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.