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# Three Card Baccarat

## Introduction

3 Card Baccarat can be found at some of the smaller casinos in Macau. The game is based on baccarat, but both sides get three cards, and the number of picture cards is also relevant to determine who wins.

The game goes by the name of Prosperity 3 Pictures at the Marina Bay Sands in Singapore.

## Rules

As usual, when writing about baccarat-based games, I capitalize the names of the Player and Banker bets and use lower case for the people playing the game.

1. The game is played with a single 52-card deck.
2. Play starts with the player making a bet on the Player or Banker. At this time, the player may make any of four optional side bets, which I will describe later.
3. The Player and Banker hands shall each receive three cards.
4. The side with more face cards wins the Main bet.
5. In the event that the player and dealer have an equal number of face cards, then the win shall go to the side with more points.
6. The number of points is scored as in baccarat, where each card has the following values:
• 10's and faces = 0
• Ace = 1
• 2-9 = Pip value
7. Suits don't matter, for any bet in the game.
8. After taking the total points of each side, the tens position is dropped, thus the maximum number of points is 9. For example Q,9,7 would be worth 6 points.
9. The side with more points shall win. In the event the number of points is equal, then the side with more face cards wins. If the number of points and face cards are equal, then the hands tie and the result is a push.
10. Winning bets pay even money, except with a winning total of six points, which pays 1 to 2.
11. Ties result in a push of the Player and Banker bets.
12. There are also side bets, which are explained below.

## Player and Banker Analysis

The following table shows the possible outcomes and return for the Player and Banker bets. 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 full win 1 170,612,616 0.419020 0.419020
Player half win 0.5 25,285,624 0.062101 0.031050
Tie 0 15,373,920 0.037758 0.000000
Banker win -1 195,898,240 0.481121 -0.481121
Total   407,170,400 1.000000 -0.031050

### 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%.

## External Links

3 Card Baccarat rules from the Macau gaming authority (in Portuguese).

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