# Roul 8: Roulette Side Bet

## Introduction

Roul 8 is a side bet I noticed at the Grand Casino in Brussels. It uses three custom dice. Wins depend on the shake of these dice and whether or not the balls lands in the number 8.

## Rules

1. The game can be played on any standard roulette wheel.
2. Between the areas on the layout for bets on red and black is an area to bet on the Roul 8.
3. Three dice are used. Each die has five blank sides and one side with an infinity symbol. I shall refer to these dice as Infinity Dice. If they sound familiar, the blackjack side bet Perfect 11's also uses them.
4. The dice are contained in a dome with a base that vibrates, shaking up the dice. Much like a Pop-O-Matic, which any American born in the 60's may remember.
5. With every spin, the Pop-O-Matic shall be invoked to shake the dice.
6. Wins depend on the number of dice that land on the ∞ symbol and whether or not the ball landed in the number 8. The pay table is below.

Following is the pay table for Roul 8. Pays are expressed on a "for one" basis.

### Roul 8 Pay Table

Ball in 8 ∞ Dice Pays
Yes 3 888
Yes 2 88
Yes 1 8
Yes 0 4
No 3 88
No 2 2
No 1 0
No 0 0

## Analysis

The following table shows the probability and contribution to the return in a single-zero roulette game. The lower right cell shows a return of 94.54%, which equates to a house edge of 5.46%.

### Return Table — Single Zero

Ball in 8 ∞ Dice Pays Combinations Probability Return
Yes 3 888 1 0.000125 0.111111
Yes 2 88 15 0.001877 0.165165
Yes 1 8 75 0.009384 0.075075
Yes 0 4 125 0.015641 0.062563
No 3 88 36 0.004505 0.396396
No 2 2 540 0.067568 0.135135
No 1 0 2,700 0.337838 0.000000
No 0 0 4,500 0.563063 0.000000
Total     7,992 1.000000 0.945445

The following table shows the probability and contribution to the return in a double-zero roulette game. The lower right cell shows a return of 93.49%, which equates to a house edge of 6.51%.

### Return Table — Double Zero

Ball in 8 ∞ Dice Pays Combinations Probability Return
Yes 3 888 1 0.000122 0.108187
Yes 2 88 15 0.001827 0.160819
Yes 1 8 75 0.009137 0.073099
Yes 0 4 125 0.015229 0.060916
No 3 88 37 0.004508 0.396686
No 2 2 555 0.067617 0.135234
No 1 0 2,775 0.338085 0.000000
No 0 0 4,625 0.563475 0.000000
Total     8,208 1.000000 0.934942