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Three Card Baccarat
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Introduction
You can find 3 Card Baccarat in some smaller casinos in Macau. This variant is based on baccarat, where both the Player and Banker are dealt three cards, and the presence of face cards plays a crucial role in determining the winner.
The game goes by the name of Prosperity 3 Pictures at the Marina Bay Sands in Singapore.
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Rules
When discussing baccarat-related games, I make it a point to capitalize the terms Player and Banker bets while using lowercase for the participants engaged in the game.
- The gameplay utilizes a single deck containing 52 cards.
- The game starts when the player places a bet on either the Player or the Banker. At this moment, the player has the option to place one of four available side bets, which I will detail later.
- Both the Player and Banker are dealt three cards each.
- The party with more face cards will win the main bet.
- If both the player and dealer have the same number of face cards, the winner will be determined based on who has accumulated more points.
- Points are counted similarly to traditional baccarat, with the following values assigned to each card:
- 10's and faces = 0
- Ace = 1
- 2-9 = Pip value
- The suits are irrelevant in any betting scenario throughout the game.
- After calculating the total points for each side, only the unit's digit is considered; hence the highest possible score is capped at 9. For instance, the combination of Q, 9, and 7 would amount to 6 points.
- The side with the greater point total will win. In case of a tie in points, the side with more face cards wins. If both points and face cards are tied, the result is a push.
- Winning bets will receive even money; however, a hand totaling six points will payout at 1 to 2.
- In instances of a tie, both Player and Banker bets will result in a push.
- There are side bets available, which I will explain further down.
Player and Banker Analysis
The table below illustrates the possible outcomes and payouts for Player and Banker bets. The bottom right cell indicates a house edge of 2.41%. A win of 0.95 is treated as even money, minus 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
Online casinos utilizing Gamesys software impose a 3% fee exclusively on the Player bet, lowering the house edge to 1.44%.
Dealer Total
There are ten different bets available depending on the dealer's total points, with combinations calculated from a total of 22,100 possibilities. The return table below highlights that betting on zero offers the most favorable odds 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 provides a payout of 20 to 1. Remember that for a tie to be valid, not only must the points be equal, but the number of face cards must match as well. The accompanying return table displays 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
In online casinos using Gamesys software, the tie bet pays out at 25 to 1, thus reducing the house edge to a much more acceptable 1.94%.
Three Faces
The Three Faces bet in 3 Card Baccarat sets a new standard for being the least favorable wager in any casino game I’m familiar with. It pays 16 to 1 on a dealer hand comprising three face cards. The probability of achieving three face cards from a single-deck setup is (12/52)*(11/51)*(10/50)=0.009954751. Therefore, the expected return for the player can be computed as 0.009954751 × 16 - (1-0.009954751) = -0.830769231, indicating an astonishing 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
However, online casinos utilizing Gamesys software offer a payout of 96 to 1 on the Three Faces bet, substantially lowering the house edge to a more reasonable 3.44%.
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External Links
3 Card Baccarat rules From the gaming authority in Macau (in Portuguese).