Each turn consists of an
**assembly phase** followed by a **scoring phase**.
The assembly phase is started by rolling all dice.
Next come *two* **modification attempts**.
In each modification attempt,
the player chooses a subset of the dice (the **keepers**)
and re-rolls the other dice.
In the scoring phase,
the player chooses a pattern on the score card with an *empty* box,
and enters a score in it.
The score is determined by the
**pattern scoring rules**
based on the final roll of the assembly phase,
and the chosen pattern.

When all boxes have been filled with scores,
the game ends.
The **final score** is determined
by the **final scoring rules**,
based on the final state of the score card.
The aim of **Solitaire Yahtzee** is to maximize the final score.

- In a modification attempt,
you may choose
*any*set of keepers, ranging from all dice to none. Keeping*all*dice boils down to skipping the modification attempt. - The two modification attempts are
*independent*. That is, there is*no*restriction on the second set of keepers, e.g. it need not be a superset of the first set. - You may choose
*any*dice pattern for scoring, as long as its box is empty. The resulting score can however be*zero*. - After scoring a dice pattern, its box is nonempty,
possibly containing a
*zero*score.

Upper Section | ||
---|---|---|

Pattern | Condition | Score |

Aces | none | total value of all aces (ones) |

Twos | none | total value of all twos |

Threes | none | total value of all threes |

Fours | none | total value of all fours |

Fives | none | total value of all fives |

Sixes | non | total value of all sixes |

Lower Section | ||

Pattern | Condition | Score |

Three of a kind | 3 or more equals | total value of all dice |

Four of a kind | 4 or more equals | total value of all dice |

Full House | 3 equals + 2 other equals | 25 |

Small Straight | sequence of 4 or more | 30 |

Large Straight | sequence of 5 | 40 |

Yahtzee | 5 equals | 50 |

Chance | none | total value of all dice |

The indicated pattern score is obtained only if the condition is met;
otherwise, the score is zero,
*unless* the
**extra Yahtzee rules** apply.
Here is a brief further explanation of the pattern conditions
when scoring a dice roll in the Lower Section:

**Three of a kind**- At least three dice show the same value:
*a, a, a, b, c*. **Four of a kind**- At least four dice show the same value:
*a, a, a, a, b*. **Full House**- Three dice show one value and two another value:
*a, a, a, b, b*with*a*<>*b*. **Small Straight**- At least four dice values are in sequence:
*a*,*a*+1,*a*+2,*a*+3,*b*. **Large Straight**- All dice values are in sequence:
*a*,*a*+1,*a*+2,*a*+3,*a*+4. **Yahtzee**- All dice values are the same:
*a, a, a, a, a*.

**Extra Yahtzee Bonus**- Each Yahtzee roll (of 5 equals) earns a bonus of 100
(the
**Extra Yahtzee Bonus**), no matter for what pattern it is scored,*provided*that the Yahtzee pattern has already been scored with 50. Note however that this bonus does*not*count toward reaching the threshold for the Upper Section Bonus. **Extra Yahtzee as Joker in Lower Section**- A Yahtzee roll (of 5 equals), say of value
*v*, can be scored*in full*for the patterns Full House (25), Small Straight (30), or Large Straight (40),*provided*that both the Yahtzee pattern and the*v*-pattern in the Upper Section have already been scored (zeroes are OK). In that case, the Yahtzee roll is said to act as a**Joker**.

Note that regular scores (i.e. without Extra Yahtzee Bonus) are less than the Extra Yahtzee Bonus. Therefore, taking a score modulo the Extra Yahtzee Bonus means that this bonus is ignored. That is how the final scoring rules capture that Extra Yahtzee Bonuses do not count toward reaching the threshold for the Upper Section Bonus. Rather than including the Extra Yahtzee Bonus in the pattern score, it is more practical to record Extra Yahtzee Bonuses in a separate box.

© 1999, Tom Verhoeff (TUE, Math/CS)

Feedback about this page is welcome