Casino Games - Mini Baccarat
Author: Yui-Bin Chen, Ph.D.
The Copyright of this article is held by the author.
Introduction
Baccarat is usually dealt from a 6-deck shoe. All players place their
bets before the dealer deals cards. The dealer will flip 2 cards on
the Banker side (B1, B2) and 2 cards on the Player side (P1, P2). All
numbers are computed in a "mod 10" base. That is, a 7 and an 8 sum to
5 (mod 10). Based on the numbers on 2 sides, the game will be played
according to 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 higher
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/Loss
The following chart shows the probabilities of events:
Number of Decks |
Banker Wins |
Player Wins |
Tie |
Infinite |
45.8428% |
44.6147% |
9.5426% |
8 |
45.8597% |
44.6247% |
9.5156% |
6 |
45.8653% |
44.6276% |
9.5069% |
4 |
45.8761% |
44.6340% |
9.4898% |
2 |
45.9073% |
44.6508% |
9.4419% |
1 |
45.9624% |
44.6760% |
9.3615% |
The following chart shows the house edges on different bets:
Number of Decks |
Banker Wins |
Player Wins |
Tie |
5% Comm. |
4% Comm. |
9:1 |
8:1 |
Infinite |
1.0640% |
0.6056% |
1.2281% |
4.5744% |
14.1170% |
8 |
1.0579% |
0.5993% |
1.2351% |
4.8440% |
14.3596% |
6 |
1.0558% |
0.5972% |
1.2374% |
4.9313% |
14.4382% |
4 |
1.0517% |
0.5929% |
1.2421% |
5.1018% |
14.5916% |
2 |
1.0389% |
0.5798% |
1.2565% |
5.5809% |
15.0228% |
1 |
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 6s and 7s
than the average of other kinds. It is similar as adding 4 6s and 4 7s
to a fresh single deck.
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