Monty Hall Problem

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <ctime>
using namespace std;

int win_changed = 0,win_unchanged = 0;

int main()
{
    srand (time(NULL)); //random number seed will be the current time
    unsigned long long int prize, player_choice, open_door;


    for (unsigned long long int i = 0; i < 1000000000; ++i)
    {
        prize = rand()%3 + 1;
        player_choice = rand()%3 + 1;
        if (prize==player_choice)
        {
            ++win_unchanged;
        }
        for (;;)
        {
            open_door = rand()%3 + 1;
            if (open_door != prize)
            {
                break;
            }
        }
        switch (player_choice) //to change the door
        {
            case 1: if (open_door == 2)
            {
                player_choice = 3;
            }
            else
            {
                player_choice = 2;
            }
            break;

            case 2: if (open_door == 1)
            {
                player_choice = 3;
            }
            else
            {
                player_choice = 1;
            }
            break;

            case 3: if (open_door == 2)
            {
                player_choice = 1;
            }
            else
            {
                player_choice = 2;
            }
            break;
        }
        if (prize == player_choice)
        {
            ++win_changed;
        }


    }
    cout << "Wins when changed = " << win_changed << endl;
    cout << "Wins when not changed = " << win_unchanged << endl;
    return 0;

}