Last Updated: November 19, 2019

# Prosperity 3 Pictures

## Introduction

I first heard of Prosperity 3 Pictures in November 2019 when it was on field trial at the Venetian in Las Vegas. Upon some research, I learned a game by the same name can be found at the Marina Bay Sands in Singapore, but dealt differently. 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.

## Las Vegas Rules

1. The game is played with a single 52-card deck.
2. Play starts with the player making what I will call the Main bet. At this time, the player may make any of four optional side bets, which I will describe later.
3. The player and dealer 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. If the number of face cards and number of points are equal, then the hands tie and the result is a push.
10. If the player wins, then the Ante pays even money, except with a winning total of six points, which pays 1 to 2.
11. If the dealer has the higher hand, then the Main bet is a push.
12. The Tie bet wins if the Ante bet is a tie. Wins pay 10 to 1, except a "Perfect Tie" pays 400 to 1. A Perfect Tie occurs if the ranks of the player and dealer hands match exactly in ranks. For example, both have K-6-3.
13. The Player Prosperity Pictures bet pays based on the player's hand only, as follows:
• Three picture cards of the same rank — Pays 250 to 1. For example, QQQ.
• Three picture cards of any combination of mixed ranks — Pays 25 to 1. For example, QQJ.
• Two picture cards of the same rank — Pays 15 to 1. For example, QQ5.
14. The Dealer Prosperity Pictures bet is the same thing as the Player Prosperity Pictures bet, except based on the dealer's hand.
15. The Picture Perfect bet compares the player and dealer hands. The bet wins according to the number of matching picture cards between the hands, as follows:
• 3 Matches — Pays 500 to 1. For example, both hands have QQJ.
• 2 Matches — Pays 100 to 1. For example, player has KQ5 and dealer has KQ4.
• 1 Match — Pays 5 to 1. For example, player has KQ5 and dealer has Q8A.

## Singapore Rules

The Singapore rules are the same as the Las Vegas rules, except the number of points is first used to determine a winner. If that results in a tie, then the number of face cards is used to break the tie. As in the Las Vegas version, if the number of points and face cards are equal between the two hands, then the result is a tie.

The base game under the Singapore is similar as Three Card Baccarat.

## Base Game Analysis

The following table shows the probability and contribution to the return for all possible events under the Las Vegas rules. The lower right cell shows a house edge of 2.60%.

### Base Game Return Table — Las Vegas Rules

Event Pays Combinations Probability Return
Player full win 1 174,717,880 0.429103 0.429103
Player half win 0.5 21,180,360 0.052018 0.026009
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 -0.026009

The following table shows the probability and contribution to the return for all possible events under the Singapore rules. The lower right cell shows a house edge of 3.11%.

### Base Game Return Table — Singapore Rules

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

## Tie Analysis

The following table shows my analysis of the Tie bet. The math is the same under the Las Vegas and Singapore rules. The lower right cell shows a house edge of 10.54%.

### Tie Analysis

Event Pays Combinations Probability Return
Perfect tie 400 505,440 0.001241 0.496539
Tie 10 14,868,480 0.036517 0.365166
All other -1 391,796,480 0.962242 -0.962242
Total   407,170,400 1.000000 -0.100537

## Picture Perfect Analysis

The following table shows my analysis of the Picture Perfect bet. The math is the same under the Las Vegas and Singapore rules. The lower right cell shows a house edge of 11.83%.

### Picture Perfect Analysis

Matches Pays Combinations Probability Return
3 500 2,160 0.000005 0.002652
2 100 929,232 0.002282 0.228217
1 5 44,008,560 0.108084 0.540419
0 -1 362,230,448 0.889629 -0.889629
Total   407,170,400 1.000000 -0.118340

## Player/Dealer Prosperity Bonus Analysis

The following table shows my analysis of both the Player and Dealer Prosperity Bonus. The math is the same under the Las Vegas and Singapore rules. The lower right cell shows a house edge of 9.77%.

### Picture Perfect Analysis

Matches Pays Combinations Probability Return
Three picture cards of the same rank 250 12 0.000543 0.135747
Three picture cards of any combination of mixed ranks 25 208 0.009412 0.235294
Two picture cards of the same rank 15 720 0.032579 0.488688
All other -1 21,160 0.957466 -0.957466
Total   22,100 1.000000 -0.097738