# Wheel

## Introduction

"Wheel" looks like the game big six, also known as Wheel of Fortune, but the rules are more easily compared to roulette. Briefly, a wheel with 19 stops, labeled one to 18 plus a trophy, is spun. Various bets are available on the outcome.

## Rules

1. A vertical wheel is used with 19 steps, numbered 1 to 18 plus as well as a picture of a trophy.
2. Six of the numbers are colored red, six black, and six grey. The trophy is not associated with any color.
3. The six numbers of any color are split evenly, three and three, between odds and even.
4. The following bets are available:
• Specific number — Pays 18
• Trophy — Pays 18
• 1 to 6 — Pays 3
• 7 to 12 — Pays 3
• 13 to 18 — Pays 3
• under 9.5 — Pays 2
• over 9.5 — Pays 2
• Grey — Pays 3
• Red — Pays 3
• Black — Pays 3
• Odd — Pays 2
• Even — Pays 2
• Even and grey — Pays 6
• Odd and grey — Pays 6
• Even and red — Pays 6
• Odd and red — Pays 6
• Even and black — Pays 6
• Odd and black — Pays 6
5. All wins are on a "for one" basis, meaning the original bet is not returned on a win.

## Analysis

The following table shows my analysis of all bets. The right column shows the return of all of them is 18/19, or 94.74%. This is the same return in double-zero roulette.

### Poker Bets

Bet Pays Combinations Probability Return
Specific number 18 1 0.052632 0.947368
Trophy 18 1 0.052632 0.947368
1 to 6 3 6 0.315789 0.947368
7 to 12 3 6 0.315789 0.947368
13 to 18 3 6 0.315789 0.947368
under 9.5 2 9 0.473684 0.947368
over 9.5 2 9 0.473684 0.947368
Grey 3 6 0.315789 0.947368
Red 3 6 0.315789 0.947368
Black 3 6 0.315789 0.947368
Odd 2 9 0.473684 0.947368
Even 2 9 0.473684 0.947368
Even and grey 6 3 0.157895 0.947368
Odd and grey 6 3 0.157895 0.947368
Even and red 6 3 0.157895 0.947368
Odd and red 6 3 0.157895 0.947368
Even and black 6 3 0.157895 0.947368
Odd and black 6 3 0.157895 0.947368