I am going to investigate the chances of getting four of a kind in Yahtzee.
1
In each turn I can roll the 5 dice three times and keep as many dice as I want. Initially I will do this
10 times and record a tick if I get 4 of a kind and a cross if I don't and then count the number I get.
I will then repeat this for some more sets of 10 so that I have more results to see a pattern.
2
I think I will get four of a kind about a quarter of the time.
Turn
4 of a kind
1

2

3

4

5

6

7

8

9

10

18

28

38

48

58

68

78

88

98

19

29

39

49

59

69

79

89

99

20

30

40

50

60

70

80

90

100

1
After 10 turns I got four of a kind once so the probability is 0.1.
Turn
4 of a kind
Turn
4 of a kind
Turn
4 of a kind
Turn
4 of a kind
Turn
4 of a kind
Turn
4 of a kind
Turn
4 of a kind
Turn
4 of a kind
Turn
4 of a kind
11

21

31

41

51

61

71

81

91

12

22

32

42

52

62

72

82

92

13

23

33

43

53

63

73

83

93

14

24

34

44

54

64

74

84

94

15

25

35

45

55

65

75

85

95

16

26

36

46

56

66

76

86

96

17

27

37

47

57

67

77

87

97

0
2
1
2
3
1
4
1
0
2
Summary
After 10
After 20
After 30
After 40
After 50
After 60
After 70
After 80
After 90
After 100
1 time
1 time
3 times
4 times
6 times
7 times
11 times
12 times
12 times
14 times
4
The number of four of a kind I got varies but the most was 4 in a set of 10 and the lowest was
none. The summary of results is what happened when I did more trials and the graph shows how
the probability changed with more trials.
I noticed that the peak in the long run frequency graph occurred in the 7th lot of 10 when I got four
of a kind four times. After 100 trials I had four of a kind 14 times which is a probability of 0.14.
After 100 trials I didn’t get four of a kind 86 times which is a probability of 0.86.
6
5