Baccarat; a Casino GameDate: 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 http://altavista.digital.com/ - here's some information on baccarat from the Web: http://www.nevadanet.com/entertainment/gambling/baccarat.html 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/ 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 |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/