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# Dice — Version 2

## Introduction

The title of this game is just "dice," which is an awful name. To make matters more confusing, there is already another game titled "Dice" analyzed on this site. To avoid confusion, or perhaps cause it, I'm going to call this game "Dice -- version 2."

The game is a simple game of luck based on the roll of five dice, like in Yahtzee. There are a whole host of bets you can make on the outcome of the roll. The game can be found at some Internet casinos using live dealers.

## Rules

Five six-sided dice are rolled. The player may wager on the following bets:

- Two Pair — There are two distinct pairs and a singleton. A full house does not count. For example, 2-2-5-5-4 Wins pay 3.15 for 1.
- Three of a Kind — Three of a kind and two singletons. A full house does not count. For example, 4-4-4-1-6. Wins pay 4 for 1.
- Low straight — A roll of 1-2-3-4-5. Wins pay 40 for 1.
- High straight — A roll of 2-3-4-5-6. Wins pay 40 for 1.
- Full House — Distinct three of a kind and a pair. Wins pay 20 for 1.
- All different — Five distinct singletons. For example, 1-2-4-5-6. Wins pay 9 for 1.
- Four of a Kind — Distinct four of a kind and a singleton. For example, 3-3-3-3-6. Wins pay 40 for 1.
- Five of a kind — All dice the same For example, 3-3-3-3-3. Wins pay 450 for 1.
- Exactly two dice with chosen number — Player chooses a number. To win, the roll must contain this chosen number exactly twice. For example, if the player chooses 5 and the roll is 1-2-3-5-5. Wins pay 5 for 1.
- Exactly three dice with chosen number — Player chooses a number. To win, the roll must contain this chosen number exactly three times. For example, if the player chooses 5 and the roll is 1-2-5-5-5. Wins pay 25 for 1.
- Chosen number will be rolled — Players chooses a number and it must appear at least once in the roll. For example, player chooses 6 and the roll is 1-2-3-3-6. Wins pay 1.4 for 1.
- Chosen number will not be rolled — Players chooses a number and it must not appear in the roll. For example, player chooses 6 and the roll is 1-2-3-3-5. Wins pay 2.1 for 1.
- Sum under 17.5 — Sum of the dice is 17 or less. For example, 1-1-2-4-5. Wins pay 1.7 for 1.
- Sum over 17.5 — Sum of the dice is 18 or more. For example, 1-3-4-6-6. Wins pay 1.7 for 1.
- Sum under 13.5 — Sum of the dice is 13 or less. For example, 1-1-2-3-3. Wins pay 5.5 for 1.
- Sum over 21.5 — Sum of the dice is 22 or more. For example, 3-4-5-6-6. Wins pay 5.5 for 1.
- Sum under 10.5 — Sum of the dice is 10 or less. For example, 1-1-1-2-3. Wins pay 25 for 1.
- Sum over 24.5 — Sum of the dice is 25 or more. For example, 4-5-5-6-6. Wins pay 25 for 1.
- More odd than even dice — At least three odd dice For example, 1-3-3-4-6. Wins pay 1.7 for 1.
- More even than odd dice — At least three even dice For example, 1-3-4-4-6. Wins pay 1.7 for 1.
- Exactly four dice with odd number — For example, 1-3-4-5-5. Wins pay 5.4 for 1.
- Exactly four dice with even number — For example, 2-2-3-4-6. Wins pay 5.4 for 1.
- All dice even — For example, 2-2-4-4-6. Wins pay 25 for 1.
- All dice odd — For example, 1-1-1-3-5. Wins pay 25 for 1.

## Analysis

The following table shows my analysis of each bet. All pays are on a "for one" basis, meaning the player does not also get his original wager back after a win. The combinations are the number of ways to win out of the possible 6^{5} = 7,776 ways to roll five dice.

### Dice

Bet | Pays | Combinations | Probability | Return |
---|---|---|---|---|

Two pairs | 3.15 | 1800 | 0.231481 | 0.729167 |

Three of a kind | 4 | 1200 | 0.154321 | 0.617284 |

Low straight | 40 | 120 | 0.015432 | 0.617284 |

High straight | 40 | 120 | 0.015432 | 0.617284 |

Full house | 20 | 300 | 0.038580 | 0.771605 |

All different | 9 | 720 | 0.092593 | 0.833333 |

Four of a kind | 40 | 150 | 0.019290 | 0.771605 |

Five of a kind | 450 | 6 | 0.000772 | 0.347222 |

Exactly two dice with chosen number | 5 | 1250 | 0.160751 | 0.803755 |

Exactly three dice with chosen number | 25 | 250 | 0.032150 | 0.803755 |

Chosen number will be rolled | 1.4 | 4651 | 0.598122 | 0.837371 |

Chosen number will not be rolled | 2.1 | 3125 | 0.401878 | 0.843943 |

Sum under 17.5 | 1.7 | 3888 | 0.500000 | 0.850000 |

Sum over 17.5 | 1.7 | 3888 | 0.500000 | 0.850000 |

Sum under 13.5 | 5.5 | 1182 | 0.152006 | 0.836034 |

Sum over 21.5 | 5.5 | 1182 | 0.152006 | 0.836034 |

Sum under 10.5 | 25 | 252 | 0.032407 | 0.810185 |

Sum over 24.5 | 25 | 252 | 0.032407 | 0.810185 |

More odd than even dice | 1.7 | 3888 | 0.500000 | 0.850000 |

More even than odd dice | 1.7 | 3888 | 0.500000 | 0.850000 |

Exactly four dice with odd number | 5.4 | 1215 | 0.156250 | 0.843750 |

Exactly four dice with even number | 5.4 | 1215 | 0.156250 | 0.843750 |

All dice even | 25 | 243 | 0.031250 | 0.781250 |

All dice odd | 25 | 243 | 0.031250 | 0.781250 |

The returns range from a low of 34.72% (on a five of a kind) to 85.00% (on any of the bets that pay 1.7). The average is 77.23%.

## More Screenshots

I think most people probably play this game for the lovely dealers. That said, here are some more screenshots of them.