# 3 Dice Baccarat

## Introduction

3 Dice Baccarat is a baccarat variant using dice by Galaxy Gaming. The game is scheduled to begin a field trial at the Planet Hollywood in Las Vegas in November, 2023.

## Rules

As usual, when writing about baccarat, I use upper case when referring to the names of bets and lower case when referring to the one playing the game. This is an attempt to avoid confusion when using the word "Player."

1. Two sets of three ordinary dice and shakers are used, one each set each to represent the Player and Banker score.
2. The primary bets are which side will have the higher score, the Player or Banker.
3. To get score of the Player or Banker hand, take the sum of the three dice used for that hand. If the total is 10 or more, drop the tens digit. For example, if the dice were 4+5+6 = 15, then the score would be 5. Thus, the highest possible score is 9.
4. Wins on the Banker and Player pay even money. However, if a 3 beats a 0, then the winning side shall push.
5. The following side bets are available:
• Tie — Wins if both Player and Banker have the same score. Wins pay 8 to 1.
• 3 Over 0 — Wins if either side wins 3 over 0. Wins pay 35 to 1.
• Banker Winning 7 — Wins if the Banker wins with a score of 7. Wins pay 14 to 1.
• Player Winning 8 — Wins if the Player wins with a score of 8. Wins pay 10 to 1.
• 1-1-1 or 6-6-6 — Wins if either or both sides have a total of 3 or 18. Wins pay 50 to 1.
• 3-3-3 — Wins if either or both sides roll a 3-3-3. Wins pay 100 to 1.

## Analysis

### Player/Banker

Event Pays Combinations Probability Return
Win 1 20316 0.435442 0.435442
3 over 0 0 594 0.012731 0.000000
Tie 0 4836 0.103652 0.000000
Loss -1 20910 0.448174 -0.448174
Total   46656 1.000000 -0.012731

### Tie

Event Pays Combinations Probability Return
Win 8 4836 0.103652 0.829218
Loss -1 41820 0.896348 -0.896348
Total   46656 1.000000 -0.067130

### Player Winning 8

Event Pays Combinations Probability Return
Win 10 3718 0.079690 0.796896
Loss -1 42938 0.920310 -0.920310
Total   46656 1.000000 -0.123414

### Banker Winning 7

Event Pays Combinations Probability Return
Win 14 2718 0.058256 0.815586
Loss -1 43938 0.941744 -0.941744
Total   46656 1.000000 -0.126157

### Golden 3

Event Pays Combinations Probability Return
Win 35 1188 0.025463 0.891204
Loss -1 45468 0.974537 -0.974537
Total   46656 1.000000 -0.083333

### 1-1-1 or 6-6-6

Event Pays Combinations Probability Return
Win 50 860 0.018433 0.921639
Loss -1 45796 0.981567 -0.981567
Total   46656 1.000000 -0.059928

### 3-3-3

Event Pays Combinations Probability Return
Win 100 431 0.009238 0.923783
Loss -1 46225 0.990762 -0.990762
Total   46656 1.000000 -0.066980