Alphabetic Roulette

Introduction

Alphabetic Roulette is a roulette variant I saw at the Fitzgerald's in Las Vegas on August 7, 2011. It is a simple roulette variant involving both colors and letters. There are 25 spaces, one for each letter from A to X, and one for both Y and Z. There are also six colors, each consisting of four letters. The YZ is treated much the way the 0 is in single-zero roulette and has no color.

Rules

There are ten types of bets, as follows:

Straight Up: Bet on any one letter, or YZ.
Split: Bet on any two neighboring letters.
Top Line: Bet on A, B, and YZ.
Four Way: Bet on any four neighboring letters.
Color: Bet on any one color.
Six Way: Bet on one of four groups of six letters: A-F, G-L, M-R, S-X.
Party Pit: Bet that any letter in "party pit," i.e. the P, A, R, T, Y, or I.
Roulette: Bet that any letter in "roulette," i.e. the R, O, U, L, E, or T.
Dozen: Bet on one of two groups of 12 letters: A-L or M-X
Column: One of two bets of alternating letter: A, C, E, ... , W or B, D, F, ... , X.

Analysis

The following table shows the probability and expected return of each bet. The right column shows that every bet has a 4.00% house edge.