C++ Problem when trying to set bernoulli distribution as an output for function

I need my program to simulate bernoulli (p) random variables with ability to change p. If i write smth like this

#include <random>
#include <iostream>
#include <chrono>
int main()
{
double prob = 0.1; //let it be const for now, no need to change it in this example
std::mt19937 gen(std::chrono::steady_clock::now().time_since_epoch().count());
std::bernoulli_distribution coin(prob);

int success = 0;
for (int i = 0; i < 1000; ++i) {
  if (coin(prob)) ++success;
}
  std::cout << success << "\n";
    
  return 0;
}

it works perfectly fine. But i need to change parameter p, so i decided to create a function which takes some switcher, simulates random variable with parameter depending on switcher, and returns true or false. Here is my code:

#include <random>
#include <iostream>
#include <chrono>

 bool coin_flip(int switcher) {
   double prob;
      switch (switcher) {
      case 1: {
    prob = 0.1;
    std::mt19937 gen(std::chrono::steady_clock::now().time_since_epoch().count());
    std::bernoulli_distribution coin(prob);
    return coin(gen);
      }
      case 2: {
    prob = 0.2;
    std::mt19937 gen(std::chrono::steady_clock::now().time_since_epoch().count());
    std::bernoulli_distribution coin(prob);
    return coin(gen);
      }

      }
    }
int main()
{
    int success = 0;
    
    for (int i = 0; i < 1000; ++i) {
      if (coin_flip(1)) {
    ++success;
      }
    }

    std::cout << success << "\n";
    
    return 0;
}

The for loop in the main body counts number of successes among 1000 tries and i expect it to be around 100, but i do get wierd results. Too many zeroes and large numbers.

So my question is why does coin(prob) breaks when passes to the output of a function?

Also, if you have good ideas, i would be grateful for any suggestions on how to simulate sequence of bernoulli r.v's with different parameters p (e.g. we are in a loop where p depends on counter i)

Thank you for your time