I put it together. Here’s the code I wrote in Python.

import random

genders = ['boy', 'girl']

def run():
    other_child_girls = 0
    for i in range(10000):
        other_child = get_other_child()
        if other_child == 'girl':
            other_child_girls += 1
    print(other_child_girls)

def get_other_child():
    children = random.choices(genders, k=2)
    first_child_index = random.randint(0, 1)
    first_child = children[first_child_index]
    if first_child == 'boy':
        other_child_index = (first_child_index + 1) % 2
        return children[other_child_index]
    # Recursively repeat this call until the child at the door is a boy
    # (i.e., discard any cases where the child at the door is a girl)
    return get_other_child()

if __name__ == '__main__':
    run()

And it turns out you were right. I ran it a few times and got answers ranging from 4942 to 5087, i.e., clustered around 50%.