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### Baccarat; a Casino Game

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Date: 5/22/96 at 9:12:3
From: Anonymous
Subject: Baccarat; a Casino Game

baccarat.  This is for an advanced math class project.

From Paula and Tara
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```
Date: 5/22/96 at 16:34:48
From: Doctor Sarah
Subject: Re: Baccarat; a Casino Game

Hi Paula and Tara:

If you have Web access there's more on baccarat to be found using the
AltaVista searcher at http://altavista.digital.com/     - here's some
information on baccarat from the Web:

Baccarat

To win: Bet on whether the player's or house's hand will be
closer to nine.

Casino edge: If you bet on the house, or "banker," the
casino will win about 1.2 percent of all bets placed. But that
percentage can go as high as 10 percent if you bet on your
hand or bet on a tie. That could lead to losses of \$120 over
four hours for a \$5 bet each time, since you'll play 50 to 70
games per hour.

Playing Baccarat:
Typically home to high rollers, baccarat is one of the easiest
casino games to play because there is little skill involved. All
players bet with the banker or the player. The object is to
come closer to nine.

Baccarat has its own card values: All numbers two through nine
count as face value. Aces count as one; all pictures cards and
tens count as 0. Whenever the card values total 10 to 19, 10 is
substracted from the total. If the hand totals 20 to 29, 20 is
subtracted from the total.

Even with the commission the banker gets on winning hands, the
banker's hand is still the best bet mathematically.

Stay away from mini-baccarat. The house deals and the
commissions are too high to make it a good bet.
_______________________________________________________

http://www.gamblingtimes.com/basbacca.html

BACCARAT

The word baccarat is derived from the Italian baccara,
which means zero. The term refers to the face cards and
tens, all of which have zero value in the game of
baccarat. In Europe, baccarat and a similar version
called chemin de fer are among the most popular casino
games.

Since baccarat's introduction in Nevada casinos, the
game has assumed an aura of glamour. In most casinos,
baccarat is played in a roped-off area. The intention was
to attract the high roller, or the more sophisticated
monied player. With the tuxedo-clad dealers, there is an
air of elegance to the game.

However, for all the enchantment, baccarat is primarily
a simple game. There are no decisions or options, no
degree of skill is required for either player or dealer.
Players may sit in any open seat at the table; seating
position does not affect the play in any manner. Each
seat corresponds to a number on the layout, one through
15. Three dealers service each table. The dealer standing
between positions one and 15 is known as the "caller."
He runs the game as cards are dealt from the shoe.

Each player gets a turn to handle the shoe. The player
must bet the bank when he has the shoe, but any player
may decline the shoe and it passes right along from
player to player. Again, there is no advantage or
disadvantage in dealing the cards, it is merely a
formality and part of the the ambience that players
enjoy.

The caller receives the cards from the player with the
shoe, places them in the appropriate boxes and then calls
for another card or declares the winner, according to
the rigid rules of the game.

Players bet by placing their chips in the numbered box
opposite their seat. Bets may be made on the player or
bank, and both are paid off at even money. In most
games, bets range from a \$20 minimum to \$2,000 maximum. After the
winner is announced, the two other dealers at the table pay off the
winning bets and collect from the losers. If the bank was the
winner, players who won must pay a 5% commission on their winnings.
Thus, if a player had a \$100 bet on the bank and it won, \$5
would be owed to the house. Rather than collecting this
after each game, a record of what is owed by each player is kept in
a numbered box just opposite where the two payoff dealers sit.
Player pay the accumulated amount after the finish of a shoe. Each
time the shoe is depleted of cards, all eight decks are
thoroughly shuffled and replaced in the shoe.

Hand Values

All cards, ace through 9, are valued according to their
count. Tens and face cards count as zero. Thus, if the first
two cards dealt are a king and a 4, the count is four. An 8 and 6,
although totaling 14, would count as four after subtracting the 10.

When any two cards total over a 10 count, 10 must be
subtracted. The remaining total is the card count.

Rules of Play

These rules apply in all American casinos. Printed copies of these
are available wherever baccarat is played.

Dealers act according to these rules without consulting
players at the table. The rules are automatic.

The highest total any baccarat hand can have is nine. A two-card
total of nine is called a "natural" and cannot lose. An eight is
the second-best hand and is also called a natural. If both player
and bank are dealt identical hands, it is a standoff (a tie) and
neither bank nor player wins. No further cards can be drawn to a
two-card draw of a six or a seven

When holding other two-card totals, player and bank draw another
card at the direction of the caller. In studying the accompanying
chart, one can easily determine the rules of the game. It is a
matter of letting the dealer do the calling, and declaring the
outcome. Players are concerned only with how much they wager
on each hand and whether they bet on the player's side
or the banker's.

The house edge in baccarat is the lowest of any casino game.
With only a 5% commission on winning bank bets and nothing
taken from winning player bets, the player's disadvantage is
only 1.37%. In some casinos, ties are permitted to be bet
on. The payoff is 8 to 1. It is a bad bet for the player as
the house edge is 14.1%.

Mini Baccarat

A number of casinos have installed smaller baccarat
tables, usually among the blackjack tables. It is the same
game but the rituals of passing the shoe, etc., are
missing and the game is staffed by only one dealer. The
layout, however, conforms to the regular baccarat table
and each seat position (one through six) corresponds to
a number and betting box. Limits are usually from \$2
to \$5 minimum and upto \$500 maximum. Mini-baccarat is
played fast but the exact same rules apply as in the
larger game.

____________________________________________________________

http://langevin.usc.edu/~yuibinch/Games/Baccarat.html

All Copyright reserved by Yui-Bin Chen, 1995

Baccarat by Yui-Bin Chen

Introduction

Baccarat is usually dealt from a 6-deck shoe. All players place their
bets before the dealer deals the cards. The dealer will flip 2 cards
on the Banker's side (B1, B2) and 2 cards on the Player's side (P1,
P2). All numbers are computed in a "mod 10" base. That is, a 7 and an
8 sum to 5 (mod 10), etc. Based on the numbers on the 2 sides, the
game will be played according to the following rules:

(1) If (P1+P2 = 8 or 9) or (B1+B2 = 8 or 9),
then it is Natural and neither hand draws.

(2) If (P1+P2 = 6 or 7),
then (a) Player hand stands
(b) Banker hand draws one card on totals of 0 to 5 and stands
on 6 to 9.

(3) If (P1+P2 <= 5),
then (a) Player hand draws one card (P3)
(b) Banker hand draws one card when one of the following is
true:
(B1+B2 <= 2)
(B1+B2 = 3) & (P3 <> 8)
(B1+B2 = 4) & (2 <= P3 <= 7)
(B1+B2 = 5) & (4 <= P3 <= 7)
(B1+B2 = 6) & (6 <= P3 <= 7)

(4) The hand closest to 9 wins (or the hand with the highest score
wins).

If Banker's and Player's hands have the same score, Tie bet wins
and get paid 9:1 (or 8:1), and both Banker's and Player's bets are
tie (and players keep their bets).

Bets

There are 3 kinds of bets in this game: Banker, Player, and Tie. The
payouts of Banker and Player are 1:1, and the payout of Tie is 9:1 (or
8:1). Winning Banker bets are charged a 5 percent commission (Binion's
Horseshoe in Las Vegas charges 4% commission).

Expected Gain/Lose

The following chart shows the probabilities of events:

Banker         Player         Tie
Wins           Wins
----------------------------------------------------
infinite     45.8428%       44.6147%      9.5426%
8-deck      45.8597%       44.6247%      9.5156%
6-deck      45.8653%       44.6276%      9.5069%
4-deck      45.8761%       44.6340%      9.4898%
2-deck      45.9073%       44.6508%      9.4419%
1-deck      45.9624%       44.6760%      9.3615%
----------------------------------------------------

The following chart shows the house edges on different bets:

Banker Wins          Player             Tie
(5% comm) (4% comm)       Wins        (9:1)     (8:1)
-------------------------------------------------------------------
infinite   1.0640%   0.6056%      1.2281%      4.5744%   14.1170%
8-deck    1.0579%   0.5993%      1.2351%      4.8440%   14.3596%
6-deck    1.0558%   0.5972%      1.2374%      4.9313%   14.4382%
4-deck    1.0517%   0.5929%      1.2421%      5.1018%   14.5916%
2-deck    1.0389%   0.5798%      1.2565%      5.5809%   15.0228%
1-deck    1.0117%   0.5521%      1.2864%      6.3846%   15.7461%
-------------------------------------------------------------------

Counting Method

When the rest of decks are 6-or-7 full (i.e., have more 6s and 7s than
as usual), it is better for the Tie bet. But in order to convert the
4.8% house edge, the rest of decks must have at least twice the 6s and
7s than the average of other kinds. It is similar to adding 4 6s and 4
7s to a fresh single deck.
____________________________________________________________

Does this help?  Good luck with your project.

-Doctor Sarah,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Date: 5/23/96 at 9:36:42
From: Anonymous
Subject: baccarat

Hi Dr. Math,

Since we can't take you out to dinner, we at least thought we should
thank you for all the useful information about baccarat.  I know it
will help us get an A on this project.  Thanks again!

Paula and Tara
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Associated Topics:
High School Probability

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