# Lucky Ball Roulette

## Introduction

Lucky Ball is a set of four side bets in roulette. It has been seen at the Stratford City casino in London. I saw it displayed at the 2019 Global Gaming Expo.

## Rules

1. In addition to all the standard roulette bets, there are four Lucky Ball bets, colored red, yellow, green, and blue.
2. After betting is closed, the game will pick a unique roulette outcome for each color and display them on a sign.
3. In addition, the game will display the win for each of the four Lucky Ball bets. The possible wins are shown below.
4. With all four Lucky Ball bets, the probability of the small win is 75% and the big win is 25%.
5. If the roulette ball lands in the number associated with any Lucky Ball bet, then the player shall win the posted amount for that color.

### Lucky Ball Wins

Color Big Win Small Win
Red 120 6
Blue 75 20
Green 100 12
Yellow 75 20

## Single-Zero Analysis

The following table shows my analysis of the Red bet. The lower right cell shows a house edge of 4.05%.

### Red Bet

Event Pays Weight Probability Return
Big Win 120 1 0.006757 0.810811
Small Win 6 3 0.020270 0.121622
Loss -1 144 0.972973 -0.972973
Total   148 1.000000 -0.040541

The following table shows my analysis of the Green bet. The lower right cell shows a house edge of 5.41%.

### Green Bet

Event Pays Weight Probability Return
Big Win 100 1 0.006757 0.675676
Small Win 12 3 0.020270 0.243243
Loss -1 144 0.972973 -0.972973
Total   148 1.000000 -0.054054

The following table shows my analysis of the Blue bet. The lower right cell shows a house edge of 6.08%.

### Blue Bet

Event Pays Weight Probability Return
Big Win 75 1 0.006757 0.506757
Small Win 20 3 0.020270 0.405405
Loss -1 144 0.972973 -0.972973
Total   148 1.000000 -0.060811

The following table shows my analysis of the Yellow bet. The lower right cell shows a house edge of 6.08%.

### Yellow Bet

Event Pays Weight Probability Return
Big Win 75 1 0.006757 0.506757
Small Win 20 3 0.020270 0.405405
Loss -1 144 0.972973 -0.972973
Total   148 1.000000 -0.060811

## Double-Zero Analysis

The following table shows my analysis of the Red bet. The lower right cell shows a house edge of 6.58%.

### Red Bet

Event Pays Weight Probability Return
Big Win 120 1 0.006579 0.789474
Small Win 6 3 0.019737 0.118421
Loss -1 148 0.973684 -0.973684
Total   152 1.000000 -0.065789

The following table shows my analysis of the Green bet. The lower right cell shows a house edge of 7.89%.

### Green Bet

Event Pays Weight Probability Return
Big Win 100 1 0.006579 0.657895
Small Win 12 3 0.019737 0.236842
Loss -1 148 0.973684 -0.973684
Total   152 1.000000 -0.078947

The following table shows my analysis of the Blue bet. The lower right cell shows a house edge of 8.55%.

### Blue Bet

Event Pays Weight Probability Return
Big Win 75 1 0.006579 0.493421
Small Win 20 3 0.019737 0.394737
Loss -1 148 0.973684 -0.973684
Total   152 1.000000 -0.085526

The following table shows my analysis of the Yellow bet. The lower right cell shows a house edge of 8.55%.

### Yellow Bet

Event Pays Weight Probability Return
Big Win 75 1 0.006579 0.493421
Small Win 20 3 0.019737 0.394737
Loss -1 148 0.973684 -0.973684
Total   152 1.000000 -0.085526