Last Updated: June 15, 2019

# San Gong

## Introduction

San Gong is a casino table game by Triple PG software, a provider of games for Internet casinos. It is like baccarat, except both sides must take three cards. Lots of side bets too.

## Rules

1. The game is played with a single 52-card deck.
2. Card are ranked as in baccarat (aces = 1 points, 2-9 = pip value, 10s and faces = 0)
3. After betting is closed, two hands, titled the Dragon and Phoenix, will get three cards each.
4. Following is the ranking of each hand:
• Three of a kind, the higher the rank the higher the hand.
• Three face cards
• Point value of 0 to 9 — The value of each hand is determined in the same way as baccarat, by taking the sum of the points in that hand, dividing by 10, and taking the remainder as the score of each hand. For example, a hand of 5, 7, 9 would be world 1 point (the terminal digit of 21).
5. The hand with more points shall win.
6. In the event of a tie for the most points, the hand with the single card with the most points shall win.
7. In the event that rule 6 doesn't break the tie, then the hand with the higher ranking suit of the highest ranking card shall win. The order of suits is spades > hearts > clubs > diamonds.
8. Bets on the winning hand, Dragon or Phoenix, pay 0.94 to 1.
9. There are three side bets on both the Player and Dragon hand:
• Odd total — Pays 0.94 to 1
• Even total — Pays 0.94 to 1
• Pair among the three cards — Pays 0.94 to 1
10. There are three bets on the total of the winning hand. I presume in the event of a tie, the total is based on either hand. All bets tie if both hands have zero points. The three bets are:
11. Total of 1 to 6 — Pays 1 to 1
12. Total of 7 or 8 — Pays 2 to 1
13. Total of 9 — Pays 4

## Analysis

The following table shows the number of winning combinations, probability of winning, and expected return from all win or lose bets. Note how everything has a house edge near 3% except the bets on a pair at 67%! That is just robbery. Fair odds would be 4.8 to 1.

### Win or Lose Bets

Bet Pays Combinations Probability Return
Dragon 0.94 11050 0.500000 -0.030000
Phoenix 0.94 11050 0.500000 -0.030000
Dragon Even 0.94 11040 0.499548 -0.030878
Dragon Odd 0.94 11060 0.500452 -0.029122
Dragon Pair 0.94 3796 0.171765 -0.666776
Phoenix Even 0.94 11040 0.499548 -0.030878
Phoenix Odd 0.94 11060 0.500452 -0.029122
Phoenix Pair 0.94 3796 0.171765 -0.666776

The next set of three tables show my analysis of the bets on the number of points of the winning hand (or either hand in the event of a push). As a reminder, a 0-0 tie results in a push for all bets. The lower right cells show a house edge of 3.76% on a total of 9, 3.67% on a total of 7 or 8, and 2.63% on a total of 1 to 6.

### Total of 9

Event Pays Combinations Probability Return
Winning Total 9 4 77,429,840 0.190166 0.760663
Winning Total 1 to 8 -1 325,017,808 0.798235 -0.798235
0-0 Tie 0 4,722,752 0.011599 0.000000
Total 407,170,400 1.000000 -0.037573

### Total of 7 or 8

Event Pays Combinations Probability Return
Winning Total 7 or 8 2 129,146,752 0.317181 0.634362
Winning Total 1, 2, 3, 4, 5, 6, 9 -1 273,300,896 0.671220 -0.671220
0-0 Tie 0 4,722,752 0.011599 0.000000
Total 407,170,400 1.000000 -0.036858

### Total of 1 to 6

Event Pays Combinations Probability Return
Winning Total 1 to 6 1 195,871,056 0.481054 0.481054
Winning Total 7 to 9 -1 206,576,592 0.507347 -0.507347
0-0 Tie 0 4,722,752 0.011599 0.000000
Total 407,170,400 1.000000 -0.026293