is played, to players who use
dealer's strategy, always hitting 16 or less and standing on 17 or more. These
players face a house edge estimated at 5 percent -- about 10 times the edge
faced by a basic strategy player.
Basic strategy takes advantage of the
player's opportunity to look at one of the dealer's cards. You're not just
blindly trying to come as close to 21 as possible. By showing you one card, the
dealer allows you to make an educated estimate of the eventual outcome and play
your cards accordingly.
One simple way to look at it is to play as if the
dealer's facedown card is a 10. Since 10-value cards (10, jack, queen, king)
comprise four of the 13 denominations in the deck, that is the single most
likely value of any unseen card. Therefore, if you have 16 and the dealer's
up-card is a 7, you are guessing that the most likely dealer total is 17. The
dealer would stand on 17 to beat your 16; therefore, you must hit the 16 to have
the best chance to win.
On the other hand, if you have 16 and the
dealer's up-card is a 6, your assumption would be that his total is 16, making
the dealer more likely than not to bust on the next card. Therefore, you stand
on 16 versus 6.
That's an oversimplification, of course, but very close
to the way the percentages work out when the effect of multiple-card draws are
taken into account.
The most common decision a player must make is
whether to hit or stand on a hard total -- a hand in which there is no ace being
used as an 11. Basic strategy begins with the proper plays for each hard total
faced by the player. You can refer to this simple chart:
If you have:
|
And dealer shows:
|
Do this:
|
8 and
under
|
Always hit,
regardless of the dealer's up-card
|
|
9
|
3, 4, 5, or 6
|
Double down
|
| |
2 or 7 and
above
|
Hit
|
10
|
2 through 9
|
Double down
|
| |
10 or ace
|
Hit
|
11
|
2 through 10
|
Double down
|
| |
Ace
|
Hit
|
12
|
2, 3, or 7 and
above
|
Hit
|
| |
4 through 6
|
Stand
|
13 through 16
|
7 and above
|
Hit
|
| |
2 through 6
|
Stand
|
17 through 21
|
Always stand,
regardless of the dealer's up-card
|
|
Many players seem to hit the
wall at 16 and stand regardless of the dealer's up-card. But that 16 is a loser
unless the dealer busts, and the dealer will make 17 or better nearly 80 percent
of the time with a 7 or higher showing. The risk of busting by hitting 16 is
outweighed by the likelihood you'll lose if you stand.
Basic strategy for
hard totals is straightforward enough, but when it comes to soft totals many
players become confused. They seem lost, like the player aboard a riverboat in
Joliet, Illinois, who wanted to stand on ace-5 --a soft 16-- against a dealer's
6. The dealer asked if he was sure, and another player piped in, "You can't HURT
that hand," so the player finally signaled for a hit. He drew a 5 to total 21
and was all grins.
In a facedown game, no friendly advice is available.
Once, at a downtown Las Vegas casino, the dealer busted, meaning all players who
hadn't busted won. One player turned up two aces and a three. "Winner five!" the
dealer called out. Though it worked out that time, five (or 15) never wins
without the dealer busting, and the player could have drawn at least one more
card without busting. That's too big an edge to give away.
Nothing you
could draw could hurt a soft 16, or a soft 15, or many other soft totals. Just
as with hard totals, guesswork is unnecessary. A basic strategy tells you to
what to do with soft hands. The hand of ace and 6 is the most misplayed hand
in blackjack. People who understand that the dealer always stands on 17 and that
the player stands on hard 17 and above seem to think 17 is a good hand, but the
dealer must bust for 17 to win. If the dealer does not bust, the best 17 can do
is tie. By hitting soft 17, you have a chance to improve it by drawing ace, 2,
3, or 4, or leave it the same with 10-jack-queen-king. That's eight of 13 cards
that either improve the hand or leave it no worse. And even if the draw is 5, 6,
7, 8, or 9, you have another chance to draw if the dealer shows 7 or better, and
you're still in position to win if the dealer busts while showing 2 through 6,
and all you've given up is a chance to tie a 17. You can refer to this chart for
soft-hand strategies:
If you have:
|
And dealer shows:
|
Do this:
|
Ace, ace
|
Split the pair
of aces
|
|
Ace, 2 or ace,
3
|
5 or 6
|
Double down
|
| |
All other
up-cards
|
Hit
|
Ace, 4 or ace,
5
|
4, 5, or
6
|
Double down
|
| |
All other
up-cards
|
Hit
|
Ace, 6
|
3 through
6 |
Double down
|
| |
All other
up-cards
|
Hit
|
Ace, 7
|
3 through 6
|
Double down
|
| |
2, 7, or 8
|
Stand
|
| |
9 , 10. or ace
|
Hit
|
Ace, 8 or ace,
9
|
Always stand,
regardless of the dealer's up-card
|
|
Ace, 10
|
Blackjack --
smile and take that 3-2 payoff
|
| Standing on soft 18 will lose
the player money in the long run when the dealer shows 9, 10, or ace. When the
dealer shows 3 through 6, the chances of the dealer busting are strong enough to
make doubling down the best play here.
The final category of hands
consists of those in which the first two cards match. Then the player must
decide whether or not to split the pair into two hands. You can refer to this
chart for pair splitting advice:
If you have:
|
And dealer shows:
|
Do this:
|
Ace,
ace
|
Always split.
|
|
2, 2 or 3, 3
|
4, 5, 6, or 7
|
Split
|
| |
All other
up-cards
|
Hit
|
4, 4
|
Never split. An
8 is a much stronger building block to a hand than a 4.
|
|
5,
5
|
2 through 9
|
Never split --
double down
|
| |
10 or ace
|
Never split --
hit
|
6, 6
|
3, 4, 5, or 6
|
Split
|
| |
All other
up-cards
|
Hit
|
7, 7
|
2 through 7
|
Split
|
| |
8 through ace
|
Hit
|
8, 8
|
Always split.
|
|
9, 9
|
2 through 6
|
Split
|
| |
7
|
Stand
|
| |
8 and 9
|
Split
|
| |
10 or ace
|
Stand
|
10, 10
|
Never split.
This hand is too strong.
|
| Some Strategy Variations: Double Down After Splits
Permitted
Many casinos allow the player
to double down after splitting pairs. This is a good rule for players -- in
fact, any rule that allows a player an option is a good one if the player knows
when to take advantage of the option. If you split 8s against a 6, for example,
and a 3 is dealt to your first 8, you now are playing this hand as an 11, and it
is to your advantage to double down if the house allows it.
If the casino
allows doubling after splits, the following strategy variations are
necessary:
If
you have 2, 2; 3, 3: Split against 2 through 7 instead of 4 through
7. If you have 4, 4: Split against 5
and 6 instead of just hitting against all. If
you have 6, 6: Split against 2 through 6 instead of 3 through
6.
Single-Deck Blackjack
You can find many single-deck games in Nevada, and
they pop up occasionally in other parts of the country. You will need a few
variations for single-deck blackjack. Basic strategy is much the same as in the
multiple-deck game, with a few twists, given below:
If you have 11:
Double down against all dealer up cards.
If you have 9: The difference comes when the
dealer shows a 2. In multiple-deck you hit; in single-deck, double
down.
If you have 8: Double down
against 5 and 6.
If you are holding ace,
8: As good as that 19 looks, it is to the player's advantage to double
down against a 6. Stand against all else.
If you are holding ace, 7: Stand against an
ace, unless you are playing in a casino in which the dealer hits soft 17. In
that case, hit.
If you are holding ace,
6: Double against 2 through 6.
If
you are holding ace, 3 or ace, 2: Double against 4, 5, and
6.
If you are holding 2, 2: Where
doubling after splits is not allowed, split against 3 through 7 in a single-deck
game. Otherwise, follow the same strategy as in multiple-deck
games.
If you are holding 3, 3: If
doubling after splits is permitted, split against 2 through 8.
If you are holding 4,
4: If doubling after splits is permitted, split against 4 through
6.
If you are holding 6, 6: If
doubling after splits is permitted, split against 2 through 7; if not, split
against 2 through 6.
If you are holding
7, 7: If doubling after splits is permitted, split against 2 through 8.
Also, stand against a 10 in the single-deck game.
In our final section,
you will learn the most advanced strategy for playing blackjack -- counting
cards.
Counting Cards Some players seem
to think counting cards means memorizing every card as it is played. If card
counting were that difficult, nobody would have thought it was practical, even
in the days when the basic game was single-deck with all the cards dealt out.
And that kind of system certainly would have disappeared with the advent of the
four-, six-, and eight-deck games that are common today. Others think counting
cards is a license to print money -- just memorize a counting system and go
start winning. It's not that easy.
What counters do is take advantage of
the constantly changing odds in blackjack. In roulette or craps, the odds are
mathematically fixed to be the same on every spin of the wheel or roll of the
dice. In blackjack, the odds turn in favor of the player when an unusually large
number of 10-value cards remain to be played. When the deck is rich in 10s, the
player gets more blackjacks. So does the dealer, but players collect 3-2 on
blackjacks while the dealer does not. In double-down situations, the percentage
of the desirable 10-value cards for the player to hit is greater, and when the
dealer's faceup card is a "stiff," or 2 through 6, it's even more likely than
usual that the dealer will bust.
Counters make no attempt to keep track
of every card in the deck. They simply track the concentration of 10s and aces.
When the deck is favorable to the player, they increase their bets. When the
deck is favorable to the dealer, they decrease their bets.
The counting
is done with a plus-and-minus system. Players who feel they are ready to tackle
blackjack on an expert level might want to seek out the more complex variations
suggested in the many blackjack books on the market. The most powerful systems
track aces as well as 10s.
The most common counting system simply assigns
a value of plus-one to 3s, 4s, 5s, and 6s and minus-one to 10s, jacks, queens,
and kings. All other cards are treated as neutral. Every time a 3 through 6 is
dealt, add one to the count. Every time a 10-value card is dealt, subtract one.
The total is called the running count. For example, if ten 3s through 6s have
been played and only four 10s, the running count is plus-six. This needs to be
normalized to the number of decks in the game, which is done by dividing by the
approximate number of decks remaining in the shoe or in the dealer's hand. In a
six-deck game, if the running count is plus-six and about three decks are left
in the shoe, divide plus-six by three to get a "true count" of
plus-two.
The final step is to adjust the bet to the count. In this
simple version, if your beginning bet is one unit of $5, when the true count
reaches plus-2, bet $10; at plus-4, bet $15, and at plus-6, bet $20.
A
few words of warning: Because you are increasing your bet whenever the deck is
favorable, playing with a counting system requires a much larger bankroll than
betting the same amount every hand -- flat betting. You may be perfectly
comfortable buying 10 bets' worth of chips -- $10 at a $1 table or $50 at a $5
table -- when flat-betting, but figure on at least 30 bets' worth when counting
cards.
Card counters, just like any basic strategy player, lose more
hands than they win no matter how good they are. They hope to more than make it
up by winning larger bets in favorable situations. But sometimes the favorable
situations just don't come -- it's possible to count down six-deck shoe after
six-deck shoe without ever coming across a really favorable situation. And even
on positive counts, sometimes the cards just turn the wrong way. There are no
guarantees, not even for those who know the count and know what to
do.
Finally, if the casino thinks you're counting cards, it can take
measures. Nowhere in the country is card-counting illegal, but in Nevada the
courts have held that the casinos are private clubs entitled to enforce their
own rules, and the casinos can bar counters from playing. In other states,
players can't be barred, but the casinos can increase the percentage of cards
cut out of play to render the count less accurate. They can also take measures
to make the player uncomfortable -- such as having a supervisor behind the table
stare directly at the player while another supervisor stands at the player's
shoulder from behind. If you're going to attempt to count cards, learn at home
first. Deal cards to yourself or practice on a computer. Keep practicing until
you're accurate every time, without moving your lips, with no brow-furrowing
concentration, and without giving any other telltale signs of counting. Limit
the size of your bets to a one-to-eight-unit range. A larger range will spark
the casino's suspicions. And limit the length of your sessions. Don't play more
than one hour in one place when counting cards.
If you wanted to increase
you bet but do not count cards, you follow these guidelines:
A $5 bettor
could begin a simple progression by increasing the bet to $10 after two wins in
a row. After winning two consecutive hands at the $10 level, the player would
increase to $15, and so on. After any loss, the player brings the bet back down
to its original level.
The progression kicks in after two consecutive
wins, so that the player never loses money on any sequence that begins with a
win. If, after two $5 wins, the player loses the $10 bet, he is even. A third
consecutive win guarantees a profit for the sequence.
Winnings can mount
fast. If a player betting a flat $5 a hand wins six hands in a row, winnings
total $30. The progression bettor has won two hands at $5, two at $10, and two
at $15 for $60.
However, the system has two major problems. The
progression usually ends with a loss on the largest bet in the sequence. And in
any sequence that starts with two wins but shows a loss on the third hand, the
progression bettor is worse off than the flat bettor. The progression bettor
would be even after two $5 wins and a $10 loss; the flat bettor would show a $5
profit after two wins and a $5 loss. And a two-wins-and-a-loss sequence happens
a lot more often than six consecutive wins.
Blackjack is a great game for
casino novices. It is more engaging that a slot machine, but is much less
complex than poker. Still, blackjack can be a favorite of card players at all
experience levels. Now that you have the tools you need to become a better
player, it's time to hit the tables.
?/sup>Publications International,
Ltd.
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