Usually, a simple function is enough:

    def make_counter(start=0):
      count = start
      def incr():
        nonlocal count
        count += 1
        return count
      return incr

Example:

    >>> c = make_counter()
    >>> c()
    1
    >>> c()
    2

But it hides nothing:

    >>> c.__closure__[0].cell_contents
    2
    >>> c.__closure__[0].cell_contents = -1
    >>> c()
    0

"private" in Python is cultural, not enforced. (you can access `self.__private` from outside too if you want).