# Dice Fever

## Introduction

Dice Fever is a video poker variant I noticed in a Las Vegas bar in March, 2014. It plays like regular video poker, except it includes a bonus feature. For the price of a sixth coin, the player qualifies for the chance to win a free game bonus. The bonus is achieved if the player gets a five of a kind with five dice within two throws.

## Rules

1. Dice Fever is based on conventional video poker.
2. For the price of a sixth coin bet, the player will enable the bonus feature.
3. If the bonus feature is enabled, then five ordinary six-sided dice will be thrown on the deal. Per Nevada law, electronic representations of dice must be fair, with a 1/6 chance of landing on each face.
4. The game will automatically hold the greatest number of matching dice.
5. On the draw, including drawing no cards at all, the game will re-roll the non-held dice.
6. If the player achieves a five of a kind with the dice (also known as a Yahtzee), then the player will earn the bonus.
7. In the bonus, the player will get five free games with a 3x multiplier. All bonus games are based on a five-coin bet.
8. A dealt royal in a free game shall get a 5x multiplier.
9. If the bonus is re-triggered, then the player will get a 5x multiplier on the hand that earned the re-trigger.
10. Free games can earn more free games, up to a maximum of 100 free games.

Rules screens. Click on any image for a larger version.

## Analysis

The following table shows the probability of getting a five of a kind (Yahtzee) and earning the bonus. An explanation of the column headings follows the table.

### Bonus Probability

Initial Dice Held Combinations Probability Probability
Yahtzee
Total
Probability
1 720 0.092593 0.000772 0.000071
2 5,400 0.694444 0.004630 0.003215
3 1,500 0.192901 0.027778 0.005358
4 150 0.019290 0.166667 0.003215
5 6 0.000772 1.000000 0.000772
Total 7,776 1.000000 0.000000 0.012631

• Initial Dice Held: The number of matching dice held after the deal.
• Combinations: The number of combinations for each outcome on the deal.
• Probability: The probability for each outcome on the deal.
• Probability Yahtzee: The conditional probability of getting a Yahtzee, given the number of dice held.
• Total Probability: Product of third and fourth columns, or the total probability of a Yahtzee given the number of matching dice on the deal.

The lower right cell shows the probability of playing the bonus is 1.26%.

The rules for the 5x multipliers make the math a bit complicated to explain here, so take it on faith that the average bonus is 80.796184 coins times the return of the base game. The bonus probability is 0.012631, so the bonus return is 5 × 0.012631 × 16.159237 × base game return = 1.020574 & base game return.

## Strategy

Whatever the return of the base game is, you're getting 2% more on the sixth coin bet. Thus, the player should always bet the full six coins.

The cards should be played according to the optimal strategy for the base game and pay table.

## Return Tables

The following table shows the games and pay table that Dice Fever is available in and the return based on a full six-coin bet and optimal strategy.

### Dice Fever Return Table

Game Pay Table Return
Bonus Poker 8-5-2 99.51%
Bonus Poker 7-5-2 98.35%
Bonus Poker 6-5-2 97.20%
Bonus Poker 8-6-1 96.11%
Bonus Poker Deluxe 9-6 99.98%
Bonus Poker Deluxe 8-6 98.83%
Bonus Poker Deluxe 8-5 97.74%
Bonus Poker Deluxe 7-5 96.58%
Deuces Wild 25-16-10-4-4-3 100.07%
Deuces Wild 25-15-9-4-4-3 99.25%
Deuces Wild 20-12-10-4-4-3 97.91%
Deuces Wild 25-16-13-4-3-2 97.10%
Deuces Wild Bonus Poker 9-4-4-3 99.79%
Deuces Wild Bonus Poker 13-4-3-3 99.14%
Deuces Wild Bonus Poker 10-4-3-3 97.70%
Deuces Wild Bonus Poker 12-4-3-2 96.55%
Double Bonus 9-7-5 99.45%
Double Bonus 9-6-5 98.14%
Double Bonus 9-6-4 96.71%
Double Bonus 8-5-4 94.51%
Double Double Bonus 9-6 99.32%
Double Double Bonus 9-5 98.21%
Double Double Bonus 8-5 97.12%
Double Double Bonus 7-5 96.04%
Jacks or Better 9-6 99.89%
Jacks or Better 9-5 98.79%
Jacks or Better 8-5 97.63%
Jacks or Better 7-5 96.48%
Triple Double Bonus 9-7 99.92%
Triple Double Bonus 9-6 98.49%
Triple Double Bonus 9-5 97.35%
Triple Double Bonus 8-5 96.30%

In general, the return for Dice Fever will be 1.003429 times the return of the base game. However, to make it easier, a simple rule of thumb would be to add 0.34%.

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