# Dice Duel

## Introduction

Dice Duel is a simple game involving two dice of different colors. There are several bets available based on the roll of both dice. The game can be found at the Crown casino in Melbourne, Australia.

## Rules

1. Two ordinary six-sided dice are used, one red and one gold.
2. The following bets are available:
• Red die higher — This bet pays even money on a win and pushes on all ties except 1-1, which is a loss.
• Gold die higher — This bet pays even money on a win and pushes on all ties except 1-1, which is a loss.
• Tie — This bet pays 4 to 1 on all ties except 6-6, which pays 8 to 1.
• Specific number — These six bets, one on each number from 1 to 6 win if at least one die lands on that number. Wins pay 2 to 1 if one die lands on the chosen number and 4 to 1 for both dice.

## Analysis

The following table shows my analysis of the bet on the Red die being higher. The odds are exactly the same for the Gold die. The lower right cell shows a house edge of 2.78%.

### Red Analysis

Event Pays Combinations Probability Return
Red higher 1 15 0.416667 0.416667
Tie: 2-2 to 6-6 0 5 0.138889 0.000000
Tie: 1-1 -1 1 0.027778 -0.027778
Gold higher -1 15 0.416667 -0.416667
Total   36 1.000000 -0.027778

The following table shows my analysis of the Tie bet. The lower right cell shows a house edge of 5.56%.

### Tie Analysis

Event Pays Combinations Probability Return
Tie: 6-6 8 1 0.027778 0.222222
Tie: 1-1 to 5-5 4 5 0.138889 0.555556
Loss -1 30 0.833333 -0.833333
Total   36 1.000000 -0.055556

The following table shows my analysis of the bets on a specific number. The lower right cell shows a house edge of 2.78%.

### Specific Number Analysis

Event Pays Combinations Probability Return
2 4 1 0.027778 0.111111
1 2 10 0.277778 0.555556
0 -1 25 0.694444 -0.694444
Total   36 1.000000 -0.027778