Breaking out in loops

Alright, I am really new and I don't know how to properly negotiate break outs.

The below code is mostly a menu shell. If you go to option 1, its a elementary tic-tac toe code. I inserted a loop into the game, but the code always breaks out into the menu loop. How do I keep it in the game?

Thanks!

NOTE: I removed a lot of the options for it will fit here

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#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
//Global Constants
//Function Prototypes
//Execution
int main(int argc, char** argv) {
    //Declare Variables
    unsigned int short choose;
    //Prompt user for number of problem to execute
<<endl;
    cout<<"5 hours is the most I am willing to admit I spent on that problem"<<endl;
    cout<<endl;
    cout<<endl;
    do {                                                        //DO LOOP BEGIN
    cout<<"Choose from the following list"<<endl;
    cout<<"1. Savitch 8th Edition Chapter 3 Problem 1-RPS"<<endl;
    cout<<"2. Savitch 8th Edition Chapter 3 Problem 2-Interest"<<endl;
    cout<<"3. Savitch 8th Edition Chapter 3 Problem 3-CUSP"<<endl;
    cout<<"4. Savitch 8th Edition Chapter 3 Problem 4-Element"<<endl;
    cout<<"5. Savitch 8th Edition Chapter 3 Problem 5-CallMe!"<<endl;
    cout<<"6. Savitch 8th Edition Chapter 3 Problem 7-Roman v1.1"<<endl;
    cout<<"7. Savitch 8th Edition Chapter 3 Problem 8-Blackjack"<<endl;
    cout<<"8. Savitch 8th Edition Chapter 3 Problem 9-Capitalism"<<endl;
    cout<<"9. Savitch 8th Edition Chapter 3 Problem 10crud(incomplete)"<<endl;
    cout<<"10. Savitch 8th Edition Chapter 3 Problem 14-Optimus"<<endl;
    cout<<"11. Savitch 8th Edition Chapter 3 Problem 15-Sphere"<<endl;
    cout<<"12. Savitch 8th Edition Chapter 3 Problem 16-Temperature"<<endl;
    cout<<"13. Savitch 8th Edition Chapter 3 Problem 17-Fat v2.0"<<endl;
    cout<<"14. Savitch 8th Edition Chapter 3 Problem 18-Keypad"<<endl;
    cout<<"15. Truth Table"<<endl;
    cout<<"16. Exit Program - All"<<endl;
    cin>>choose;
    //Catch invalid input
    if (!(choose<=16)) {
        cout<<"Not an option!"<<endl;
    }
    //Utilize switch to implement the menu
    switch(choose) {
        
        case 1:{ 
///////////////////////////////PROBLEM 1 Savitch Chp3Prb1//////////////////////// 
            cout<<"Welcome to Option 1.";
            cout<<endl;
            //START CODE//////////////////////////////
            //Variables
    char player1, player2, exit;
    //Prompt
    do {
    cout<<"Lets play rock paper scissors"<<endl;
    cout<<"Player 1, press R for Rock, P, for paper, and S for scissors"<<endl;
    //Player 1 input
    cin>>player1;
    cout<<"Player 2, press R for Rock, P, for paper, and S for scissors"<<endl;
    //Player 2 input
    cin>>player2;
    //Player 1 deciphered first, then player 2. Game ends
    //Rock
    if ((player1=='r')||(player1=='R')) {
        if ((player2=='r')||(player2=='R')) {
            cout<<"You tied!"<<endl;
            break;
        }
        if ((player2=='s')||(player2=='S')) {
            cout<<"Player 1 wins with Rock smashing Scissors!"<<endl;  
            break;
        }
        if ((player2=='p')||(player2=='P')) {
            cout<<"Player 2 wins with Paper smothering Rock!"<<endl;
            break;
        }
        else {
            cout<<"Player2 made an invalid entry!!!"<<endl;
            break;
        }
    }
    //Scissors
    else if ((player1=='s')||(player1=='S')) {
        if ((player2=='s')||(player2=='S')) {
            cout<<"You tied!"<<endl;
            break;
        }
        if ((player2=='p')||(player2=='P')) {
            cout<<"Player 1 wins with Scissors cutting Paper!"<<endl;  
            break;
        }
        if ((player2=='r')||(player2=='R')) {
            cout<<"Player 2 wins with Rock smashing scissors!"<<endl;
            break;
        }
        else {
            cout<<"Player2 made an invalid entry!!!"<<endl;
            break;
        }
    }
    //Paper
    else if ((player1=='p')||(player1=='P')) {
        if ((player2=='p')||(player2=='P')) {
            cout<<"You tied!"<<endl;
            break;
        }
        if ((player2=='r')||(player2=='R')) {
            cout<<"Player 1 wins with Paper smothering Rock!"<<endl;  
            break;
        }
        if ((player2=='s')||(player2=='S')) {
            cout<<"Player 2 wins with Scissors cutting Paper!"<<endl;
            break;
        }
        else {
            cout<<"Player2 made an invalid entry!!!"<<endl;
            break;
        }
    }
    else {
        cout<<"Player1 made an invalid entry!"<<endl;
    }
    cout<<"Game over!"<<endl;
    cout<<"Would you like to play again? Y for Yes, N for No";
    cin>>exit;
    } while ((exit!='n')||(exit!='N'));
            //FINISH CODE/////////////////////////////
            cout<<endl;
            cout<<endl;
            cout<<"End problem"<<endl;break;
        } //End option 1
        
        case 2:{
////////////////////////////////PROBLEM 2 Savitch Chp3Prb2//////////////////////
            cout<<"Welcome to Option 2.";
            cout<<endl;
            //START CODE//////////////////////////////
            
            //FINISH CODE/////////////////////////////
            cout<<endl;
            cout<<endl;
            cout<<"End problem"<<endl;break;
        } //End option 2
////////////////////////////////////////////////////////////////////////////////
        
        case 15:{
////////////////////////////////PROBLEM 14 TRUTH TABLE//////////////////////////
            cout<<"Welcome to Option 15.";
            cout<<endl;
            //START CODE//////////////////////////////
            
            //FINISH CODE/////////////////////////////
            cout<<endl;
            cout<<endl;
            cout<<"End problem"<<endl;break;
        } //End option 15
////////////////////////////////////////////////////////////////////////////////
        
        case 16: {
            cout<<"Good Bye!"<<endl;break;
        }
////////////////////////////////////////////////////////////////////////////////        
    } // switch statement end bracket
////////////////////////////////////////////////////////////////////////////////   
    } while (choose!=16); // do-while end bracket
////////////////////////////////////////////////////////////////////////////////        
//Exit Stage Right
    return 0;
}

I figured it out.

For reference:

I removed my "break;" statements and replaced them with else if statements. For some reason I remember having issues with that before.

I also had to change my exit bool statement to && from ||
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