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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
- A double-zero roulette wheel and a 38-card deck are used.
- 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.
- The deck of cards consist of all cards between rank six to ace and two jokers of different colors.
- In addition to all the standard roulette bets, the player may make the Royal Flop Roulette bet.
- 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.
- All jokers are wild.
- 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 |