3 Card Baccarat

Last update: Sep. 27, 2007

Introduction

3 Card Baccarat is a game fairly easily found in the casinos of Macau. In my rough estimation, I would say it has about 2% of the tables in the main casinos, open to the public.

Rules

The game is played with a single 52-card deck. As in conventional baccarat, face cards are worth 0 points, and all others according to pip value. Three cards each are dealt to both a player and dealer hand every time.

The highest hand is three face cards. After that the hands are scored as in baccarat, the hand with more points wins. If both hands have the same number of points, then the hand with more face cards will win. If both hands have the same number of points and face cards, then the hands will tie.

There are several bets to choose from, as follows.

Player Bet

The following table shows the possible outcomes and return for the player bet. The lower right cell shows a house edge of 2.41%. The 0.95 win is adjudicated as even money, less a 5% commission.

Player Bet
Event	Pays	Combinations	Probability	Return
Player win	0.95	195907080	0.481143	0.457086
Dealer win	-1	195907080	0.481143	-0.481143
Tie	0	15356240	0.037715	0
Total		407170400	1	-0.024057

Dealer Total

There are ten bets available on the dealer's total points. The number of combinations is out of a total possible of 22,100. The return table below shows the best of these bets to be on the zero, with a house edge of 2.91%.

Dealer Total Bets
Points	Pays	Combinations	Probability	Return
0	8	2384	0.107873	-0.029140
1	8	2212	0.100090	-0.099186
2	8	2164	0.097919	-0.118733
3	8	2212	0.100090	-0.099186
4	8	2164	0.097919	-0.118733
5	8	2212	0.100090	-0.099186
6	8	2164	0.097919	-0.118733
7	8	2212	0.100090	-0.099186
8	8	2164	0.097919	-0.118733
9	8	2212	0.100090	-0.099186

Tie

The tie bet pays 20 to 1. Remember, to tie not only must the points equal, but also the number of face cards. Here is the return table. The lower right cell shows a house edge of 20.80%.

Tie Bet
Points	Pays	Combinations	Probability	Return
Tie	20	15356240	0.037715	0.754291
Not Tie	-1	391814160	0.962285	-0.962285
Total		407170400	1	-0.207995

Three Faces

Setting a new record for the worst bet in any casino game, as far as I know, is the Three Faces bet in 3 Card Baccarat. It wins if the dealer hand is three face cards and pays 16 to 1. It is easy to see the probability of three face cards in a single-deck game is (12/52)*(11/51)*(10/50)=0.009954751. The return to the player is easily calculated as 0.009954751 × 16 - (1-0.009954751) = -0.830769231. That is an 83% house advantage!

Three Faces Bet
Points	Pays	Combinations	Probability	Return
Three Faces	16	220	0.009955	0.159276
Two or Less Faces	-1	21880	0.990045	-0.990045
Total		22100	1	-0.830769

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