#include <iostream>
#include <iomanip>
#include <array>
#include <random>

using namespace std;


int main()
{
  random_device rnd;
  uniform_int_distribution<int> d(0,2);

  int win_count = 0;
  
  for ( int i = 0; i < 1000000; ++i)
  {
    array<int,3> a{0,0,0};

    a.at(d(rnd)) = 1;

    // we always select box 0
    
    if ( a.at(1) == 0 ) // host open box 1 if it's a goat
      win_count += a.at(2); // we switch to box 2
    else // host open box 2 (must be goat since only one car)
      win_count += a.at(1); // we switch to box 1
  }

  cout << setprecision(1) << fixed
       << "We win the car " << win_count/10000.00
       << "% of the time if we switch." << endl;
  
  return 0;
}