# Super Hot Roll

## Introduction

I first noticed Super Hot Roll at the Red Rock casino in Las Vegas on May 3, 2021. It is a variation of the game Hot Roll, adding a feature where multipliers apply to both the current game and the next one.

## Rules

1. Super Hot Roll is an optional feature added to 3-, 5-, and 10-play video poker.
2. If the player bets one to five coins per hand, then the feature is not activated and the game plays like conventional multi-play video poker.
3. If the player bets ten coins per hand, then the feature will be enabled. Wins will be based on a five coin bet per hand. The other five coins bet per hand is a fee to pay for the feature.
4. If the feature is enabled, then randomly the player will earn a multiplier.
5. The multiplier shall be determined by the total of two six-sided dice.
6. Usually, the multiplier shall be awarded on the draw and applied to one hand only. Sometimes, and I don't know how often, the multiplier will be awarded on the deal and apply to all hands.
7. After the draw, wins shall be evaluated including any multipliers for that game. Then, any multipliers earned that hand shall be carried over to the same positions in the next hand.
8. If the player earns a multiplier for a hand that already had one from the previous game, then for that hand the player shall keep the multiplier from the previous game. The subsequent multiplier shall apply to the next game only.

If my explanation of the rules was unclear, here are the help screens from the game. Click on any image for a larger version.

## Assumed Rules

In Hot Roll Poker, the probability of the feature is 1/6, making the average multiplier, including 1x, (5/6)*(1/6)*7 = 12/6 = 2. I assume the same is true of Hot Roll Poker, that the average multiplier, including 1x, is 2.0.

In 3-play, the rules say the probability of at least one multiplier is 1 in 4.99. To get to that probability and an average multiplier of 2.0, I calculate the probability of a multiplier on the deal is 2.48%. Assuming that didn't happen, the probability of a multiplier on any given play on the draw is 6.39%.

In 5-play, the rules say the probability of at least one multiplier is 1 in 3.77. To get to that probability and an average multiplier of 2.0, I calculate the probability of a multiplier on the deal is 3.65%. Assuming that didn't happen, the probability of a multiplier on any given play on the draw is 5.25%.

In 10-play, the rules say the probability of at least one multiplier is 1 in 2.78. To get to that probability and an average multiplier of 2.0, I calculate the probability of a multiplier on the deal is 5.09%. Assuming that didn't happen, the probability of a multiplier on any given play on the draw is 3.82%.

## Example

In the image above, I invoked the feature by betting 10 coins per play. I was dealt a pair of aces on the deal, which I kept.

My pair of aces improved to a two pair on the top hand. On the bottom hand, I randomly won an 11x multiplier. The base game was 6-5 Bonus Poker, which pays 1 for 1 for jacks or better and 2 for 1 on a two pair. With a wager of 5 coins per play, my total "win" was 5×(2 + 1 + 1×11) = 70 credits.

The 11x multiplier on the bottom hand carried over to the next game. I was dealt a two pair on the deal, which I held.

Unfortunately, none of my plays improved on the draw and I earned no additional multipliers. However, I had my 11x multiplier on the bottom play from the previous game. Thus, my "win" for this game is 5×(2 + 2 + 11×2) = 130 credits.

Old Example Screens:

## Analysis

I assume that invoking the feature cuts the house edge in half. This is the case in conventional Hot Roll Poker. That said, the following list shows some common games and pay tables both with and without the feature. This list is just hypothetical, based on common video poker games.

### Super Hot Roll Poker

Game Pay Table Return w/o Feature Return w/ Feature
Jacks or Better 9-6 99.54% 99.77%
Jacks or Better 9-5 98.45% 99.22%
Jacks or Better 8-6 98.39% 99.20%
Jacks or Better 8-5 97.30% 98.65%
Jacks or Better 7-5 96.15% 98.07%
Jacks or Better 6-5 95.00% 97.50%
Bonus Poker 8-5 99.17% 99.58%
Bonus Poker 7-5 98.01% 99.01%
Bonus Poker 6-5 96.87% 98.43%
Bonus Poker Deluxe 9-6 99.64% 99.82%
Bonus Poker Deluxe 9-5 98.55% 99.27%
Bonus Poker Deluxe 8-6 98.49% 99.25%
Bonus Poker Deluxe 8-5 97.40% 98.70%
Bonus Poker Deluxe 7-5 96.25% 98.13%
Bonus Poker Deluxe 6-5 95.36% 97.68%
Double Bonus 9/7/5 99.11% 99.55%
Double Bonus 9/6/5 97.81% 98.90%
Double Bonus 10/6/4 97.46% 98.73%
Double Bonus 9/6/4 96.38% 98.19%
Double Bonus 9/5/4 95.27% 97.64%
Double Bonus 7/5/4 93.11% 96.55%
Double Double Bonus 9-6 98.98% 99.49%
Double Double Bonus 9-5 97.87% 98.94%
Double Double Bonus 8-5 96.79% 98.39%
Double Double Bonus 7-5 95.71% 97.86%
Double Double Bonus 6-5 94.66% 97.33%
Triple Double Bonus 10-6 99.22% 99.61%
Triple Double Bonus 9-6 98.15% 99.08%
Triple Double Bonus 9-5 97.02% 98.51%
Triple Double Bonus 8-6 97.11% 98.55%
Triple Double Bonus 8-5 95.97% 97.98%
Triple Double Bonus 7-5 94.92% 97.46%
Triple Triple Bonus 9-6 99.75% 99.88%
Triple Triple Bonus 9-5 98.61% 99.30%
Triple Triple Bonus 8-5 97.55% 98.78%
Triple Triple Bonus 7-5 96.49% 98.25%
Triple Triple Bonus 6-5 95.44% 97.72%
Deuces Wild 25/15/10/4/4/3 99.42% 99.71%
Deuces Wild 25/15/9/4/4/3 98.91% 99.46%
Deuces Wild 20/12/10/4/4/3 97.58% 98.79%
Deuces Wild 25/16/13/4/3/2 97.09% 98.54%
Deuces Wild 20/10/8/4/4/3 95.96% 97.98%
Deuces Wild 25/15/10/4/3/2 94.82% 97.41%
Deuces Wild Bonus 9/4/4/3 99.45% 99.73%
Deuces Wild Bonus 8/4/4/3 99.06% 99.53%
Deuces Wild Bonus 7/4/4/3 98.69% 99.34%
Deuces Wild Bonus 13/4/3/3 98.80% 99.40%
Deuces Wild Bonus 10/4/3/3 97.36% 98.68%
Deuces Wild Bonus 12/4/3/2 96.22% 98.11%
Deuces Wild Bonus 11/4/3/2 95.76% 97.88%
Deuces Wild Bonus 10/4/3/2 95.34% 97.67%
Super Double Bonus 9/5 99.69% 99.85%
Super Double Bonus 8/5 98.69% 99.34%
Super Double Bonus 7/5 97.77% 98.89%
Super Double Bonus 6/5 96.87% 98.44%
Super Double Double Bonus 50/7/5 98.61% 99.31%
Super Double Double Bonus 50/6/5 97.69% 98.85%
White Hot Aces 9/5 99.57% 99.79%
White Hot Aces 8/5 98.50% 99.25%
White Hot Aces 7/5 97.44% 98.72%
White Hot Aces 6/5 96.39% 98.19%
Super Bonus Deuces Wild 25/12/9/4/3 98.84% 99.42%
Super Bonus Deuces Wild 25/10/8/4/3 97.87% 98.94%
Super Bonus Deuces Wild 25/10/6/4/3 97.12% 98.56%
Super Bonus Deuces Wild 20/10/8/4/3 96.94% 98.47%

## Vulturing

If the previous player left enough multipliers, then the game will offer a player advantage on the next bet. How much is enough? First add, the total multipliers left by the last player. This sum should count no multiplier as a multiplier of 1x. Based on a lot of math and simulations, here is my advice on how many multipliers you need by number of plays.

• 3-play: 6x or more
• 5-play: 9x or more
• 10-play: 16x or more