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Baccarat; a Casino Game

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

Please send information about the mathematics and probabilities of 
baccarat.  This is for an advanced math class project.

From Paula and Tara

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     - here's some 
information on baccarat from the Web:   


      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.


   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

   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

   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.


All Copyright reserved by Yui-Bin Chen, 1995 

Baccarat by Yui-Bin Chen


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
             (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  
    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).


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!   

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

Associated Topics:
High School Probability

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