STAtistics / Mr. Hansen

5/3/2011

 

Sample Tabulation for Games 1 and 2

(showing value of Game 1 only)

 

Rules for Game 1:

            The value of Game 1 is defined to be the outcome of a die roll, provided the roll is 1, 2, 3, or 4. However, if the die comes up 5 or 6, then the value of Game 1 is determined by performing a different game called “Game 2.”

 

Rules for Game 2:

                The specific rules of Game 2 will be e-mailed to you. However, for purposes of this example, suppose that Game 2 is defined by rolling the die again, and if this new die roll is 3, 4, 5, or 6, then that is the value of the game; otherwise, the value of Game 2 equals whatever one gets by starting afresh with Game 1 (and another roll of the die).

 

Tabulation Format:

                The simulated die rolls are in column 1. The outcome of Game 1 is listed either in column 2 or column 3, depending on whether the game is settled immediately (by a roll of 1, 2, 3, or 4) or has to be continued with Game 2 in order to determine an outcome. Note that sometimes, Game 2 requires restarting Game 1 with a new die roll, which can become rather confusing. Important: All the entries in the table are outcomes for Game 1 only. The word “punt” indicates that the outcome cannot be determined by the roll shown in the current row; instead, the game must be switched and a new die roll generated in order to try to find the value.

 

In this table, 120 iterations are shown, and the sample mean value of Game 1 equals 2.942. Your results will be different, since you will have slightly different rules for Game 2.

 

Die Roll

Game 1

Game 2

Iteration Count

5

punt

 

 

1

 

punt

 

1

1

 

1

5

punt

 

 

1

 

punt

 

6

punt

 

 

5

 

5

2

2

2

 

3

5

punt

 

 

5

 

5

4

5

punt

 

 

5

 

5

5

3

3

 

6

6

punt

 

 

2

 

punt

 

6

punt

 

 

4

 

4

7

2

2

 

8

5

punt

 

 

4

 

4

9

4

4

 

10

1

1

 

11

3

3

 

12

3

3

 

13

1

1

 

14

2

2

 

15

2

2

 

16

2

2

 

17

3

3

 

18

3

3

 

19

1

1

 

20

1

1

 

21

2

2

 

22

5

punt

 

 

2

 

punt

 

4

4

 

23

6

punt

 

 

5

 

5

24

6

punt

 

 

3

 

3

25

3

3

 

26

2

2

 

27

6

punt

 

 

1

 

punt

 

1

1

 

28

6

punt

 

 

1

 

punt

 

2

2

 

29

4

4

 

30

3

3

 

31

6

punt

 

 

1

 

punt

 

4

4

 

32

2

2

 

33

5

punt

 

 

4

 

4

34

1

1

 

35

4

4

 

36

3

3

 

37

2

2

 

38

5

punt

 

 

1

 

punt

 

5

punt

 

 

3

 

3

39

5

punt

 

 

1

 

punt

 

3

3

 

40

4

4

 

41

3

3

 

42

1

1

 

43

4

4

 

44

6

punt

 

 

2

 

punt

 

5

punt

 

 

4

 

4

45

2

2

 

46

6

punt

 

 

4

 

4

47

3

3

 

48

6

punt

 

 

6

 

6

49

5

punt

 

 

5

 

5

50

5

punt

 

 

3

 

3

51

4

4

 

52

2

2

 

53

4

4

 

54

6

punt

 

 

2

 

punt

 

4

4

 

55

1

1

 

56

5

punt

 

 

6

 

6

57

2

2

 

58

3

3

 

59

6

punt

 

 

3

 

3

60

6

punt

 

 

2

 

punt

 

3

3

 

61

6

punt

 

 

1

 

punt

 

4

4

 

62

2

2

 

63

6

punt

 

 

6

 

6

64

3

3

 

65

5

punt

 

 

2

 

punt

 

3

3

 

66

1

1

 

67

4

4

 

68

2

2

 

69

4

4

 

70

4

4

 

71

2

2

 

72

6

punt

 

 

3

 

3

73

1

1

 

74

5

punt

 

 

1

 

punt

 

6

punt

 

 

4

 

4

75

1

1

 

76

6

punt

 

 

4

 

4

77

2

2

 

78

4

4

 

79

3

3

 

80

3

3

 

81

1

1

 

82

1

1

 

83

2

2

 

84

5

punt

 

 

5

 

5

85

3

3

 

86

2

2

 

87

1

1

 

88

2

2

 

89

6

punt

 

 

2

 

punt

 

1

1

 

90

2

2

 

91

1

1

 

92

4

4

 

93

2

2

 

94

5

punt

 

 

2

 

punt

 

4

4

 

95

2

2

 

96

4

4

 

97

1

1

 

98

6

punt

 

 

1

 

punt

 

2

2

 

99

2

2

 

100

6

punt

 

 

3

 

3

101

3

3

 

102

1

1

 

103

6

punt

 

 

2

 

punt

 

4

4

 

104

6

punt

 

 

5

 

5

105

4

4

 

106

4

4

 

107

2

2

 

108

5

punt

 

 

5

 

5

109

3

3

 

110

4

4

 

111

2

2

 

112

3

3

 

113

4

4

 

114

3

3

 

115

5

punt

 

 

1

 

punt

 

6

punt

 

 

3

 

3

116

3

3

 

117

4

4

 

118

2

2

 

119

6

punt

 

 

1

 

punt

 

5

punt

 

 

6

 

6

120