Question

using simple and basic C++

2. In a game called "lucky 6", for each game, a biased die is tossed repeatedly, and a payoff of 2 dollars is made, where n is the number of the toss on which the first "6" appears. The die is biased such that obtaining a "4" or "5" is twice more likely of showing up on a toss than the other numbers. Some examples follow. TOSS SEQUENCE 1 6 PAYOFF 22 $4 24 $16 23=$8 2 -128א 5436 1 26 1 23 15 46 Write code to simulate 100 games of "lucky 6". At the end, print the average payoff made. Note that if no "6" appears within the first 9 throws of the die, the payoff is $0 and that game ends. Note: You are also required to print all the die values for each game. [10 marks]

Answer 1

1 #include <iostream> #include <time.h 2 3 #include <cmath> using namespace std int rollDice ( 6 7 rand % 8 1; int num = == 4 | if (num 7) 9 num == 10 return 4; 5 || if (num 8) 11 num == return 8 12 return num } 13 14 15 int main( srand(time (NULL)); 16 17 18 long long int payoff 19 int games 1; = 20 m Ln O

while(games <= 100) 21 22 rollDice) ") " " "; 23 int dice = 24 cout < games << 25 cout << dice << 26 int count 1; while(dice != 6) 27 28 rollDice (); count++ 29 dice 30 31 cout < dice << } 32 if (count < 9) 33 "Payoff $0" << endl 34 cout << else 35 { cout < "Payoff 36 $" << pow(2, count) endl 37 pow(2, count); 38 payoff } + 39 games++ } cout <"Average payoff 40 41 payoff 100; 42 43

#include <iostream>

#include <time.h>

#include <cmath>

using namespace std;

int rollDice()

{

int num = rand() % 8 + 1;

if(num == 4 || num == 7)

return 4;

if(num == 5 || num == 8)

return 8;

return num;

}

int main() {

srand(time(NULL));

long long int payoff = 0;

int games = 1;

while(games <= 100)

{

int dice = rollDice();

cout << games << ") ";

cout << dice << " ";

int count = 1;

while(dice != 6)

{

dice = rollDice();

count++;

cout << dice << " ";

}

if(count <= 9)

cout << "Payoff = $0" << endl;

else

{

cout << "Payoff = $" << pow(2,count) << endl;

payoff += pow(2, count);

}

games++;

}

cout << "Average payoff = " << payoff / 100;

}

/*Sample Output

1) 4 8 1 4 1 8 2 6 Payoff = $0

2) 3 8 3 8 3 1 1 2 8 8 3 4 8 1 4 8 3 6 Payoff = $262144

3) 4 8 3 1 4 6 Payoff = $0

4) 8 8 2 6 Payoff = $0

5) 4 3 3 6 Payoff = $0

6) 4 8 2 1 8 3 2 8 4 8 3 3 8 6 Payoff = $16384

7) 3 4 3 6 Payoff = $0

8) 3 8 4 4 3 3 3 4 8 6 Payoff = $1024

9) 6 Payoff = $0

10) 2 3 4 4 4 4 3 6 Payoff = $0

11) 6 Payoff = $0

12) 4 4 2 1 4 6 Payoff = $0

13) 6 Payoff = $0

14) 1 4 8 6 Payoff = $0

15) 6 Payoff = $0

16) 8 4 4 4 4 6 Payoff = $0

17) 2 6 Payoff = $0

18) 3 4 8 8 2 6 Payoff = $0

19) 1 8 8 6 Payoff = $0

20) 2 4 2 3 4 8 8 8 8 3 4 8 1 8 1 4 6 Payoff = $131072

21) 4 2 4 4 4 8 3 1 6 Payoff = $0

22) 8 1 3 8 6 Payoff = $0

23) 4 6 Payoff = $0

24) 4 4 4 6 Payoff = $0

25) 6 Payoff = $0

26) 8 8 1 4 2 1 3 2 4 1 8 8 4 3 1 4 6 Payoff = $131072

27) 1 1 8 1 3 4 6 Payoff = $0

28) 4 1 8 8 8 2 2 4 4 2 4 8 2 2 1 6 Payoff = $65536

29) 2 8 2 8 2 2 3 4 2 4 4 2 6 Payoff = $8192

30) 4 8 4 8 4 8 4 8 2 4 3 3 6 Payoff = $8192

31) 2 8 4 2 2 8 1 3 4 3 8 2 1 6 Payoff = $16384

32) 8 4 8 2 3 4 6 Payoff = $0

33) 2 2 8 8 6 Payoff = $0

34) 6 Payoff = $0

35) 3 1 1 8 2 8 6 Payoff = $0

36) 4 6 Payoff = $0

37) 8 4 8 4 6 Payoff = $0

38) 4 8 4 2 1 2 1 2 4 4 4 8 8 4 1 8 1 4 8 1 3 4 8 1 2 2 8 8 2 8 3 8 4 1 6 Payoff = $3.43597e+10

39) 4 2 6 Payoff = $0

40) 6 Payoff = $0

41) 6 Payoff = $0

42) 4 4 2 3 4 3 8 8 6 Payoff = $0

43) 4 8 8 2 8 8 3 6 Payoff = $0

44) 8 8 4 4 2 4 8 2 1 3 3 4 8 8 2 4 2 8 2 4 4 1 1 4 1 8 1 8 8 3 2 4 2 1 4 3 46 Payoff = $2.74878e+11

45) 4 4 1 4 2 8 6 Payoff = $0

46) 4 3 4 8 8 2 3 8 2 1 8 2 1 1 1 4 3 4 8 3 2 8 6 Payoff = $8.38861e+06

47) 8 3 1 8 1 3 4 4 6 Payoff = $0

48) 2 8 8 6 Payoff = $0

49) 4 4 2 8 4 4 1 8 4 1 3 1 4 4 3 6 Payoff = $65536

50) 6 Payoff = $0

51) 8 8 1 1 4 1 3 2 4 8 3 4 4 8 2 2 2 1 8 8 2 4 6 Payoff = $8.38861e+06

52) 2 1 4 6 Payoff = $0

53) 8 1 3 8 1 4 8 1 2 6 Payoff = $1024

54) 3 3 4 2 6 Payoff = $0

55) 4 8 8 8 6 Payoff = $0

56) 6 Payoff = $0

57) 1 8 8 2 4 3 3 4 1 8 3 1 2 8 1 8 4 1 1 1 3 4 8 4 1 3 8 8 3 8 3 3 2 4 4 8 16 Payoff = $2.74878e+11

58) 8 1 6 Payoff = $0

59) 3 2 4 2 2 4 8 3 4 6 Payoff = $1024

60) 8 2 2 1 2 4 8 4 6 Payoff = $0

61) 8 1 8 6 Payoff = $0

62) 4 3 2 8 1 1 8 6 Payoff = $0

63) 3 1 4 4 3 2 1 8 1 6 Payoff = $1024

64) 1 2 4 1 4 2 1 2 8 8 2 4 2 8 2 3 4 2 3 4 4 6 Payoff = $4.1943e+06

65) 4 2 1 1 4 1 8 4 6 Payoff = $0

66) 6 Payoff = $0

67) 8 4 6 Payoff = $0

68) 8 6 Payoff = $0

69) 6 Payoff = $0

70) 1 8 2 2 3 3 2 4 8 8 8 8 6 Payoff = $8192

71) 3 8 8 8 8 8 8 6 Payoff = $0

72) 2 3 3 4 4 4 4 4 4 2 4 8 3 1 2 6 Payoff = $65536

73) 2 6 Payoff = $0

74) 2 1 2 1 4 8 8 3 1 2 4 8 4 8 2 1 6 Payoff = $131072

75) 8 4 2 6 Payoff = $0

76) 2 3 8 1 8 8 3 2 6 Payoff = $0

77) 8 4 6 Payoff = $0

78) 1 4 4 8 1 6 Payoff = $0

79) 8 2 8 4 8 4 8 8 2 8 4 3 2 8 8 6 Payoff = $65536

80) 1 1 2 3 3 4 2 6 Payoff = $0

81) 8 2 1 8 4 1 6 Payoff = $0

82) 3 2 2 4 1 8 3 1 6 Payoff = $0

83) 4 4 8 1 6 Payoff = $0

84) 4 6 Payoff = $0

85) 6 Payoff = $0

86) 8 8 8 4 6 Payoff = $0

87) 1 4 2 3 4 2 1 8 4 3 6 Payoff = $2048

88) 8 1 4 4 4 4 2 2 8 1 2 2 8 8 8 1 4 4 4 4 8 2 6 Payoff = $8.38861e+06

89) 2 8 4 2 1 8 4 4 4 8 8 4 8 3 8 1 4 1 3 8 8 2 4 8 8 6 Payoff = $6.71089e+07

90) 3 3 8 4 8 6 Payoff = $0

91) 8 6 Payoff = $0

92) 4 1 2 2 4 8 6 Payoff = $0

93) 3 4 8 8 3 6 Payoff = $0

94) 3 3 8 2 4 1 1 3 8 6 Payoff = $1024

95) 8 2 2 8 2 4 8 4 8 8 1 6 Payoff = $4096

96) 6 Payoff = $0

97) 8 4 8 8 8 4 3 8 6 Payoff = $0

98) 8 4 4 4 4 4 6 Payoff = $0

99) 3 4 3 8 8 2 6 Payoff = $0

100) 3 1 4 4 8 4 8 8 1 8 4 8 4 4 2 4 4 4 4 3 2 3 1 4 8 8 1 1 1 3 6 Payoff = $2.14748e+09

Average payoff = 5863604910

*/