Casino Yahtzee Replacement Dice
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Introduction
Nice Dice is a casino game played with five dice and follows the same three roll rules of Yahtzee. The game is made by Roxor Gaming for use by Internet casinos.
Rules
The rules are the same as Yahtzee, with the five dice scored according to the pay table below. If you're not familiar with Yahtzee, please see the rules below.
- Five ordinary six-sided dice are used. Poker dice may also be used.
- After making a bet, the player rolls the five dice.
- If the player rolls a five of a kind on the first roll, known as a 'Nice Dice,' he immediately is paid at 9 to 1 odds.
- Otherwise, the player may hold any dice he wishes, or none at all, and re-rolls the rest.
- Again, the player may hold any of the five dice he wishes and re-rolls the rest.
- After the third roll or if the player chooses to hold all five dice after the first or second roll, the dice will be scored according to the pay table below.
Nice Dice Pay Table
| Event | Pays |
|---|---|
| Five of a kind on first roll | 9 to 1 |
| Five of a kind | 3 to 1 |
| Four of a kind | 3 to 2 |
| Straight | 1 to 1 |
| Full house | Push |
Strategy
The following is the strategy after the first roll according to the roll.
- Five of a kind — Hold all five dice
- Four of a kind — Re-roll the singleton
- Full house ‐ Re-roll the pair.
- Straight — Hold all five dice
- Two pair (1's and 6's) — Hold either pair and re-roll other three dice.
- Two pair (all other) — Hold a pair of 2's to 5's and re-roll other three dice.
- Three of a kind — Re-roll two singletons
- Outside straight draw with pair (2's - 5's) (example 2-3-3-4-5) — Re-roll one of the dice in the pair.
- Inside straight draw with pair (2's - 5's) (example 2-3-3-4-6) — Re-roll three singletons.
- Any pair (1's or 6's) — Re-roll three singletons
- All other (Five singletons including a 1 and 6) — Re-roll 1 and 6
The following is the strategy after the second roll according to the roll.
- Five of a kind — Hold all five dice
- Four of a kind — Re-roll the singleton
- Full house ‐ Hold all five dice.
- Straight — Hold all five dice
- Two pair (any) — Re-roll singleton.
- Three of a kind — Re-roll two singletons
- Pair (2's - 5's) — Re-roll one of the dice in the pair.
- Any pair (1's or 6's) — Re-roll three singletons
- All other (Five singletons including a 1 and 6) — Re-roll 1 or 6
This strategy is also available in PDF form.
Analysis
The following table shows my analysis of Nice Dice, assuming optimal strategy. The lower right cell shows a house edge of 0.46%.
Nice Dice Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Five of a kind on first roll | 9 | 362,797,056 | 0.000772 | 0.006944 |
| Five of a kind | 3 | 18,570,954,240 | 0.039497 | 0.118491 |
| Four of a kind | 1.5 | 86,360,256,000 | 0.183673 | 0.275509 |
| Straight | 1 | 39,907,676,160 | 0.084877 | 0.084877 |
| Full house | 0 | 94,383,221,760 | 0.200736 | 0.000000 |
| Loser | -1 | 230,600,079,360 | 0.490445 | -0.490445 |
| Total | 470,184,984,576 | 1.000000 | -0.004624 |
The total number of combinations is 615 = 470,184,984,576. This is the number of ways five dice can be rolled up three times each.
Casino Yahtzee Replacement Dice Game
Acknowledgements
I would like to thank the following members of my Wizard of Vegas forum for their contributions to the analysis of Nice Dice — MattUK, CharliePatrick, ThatDonGuy, CrystalMath, and rsactuary. I also give credit and thanks to MattUK for the strategy above.
How To Play Casino Yahtzee
External Links
- Discussion about Nice Dice in my forum at Wizard of Vegas.
- Demo video by Roxor Gaming.