# Blazing 7s Roulette

## Introduction

Blazing 7s Roulette is a roulette game by Scientific Games. It plays the same way as American double-zero roulette, except adds a side bet called the Blazing 7s.

## Rules

All the rules are the same as American double-zero roulette, except the game adds the Blazing 7s side bet. The rules of the side bet are as follows.

1. The side bet wins if the ball lands in 7, 17, or 27.
2. If the side bet wins, then three numbers are drawn without replacement from the 38-number range on the wheel.
3. The player is paid according to the number of balls drawn that contain a 7, as follows:
• Three sevens pays 1000 to 1
• Two sevens pays 100 to 1
• One sevens pays 17 to 1
• Zero sevens pays 7 to 1

## Analysis

The following table shows the number of combinations, probability, and expected win from the side bet, assuming the side bet does win. The lower right cell shows the average win on the side bet is 10.391181 to 1.

### Side Bet Win

Event Pays Combinations Probability Return
Three 7s 1000 1 0.000119 0.118540
Two 7s 100 105 0.012447 1.244666
One 7 17 1,785 0.211593 3.597084
Zero 7s 7 6,545 0.775842 5.430891
Total   8,436 1.000000 10.391181

The following table shows the overall return of the side bet, including when it doesn't win. The lower right cell shows a house edge of 10.07%.

### Side Bet Win

Event Pays Combinations Probability Return
Three 7s 1000 3 0.000009 0.009358
Two 7s 100 315 0.000983 0.098263
One 7 17 5,355 0.016705 0.283980
Zero 7s 7 19,635 0.061251 0.428755
Loss -1 295,260 0.921053 -0.921053
Total   320,568 1.000000 -0.100696

By the way, if the three numbers were drawn without replacement, the house edge would be 4.48%.