Question

C++ Code:

Suppose there is a game with two options: A and B. Each of these options adds a different amount of points from a range of numbers. You start with 0 points and your goal is to reach 19 or 20 points.

For example, suppose you had the following options:

A = number between 4 through 7.

B = number between 1 through 8.

A sample game might go:

Points = 0, choose option A(add 4-7).

Points = 4, choose option B(add 1-8).

Points = 12, choose option B(add 1-8).

Points = 16, choose option B(add 1-8).

Points = 21, you lose.

Make a program that asks the user to give the ranges for both options A and B. You may assume that both options A and B have a minimum of adding at least one point.

To figure out which moves are the best, simulate 10,000,000 games (this should take about 5 seconds to run) with random choices at each turn. Record how often you won/lost the game for each point value and each option picked. If you won the game, each point/option along the whole game should get a +1 and each loss a -1.

Thus if the sample game above was the first game played, you should keep the tally:

0 Points: A=-1, B=0

1Points: A=0, B=0

2 Points: A=0, B=0

3 Points: A=0, B=0

4 Points: A=0, B=-1

5 Points: A=0, B=0

6 Points: A=0, B=0

7 Points: A=0, B=0

8 Points: A=0, B=0

9 Points: A=0, B=0

10 Points: A=0, B=0

11 Points: A=0, B=0

12 Points: A=0, B=-1

13 Points: A=0, B=0

14 Points: A=0, B=0

15 Points: A=0, B=0

16 Points: A=0, B=-1

17 Points: A=0, B=0

18 Points: A=0, B=0

At the end, show which option is best to play for each point value (i.e. whichever tally is higher). (Note: there is also a mathematical way to figure out the best moves in games like this involving expected values of random variables.)

------------------------------------------------------------------------------------------

Example 1:

Enter Option A range:

4-7

Enter Option B range:

1-8

Points=0, should play B

Points=1, should play A

Points=2, should play A

Points=3, should play A

Points=4, should play B

Points=5, should play B

Points=6, should play B

Points=7, should play A

Points=8, should play A

Points=9, should play A

Points=10,should play B

Points=11, should play B

Points=12, should play B

Points=13, should play A

Points=14, should play A

Points=15, should play A

Points=16, should play B

Points=17, should play B

Points=18, should play B

--------------------------------------

Example 2:

Enter Option A range:

1-10

Enter Option B range:

5-5

Points=0, should play B

Points=1, should play A

Points=2, should play A

Points=3, should play A

Points=4, should play B

Points=5, should play B

Points=6, should play A

Points=7, should play A

Points=8, should play A

Points=9, should play B

Points=10, should play B

Points=11, should play A

Points=12, should play A

Points=13, should play A

Points=14, should play B

Points=15, should play B Points=16, should play A

Points=17, should play A

Points=18, should play A

Answer 1

Code //Include the needed #include <iostream> #include <fstream> #include <string> #include <cs tring> #include <stdlib.h> #include <ve ctor> #include <limits.h> # include <time . h> using namespace std; header files / /Driver int main () //Function srand () srand (time (NULL)) //Declare the needed variable int minimumA, maximumA, minimumB, maximumB //Prompt for input cout << "Enter range for A:"; //Read input cin > minimumA; //Read input cin >> maximumA; //Prompt for input cout<K "Enter range for B: "; //Read input cin >> minimumB //Read input cin >> maximumB //Declare an array int pointToACounter [19]; //Declare an array int pointToBCounter[19]; //Declare and initialize A range int rangeA maximumA-minimumA+1; //Declare and initialize B range int rangeB maximumB-minimumB+1;

//Declare and initialize point int polnt 0; //Loop for (int inc1-0 inc1K10000 inc1++) //Declare and initialize listofPoints int listofPoints [100000] -1; //Declare and initialize listofoptions int listofoptions [100000]-1; //Declare and initialize indices int indexl 0, index2- 0 //Initialize point point 0 //Loop while (point <- 18) //Initialize int choice rand ( ) % (2) ; //Update listofPoints listofPoints [index1]point; //Update listofoptions listofoptions[index2]choice; //Increment index1 index1++ //Increment index2 index2++; //Check condition if (choice 0) //Update point +- point (rand () % (rangeA) + minimumA) ; //otherwise else //Update point +- point (rand () % (rangeB) + minimumB);

//Update int totaloffset- -1; //Check condition if (point - 19 11 point- 20) //Update totalOffset-1; for (int inc2-0; inc2 < indexl; inc2++) //Check condition if ( listofoptions [inc2]-1) /Check condition if (listofoptions [inc2]0) //Update pointToACounter [listOfPoints [inc2]1 - totalOffset; //otherwise else //Update pointToBCounter [listOfPoints [inc2]1 - totalOffset; //Loop for (int inc1-0; inc1<-18 inc1++) //Display cout << "Point=" << incl << ", should play ((pointToACounter [inc1] >= pointToBCounter [inc 1 ] ? "A" << endl; " << "B")) // Pause cin.get ); cin.get //stop return 0;

Sample output clusers 3015951documentslvisual studio 20121Projects lQuasar DebugiQuasar.exe Enter range for A 4- Enter range for B: 1-8 Point-0. should play B Point-1. should play A Point-2. should play A Point-3. should play B Point-4, should play B Point-5, should play B Point-6. should play A Point-7. should play A Point-8. should play A Point-9. should play A Point-10, should play A Point-11. should play B Point-12. should play B Point-13. should play B Point-14. should play B Point-15. should play B Point-16. should play B Point-17. should play B Point-18. should play B

Executable code

//Include the needed header files
#include <iostream>
#include <fstream>
#include <string>
#include <cstring>
#include <stdlib.h>
#include <vector>
#include <limits.h>
#include <time.h>
using namespace std;

//Driver
int main ()
{
    //Function srand()
    srand(time(NULL));
   
    //Declare the needed variable
    int minimumA, maximumA, minimumB, maximumB;
   
    //Prompt for input
    cout << "Enter range for A: ";
   
    //Read input
    cin >> minimumA;
   
    //Read input
    cin >> maximumA;
   
    //Prompt for input
    cout << "Enter range for B: ";
   
    //Read input
    cin >> minimumB;
   
    //Read input
    cin >> maximumB;
   
    //Declare an array
    int pointToACounter[19];
   
    //Declare an array
    int pointToBCounter[19];
   
    //Declare and initialize A range
    int rangeA = maximumA-minimumA+1;
   
    //Declare and initialize B range
    int rangeB = maximumB-minimumB+1;
   
    //Declare and initialize point
    int point = 0;

    //Loop
    for (int inc1=0; inc1<10000; inc1++)
    {
        //Declare and initialize listOfPoints
        int listOfPoints[100000] = {-1};
       
        //Declare and initialize listOfOptions
        int listOfOptions[100000] = {-1};
       
        //Declare and initialize indices
        int index1 = 0, index2= 0;
       
        //Initialize point
        point = 0;
       
        //Loop
        while (point <= 18)
        {
            //Initialize
            int choice = rand()%(2);
           
            //Update listOfPoints
            listOfPoints[index1] = point;
           
            //Update listOfOptions
            listOfOptions[index2] = choice;
           
            //Increment index1
            index1++;
           
            //Increment index2
            index2++;
           
            //Check condition
            if (choice == 0)
            {
                //Update point
                point += (rand()%(rangeA) + minimumA);
            }
           
            //Otherwise
            else
            {
                //Update point
                point += (rand()%(rangeB) + minimumB);
            }
        }
       
        //Update
        int totalOffset = -1;
       
        //Check condition
        if (point == 19 || point == 20)
        {
            //Update
            totalOffset = 1;
        }       
        for (int inc2=0; inc2 < index1; inc2++)
        {
            //Check condition
            if( listOfOptions[inc2] != -1)
            {
                //Check condition
                if (listOfOptions[inc2] == 0)
                {
                    //Update
                    pointToACounter[listOfPoints[inc2]] += totalOffset;
                }
               
                //Otherwise
                else
                {
                    //Update
                    pointToBCounter[listOfPoints[inc2]] += totalOffset;
                }
            }
        }
    }
   
    //Loop
    for (int inc1=0; inc1<=18; inc1++)
    {
        //Display
        cout << "Point=" << inc1 << ", should play " << ((pointToACounter[inc1] >= pointToBCounter[inc1] ? "A" : "B")) << endl;
    }
   
    //Pause
    cin.get();cin.get();
   
    //Stop
    return 0;
}