Baccarat Odds

Baccarat is one of the oldest and most popular games in casinos all over the world. It is especially popular among high-rollers and Asian gamblers. In Macau, baccarat is extremely dominant. Although the game seems serious and elegant, it is really as simple as betting on the flip of a coin.

Format

There are three types of baccarat tables:
Big Table Baccarat is played in a snooty roped off area to separate itself from the other games. The players are usually very well dressed and the table minimums are often high. The regular baccarat table is about the size of a craps table with 3 casino dealers and up to 12 or 14 players. Each player, including the player dealing, may still bet on either the player or the banker but it is customary for the dealer to bet on the banker.
The deal will rotate around the table, much like the dice rotate around the craps table. If a player does not want to deal they may pass the shoe to the next player. The same person will keep dealing as long as the banker keeps winning. The person dealing will put two cards, face down, tucked under the shoe, and give the player with the greatest bet on the player the other two cards, face down. This player then looks at the cards and then gives them back to the player who is dealing. Then the player who is dealing will turn over the cards and one of the casino dealers will announce the totals. Depending on the totals, the dealer may then instruct the person dealing the cards to deal a third card. Finally the dealers will pay winning wagers and collect losing ones out of the dealer's tray. The player who actually deals is not assuming any financial responsibility of the other players bets, unlike pai gow, and is just turning over cards.
Mini baccarat has the same rules are big table baccarat. However, unlike the game at the big table, the dealer turns over all the cards, making for a much faster game. The odds are exactly the same as those of the big table, assuming the same number of decks. Mini baccarat is sometimes dealt from a six-deck shoe, changing the odds slightly. It can usually be found in the main casino areas.
Midi baccarat is the same as mini baccarat, except the size of the table is larger, and it is usually found in the high-limit rooms, as opposed to the main casino floor.

Rules

• Usually eight decks of cards are used.
• Cards are given point values as follows: Ace = 1, 2-9 = pip value, 10 and face cards = 0.
• At the start of a new shoe, the dealer will turn over one card. This will determine how many cards the dealer will burn, according to the baccarat value, except a 10 or face card will result in 10 cards burned.
• The cut card will be placed 16 cards from the bottom of the shoe. When the cut card appears, the dealer will finish that hand, play one more hand, and then start a new shoe. If the cut card comes out instead of the first card, the dealer will finish that hand, and then start a new shoe.
• Play begins by all players betting either on the "player", "banker", or a tie. At some tables you may also bet on a player pair and banker pair.
• After all bets are down, the dealer gives two cards each to the player and the banker. The score of the hand is the right digit of the total of the cards. For example, if the two cards were an 8 and 7, then the total would be 15 and the score would be a 5. The scores will always range from 0 to 9 and it is impossible to bust.
• A third card may or may not be dealt to either the player or the dealer depending on the following rules.:
  
  • If either the player or the banker has a total of an 8 or a 9 they both stand. This rule overrides all other rules.
  • If the player's total is 5 or less, then the player hits, otherwise the player stands.
  • If the player stands, then the banker hits on a total of 5 or less. If the player does hit then use the chart below to determine if the banker hits (H) or stands (S):
    

    Baccarat Drawing Rules
    Banker's Score	Player's Third Card
    	0	1	2	3	4	5	6	7	8	9
    7	S	S	S	S	S	S	S	S	S	S
    6	S	S	S	S	S	S	H	H	S	S
    5	S	S	S	S	H	H	H	H	S	S
    4	S	S	H	H	H	H	H	H	S	S
    3	H	H	H	H	H	H	H	H	S	H
    2	H	H	H	H	H	H	H	H	H	H
    1	H	H	H	H	H	H	H	H	H	H
    0	H	H	H	H	H	H	H	H	H	H

• The score of the player and dealer are compared; the winner is the one that is greater. Winning bets on the banker pay 19 to 20 (even money less a 5% commission), winning bets on the player pay 1 to 1, winning bets on a tie usually pay 8 to 1. In the event of a tie, banker and player bets will push.
• On winning banker bets, the player will be paid even money. Meanwhile, the dealer will keep track of the 5% commission owed with small laminated markers. At the end of each shoe, or when a player wants to leave, the dealer will collect all commissions owed.

Odds

8 Decks

The following return tables show the possible outcomes of the banker, player, and tie bets for an 8-deck game. As the lower left cells in each table show, the house edge is 1.06% on the banker bet, 1.24% on the player bet, and 14.36% on the tie.

Banker Bet — 8 Decks
Event	Pays	Combinations	Probability	Return
Banker wins	0.95	2,292,252,566,437,888	0.458597	0.435668
Player wins	-1	2,230,518,282,592,256	0.446247	-0.446247
Tie	0	475,627,426,473,216	0.095156	0
Total		4,998,398,275,503,360	1	-0.010579

Player Bet — 8 Decks
Event	Pays	Combinations	Probability	Return
Banker wins	-1	2,292,252,566,437,888	0.458597	-0.458597
Player wins	1	2,230,518,282,592,256	0.446247	0.446247
Tie	0	475,627,426,473,216	0.095156	0
Total		4,998,398,275,503,360	1	-0.012351

Tie Bet — 8 Decks
Event	Pays	Combinations	Probability	Return
Banker wins	-1	2,292,252,566,437,888	0.458597	-0.458597
Player wins	-1	2,230,518,282,592,256	0.446247	-0.446247
Tie	8	475,627,426,473,216	0.095156	0.761248
Total		4,998,398,275,503,360	1	-0.143596

Pair Bets — 8 Decks
Event	Pays	Combinations	Probability	Return
Pair	11	6448	0.074699	0.821687
No pair	-1	79872	0.925301	-0.925301
Total		86320	1	-0.103614

6 Decks

The following return tables show the possible outcomes of the banker, player, and tie bets for a 6-deck game. As the lower left cells in each table show, the house edge is 1.06% on the banker bet, 1.24% on the player bet, and 14.44% on the tie.

Banker Bet — 6 Decks
Event	Pays	Combinations	Probability	Return
Banker wins	0.95	403095751234560	0.458653	0.43572
Player wins	-1	392220492728832	0.446279	-0.446279
Tie	0	83552962932288	0.095069	0
Total		878869206895680	1	-0.010558

Player Bet — 6 Decks
Event	Pays	Combinations	Probability	Return
Banker wins	-1	403095751234560	0.458653	-0.458653
Player wins	1	392220492728832	0.446279	0.446279
Tie	0	83552962932288	0.095069	0
Total		878869206895680	1	-0.012374

Tie Bet — 6 Decks
Event	Pays	Combinations	Probability	Return
Banker wins	-1	403095751234560	0.458653	-0.458653
Player wins	-1	392220492728832	0.446279	-0.446279
Tie	8	83552962932288	0.095069	0.76055
Total		878869206895680	1	-0.144382

Pair Bets — 6 Decks
Event	Pays	Combinations	Probability	Return
Pair	11	3588	0.073955	0.813505
No pair	-1	44928	0.926045	-0.926045
Total		48516	1	-0.11254

1 Deck

The following return tables show the possible outcomes of the banker, player, and tie bets for a single deck game. As the lower left cells in each table show, the house edge is 1.01% on the banker bet, 1.29% on the player bet, and 15.75% on the tie.

Banker Bet — 1 Deck
Event	Pays	Combinations	Probability	Return
Banker wins	0.95	6737232640	0.459624	0.436643
Player wins	-1	6548674432	0.44676	-0.44676
Tie	0	1372227328	0.093615	0
Total		14658134400	1	-0.010117

Player Bet — 1 Deck
Event	Pays	Combinations	Probability	Return
Banker wins	-1	6737232640	0.459624	-0.459624
Player wins	1	6548674432	0.44676	0.44676
Tie	0	1372227328	0.093615	0
Total		14658134400	1	-0.012864

Tie Bet — 1 Deck
Event	Pays	Combinations	Probability	Return
Banker wins	-1	6737232640	0.459624	-0.459624
Player wins	-1	6548674432	0.44676	-0.44676
Tie	8	1372227328	0.093615	0.748923
Total		14658134400	1	-0.157461

Pair Bets — 1 Deck
Event	Pays	Combinations	Probability	Return
Pair	11	78	0.058824	0.647059
No pair	-1	1248	0.941176	-0.941176
Total		1326	1	-0.294118

Reduced Commission Baccarat

A less than 5% commission on winning banker bets has been known to happen. For years the Horseshoe in Las Vegas offered a 4% commission on their big table game. For a short time in 1989 the Sahara offered 0% commission. The Betfair Internet casino offers a 2.75% commision in their "Zero Lounge." The following table shows the expected value on the banker bet according to the number of decks and commission.

Reduced Commission Baccarat
Commission	1 Deck	6 Decks	8 Decks
5.00%	-1.012%	-1.056%	-1.058%
4.00%	-0.552%	-0.597%	-0.599%
3.00%	-0.092%	-0.139%	-0.141%
2.75%	0.022%	-0.024%	-0.026%
0.00%	1.286%	1.237%	1.235%

9 to 1 Tie Bet

The tie has been known to pay 9 to 1 at some casinos. For examle Binion's Horseshoe in Las Vegas used to, and the Bodog online casino pays 9 to 1. Here is the expected value on the tie bet if it pays 9 to 1.

• 8 decks: -4.844%
• 6 decks: -4.931%
• 1 deck: -6.385%

Egalite Bets

I have heard that some casinos in London offer "egalite" bets on specific ties, by the total of the tie. For example, a 5-5 tie pays 110 to 1. The following table shows the probability and return for each bet, based on eight decks.

Egalite Bets — Eight Decks
Tie	Pays	Permutations	Probability	Return
9	80	55,146,054,060,032	0.011033	-0.106348
8	80	54,879,416,675,072	0.010979	-0.110669
7	45	101,717,538,899,968	0.020350	-0.063899
6	45	96,170,001,308,416	0.019240	-0.114952
5	110	39,684,046,743,808	0.007939	-0.118732
4	120	36,294,133,463,040	0.007261	-0.121401
3	200	22,250,510,129,408	0.004452	-0.105243
2	225	20,006,606,104,576	0.004003	-0.095412
1	215	20,499,217,668,352	0.004101	-0.114150
0	150	28,979,901,420,544	0.005798	-0.124527

Riding Trends

Every baccarat table will have plenty of score cards and pencils for the players to keep track of the outcome of every hand. Most players will do so religiously and carefully analyze their card for trends as the winning hand switches back and forth from the banker to the player. This is a big waste of time! The smart player will bet on the banker every time and leave the score cards alone.

Calculator