# Royal Flop Roulette

## Introduction

Royal Flop Roulette is a side bet in roulette based on two playing cards from a 38-card deck and the outcome of a spin in double-zero roulette. As of this writing in March 2019, it can be found at the Orchid casino in the Riu hotel in Aruba.

## Rules

1. A double-zero roulette wheel and a 38-card deck are used.
2. The 1 to 36 numbers on the roulette layout are also marked with a card of rank 6 to ace. The zero and double-zero are also marked with jokers of two different colors.
3. The deck of cards consist of all cards between rank six to ace and two jokers of different colors.
4. In addition to all the standard roulette bets, the player may make the Royal Flop Roulette bet.
5. After the normal outcome of the roulette spin, the dealer shall deal two random cards from the deck. If one of them matches the outcome of the roulette spin, it shall be burned and the next card used instead.
6. All jokers are wild.
7. The poker value between the roulette spin and two cards will be determined. The side bet will pay according to that hand and the following pay table:
• Royal flush in diamonds — 150 to 1
• Other natural royal — 50 to 1
• Wild royal — 20 to 1
• Straight Flush — 8 to 1
• Three of a kind — 8 to 1
• Flush — 5 to 1

## Analysis

The following table shows my analysis of Royal Flop Roulette. The lower right cell shows a house edge of 22.85%.

### Royal Flop Roulette Return Table

Event Pays Combinations Probability Return
Royal flush in diamonds 150 1 0.000119 0.017781
Other natural royal 50 3 0.000356 0.017781
Wild royal 20 36 0.004267 0.085349
Straight Flush 8 144 0.017070 0.136558
Three of a kind 8 144 0.017070 0.136558
Flush 5 476 0.056425 0.282124
All other -1 7,632 0.904694 -0.904694
Total   8,436 1.000000 -0.228544

The math of this makes for a good combinatorial math challenge. Here are the number of combinations of each hand by number of wilds.

### Royal Flop Roulette Combinations

Event Zero Wilds One Wild Two Wild Total
Royal flush 4 24 12 40
Straight Flush 24 96 24 144
Three of a kind 36 108 0 144
Flush 308 168 0 476
Straight 420 360 0 780
Pair 1728 504 0 2232
Nonpaying hand 4620 0 0 4620
Total 7140 1260 36 8436