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:
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.
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
|
|
|
|