Optimal Solitaire Yahtzee Player: Trivia

Yahtzee is a registered trademark of Milton Bradley, which is owned by Hasbro, Inc..

History of Yahtzee.

There are many variations on the rules of Yahtzee, such as Triple Yahtzee.

The game is also available under many other names (Kniffel, Quintzee, Omniscore, ...).

Characteristics of the Optimal Solitaire Yahtzee Player

Noteworthy is that the Optimal Solitaire Yahtzee Player never opts for Four of a Kind in its first turn, but any other category is a candidate (if circumstances demand so). It is also interesting to see that OSYP delays zeroing out for Small Straight until at least the 10th turn. Aces and Four of a Kind, however, can be sacrificed as early as the 2nd turn, and Yahtzee as early as the 3rd turn.

  • Under worst case conditions (extremely bad luck with the dice), the Optimal Solitaire Yahtzee Player obtains a minimum score of 12.
    TurnFinal RollScoreCategory
    11 4 4 5 51Aces
    21 2 3 5 52Twos
    31 1 2 2 60Four of a Kind
    41 2 2 4 60Yahtzee
    51 1 2 2 60Threes
    61 2 2 3 30Fours
    71 2 2 3 30Fives
    81 2 2 3 30Full House
    91 2 2 3 30Sixes
    101 1 2 3 30Large Straight
    111 1 2 2 39Chance
    124 5 5 6 60Three of a Kind
    135 6 6 6 60Small Straight
    12GRAND TOTAL

    If you are paranoid, then you can guarantee a minimum score of 18. (But you will not do well on average!)


    © 1999, Tom Verhoeff (TUE, Math/CS)
    Feedback about this page is welcome