Optimal Solitaire Yahtzee Player: Instructions

[ Overview | Notes | Examples | Details ]

Overview

1. You provide the current state of a Solitaire Yahtzee game:
   Fill out Score Card and Dice Values, and click Submit button (below Score Card).
   • To set the start state: Click New Game button.
   • To let your browser roll the unkept dice: Click Roll button.
2. The server lists all Options for the given state,
   sorted by expected final score under optimal play.
   • After Rolls #1 and #2, the dice to keep and categories to score are listed.
   • After Roll #3, only the categories to score are listed.
3. You can apply an option to update the Score Card and Dice:
   Click Do button.
   • You can undo the update by clicking Undo.

Notes

• Play is optimized for maximizing the expected final score, that is, to maximize the long-term average of the final score. Low final scores cannot be excluded, but are `averaged out' by higher scores. Also see Disclaimers.

Examples

1. You are playing a game of Yahtzee, and suddenly you encounter a situation for which you would like to have expert advise.
   1. Enter your situation in the Score Card and Dice fields.
   2. Submit it to the Optimal Solitaire Yahtzee Player.
   3. Read the numerically motivated advice under Options.

   Examples:

   • You are in your first turn, last (third) roll, and the dice show 6, 6, 6, 6, 1.
     Where to score: Sixes, or Four of a Kind, or elsewhere still?

   • You have just scored 40 for a Large Straight, and now you roll 2, 3, 4, 5, 6 (another large straight).
     What to do: Score immediately as Small Straight, or keep some dice (if so, which)?

   NOTE: If you do not know the exact scores for each of the categories already scored, then you can fill in 0 (zero) in most cases. Keep in mind the following:

   • The set of categories still open for scoring is important. A zero score for a category indicates that it is no longer available.
   • The exact total score of the Upper Section is important if it is less than 63. It is NOT important how that score is distributed over the various categories.
   • Whether you scored 0 or 50 for Yahtzee is important.
   Other aspects do NOT affect the order of all choices and hence the optimal choice. The only difference is a shift in all expected final scores by the same amount.

2. You are about to play a game of Yahtzee and would like the Optimal Solitaire Yahtzee Player to make all your choices.

   New Game.
   Repeatedly

   1. Enter the Dice Values in the empty fields,
   2. Click Submit, and
   3. Do the top line under Options.

3. You want to quiz yourself and see how well you choose compared to the Optimal Solitaire Yahtzee Player. (A better alternative is to do the Yahtzee Proficiency Test.)

   New Game.
   Repeatedly

   1. Click Roll (to enter random Dice Values in the empty fields),
   2. Make your choice (in your mind),
   3. Click Submit,
   4. Compare your choice to the top line under Options, and
   5. Do your choice line.

Details for Interface Elements

New Game Button

Postcondition: All input fields on the Score Card are empty (Turn #1), all input fields for the Dice are empty (Roll #1).

Score Card Score Fields

The input fields for the thirteen categories

Aces, Twos, Threes, Fours, Fives, Sixes,
Three of a Kind, Four of a Kind, Full House, Small Straight, Large Straight, Yahtzee, Chance,

and the Extra Yahtzee Bonus can be set to the score obtained so far.
Input is checked for validity.
An empty category field indicates that it still needs to be scored.
Turn #, Upper Section Bonus, and GRAND TOTAL are automatically computed.

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Roll # Field

The Roll # (1, 2, or 3) can be set through a drop-down menu.

Roll Button

Postcondition: The values of all unkept dice have been set randomly.

Submit Button

Submit game state (Score Card and Dice) for evaluation.
Precondition: There is at least one empty category on the Score Card and all Dice Values are set (not empty).
Postcondition: Options Table is shown.

Dice Value Fields

The input fields for each of the five dice can be set through a drop-down menu to the value rolled.
Precondition: Die is unkept.

Dice Keep Checkboxes

The checkboxes indicate which dice are kept.
Invariant: Keep implies value field is not empty.

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Options Table

Lists all options in the submitted game state.
For each option, the expected final score under continued optimal play is indicated to the right, together with its standard deviation, in the form E±S.

Options Do Buttons

Postcondition: The game state is updated according to the selected option:

• When keeping: Keep checkboxes of Dice are set accordingly.
• When scoring: Score card is updated: score field for category is set accordingly.

Roll # is cycled: 1 -> 2 -> 3 -> 1.
The selected option is shown next to the Undo button.

Options Undo Button

Postcondition: The game state is reset to the one giving rise to the options.
The field next to the Undo button is emptied.