# Multicolor Roulette

## Introduction

Multicolor Roulette is a roulette variant found in France. To name one placement, the Imperial Club in Paris. The game is played on a colored wheel where the slots are numbered with what winning bets pay.

## Rules

1. The game is played on a wheel with 25 positions.
2. Each position is colored. The number of positions per color is as follows:
• Red — 6
• Green — 6
• White — 6
• Yellow — 6
• Blue — 1
3. The six positions for each color, besides blue, will also be marked with a number. The number of positions per number is as follows:
• 2 — 2
• 3 — 3
• 4 — 1
4. The blue position is marked with the number 24.
5. The player may bet on any of the five colors that appear on the wheel.
6. A ball wall be rolled on the wheel, which will eventually land in an indentation on one of the positions.
7. Bets on the color the ball landed in will win and pay according to the number that appears on that position. For example, if the player bet on red and the ball landed in Red 3, then wagers on red would pay 3 to 1.

## Analysis

The following table shows my analysis of the red, white, green and yellow bets. The lower right cell shows a house edge of 8.00%.

### Red, White, Yellow, Green Analysis

Cards Pays Positions Probability Return
Correct color -- 4x 4 1 0.040000 0.160000
Correct color -- 3x 3 3 0.120000 0.360000
Correct color -- 2x 2 2 0.080000 0.160000
Loss -1 19 0.760000 -0.760000
Total   25 1.000000 -0.080000

The following table shows my analysis of the blue bet. The lower right cell shows a house edge of 0.00%. That is right, zero house advantage.

### Blue Analysis

Cards Pays Positions Probability Return
24 1 0.040000 0.960000
-1 24 0.960000 -0.960000
Total 25 1.000000 0.000000