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If a player scores a Yahtzee and places it into the Yahtzee box, each additional Yahtzee is awarded with 100 points during the rest of the game. In this case for example the combination 2,2,2,2,2 used in the box Ones counts as 100 points. The extra Yahtzee bonus amends the values of the boxes. Similar to the Upper Score bonus, the probabilistic value of a box depends on the already obtained upper section score.
In the table below you find the probabilistic values of the box Ones depending on the missing upper section’s score to 63.
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Upper Score missing from the minimum of 63 points
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Probabilistic value of the box Ones
WITHOUT extra Yahtzee bonus
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Probabilistic value of the box Ones
WITH extra Yahtzee bonus*
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0
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37.10
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40.77
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1
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34.83
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26.68
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2
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26.56
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18.46
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3
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14.52
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12.67
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4
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5.76
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8.09
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5
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2.57
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6.11
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6
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2.10
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5.77
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7
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2.10
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5.77
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…
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…
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…
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63
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2.10
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5.77
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* in this case the Yahtzee box has already been used with a maximum score of 50 points.
The extra Yahtzee bonus can be taken into account if we differentiate three cases:
- The Yahtzee box still is unused (U).
- The Yahtzee box has already been used with a maximum score of 50 (Y).
- The Yahtzee box has already been used with a score of 0 (0).
Thus all unused box combinations will have different probabilistic values depending on the status of the Yahtzee box. For example:
- Boxes Ones, Twos and Chance are only the unused ones. This combination has two set of probabilistic values: a. Yahtzee box=0 or b. Yahtzee box=Y.
- Boxes Ones, Twos, Yahtzee and Chance are only the unused ones. This combination has only one set of probabilistic value: Yahtzee box=U.
Please note that these sets of probabilistic values are each a matrix of 64 numbers: one value for each missing upper section score from 63 points.
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