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Last Updated: February 28, 2015

Three Card Baccarat

Introduction

3 Card Baccarat is a game found in some of the casinos of Macau. I know it is at the Venetian and Lisboa, and probably others a well.

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

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

3% Commission

Internet casinos using Gamesys software charge 3% only on the Player bet. This lowers the house edge to 1.44%.

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

25 to 1 Odds

Internet casinos using Gamesys software pay 25 to 1 on the Tie bet. This lowers the house edge to 1.94%.

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

96 to 1 Odds

Internet casinos using Gamesys software pay 96 to 1 on the Three Faces bet. This lowers the house edge to a much more reasonable 3.44%.

Written by: Michael Shackleford

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