Outcome - 1

Yahtzee with Upper Section bonus and extra Yahtzee bonus

 

Upper Section bonus:  63 points

Extra Yahtzee bonus:  100 points each extra, additional Yahtzee

The theoretical outcome of the game is 254.4067. The outcome of the game was calculated with an exact method. The distribution of the scores is astonishing:

Fig01

This empirical distribution was generated by P-Yahtzee professional playing 10 million random games in about two hours. The average score was 254.33, a good estimation of the theoretical score. The program obtained in total 4,3 million Yahtzees (used either for the Yahtzee box or other boxes). The most probable/popular score is 266.

Fig02

The maximum score obtained during these games was 943. The combinations were as follows:

Box

Combination

Value

Extra Yahtzee bonus

Ones

11111

5

100

Twos

22355

4

0

Threes

33336

12

0

Fours

44444

20

100

Fives

55555

25

100

Sixes

15666

18

0

3ofaKind

45555

24

0

4ofaKind

66666

30

100

FullHouse

44444

25

100

SmStraight

33456

30

0

LgStraight

44444

40

100

Yzee

44444

50

0

Chance

35566

25

0

 

Upper Section bonus

63

 

 

Total Score

934

 

The minimum score obtained during these games was 75. The combinations were as follows:

Box

Combination

Value

Extra Yahtzee bonus

Ones

13356

1

0

Twos

22246

6

0

Threes

34455

3

0

Fours

44456

12

0

Fives

25556

15

0

Sixes

13666

18

0

3ofaKind

13556

0

0

4ofaKind

24466

0

0

FullHouse

12445

0

0

SmStraight

33346

0

0

LgStraight

34455

0

0

Yzee

23356

0

0

Chance

23366

20

0

 

Upper Section bonus

0

 

 

Total Score

75

 

 

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