Balanced smileys check algorithm (part 3)
Correctness

I suggest you add a test case for :)(.  It should be False, but is not.

Testability

Consider adding assert tests for ease of testing and evaluation.  Perhaps something like

def verify(test_input, expected_result):
    actual_result = check_balance(test_input)
    assert actual_result == expected_result, "{} expected {} failed".format(test_input, expected_result)
    print(test_input, actual_result)

if __name__ == "__main__":
    verify(':)(', False)
    verify(':()', True)
    verify('abc(b:)cdef(:()', True)
    verify('a)', False)
    verify(')(' , False)


Besides, if provided, it is easier to refactor and propose alternatives when providing feedback. :)

Clarity

A key part of the challenge is that smiles and frowns are optionally allowed to balance parens.  This is an important not immediately obvious point that is worth documenting in the code.

Though somewhat minor for this simple example, I prefer not to repeatedly test for pre == ':' since ":" is the only character you care about.  Instead I would opt for something like eyes_flag which can be set at the end of loop as eyes_flag = c == ':'.

Though the criteria may change after fixing the implementation, expressions like this

if left &gt; right + smile:
    return False
return True


can be simplified to

return left &lt;= right + smile


Naming

This is a matter of opinion, but for me smiley and frown require too much effort to map to open and close parens.  I prefer calling them optional open parens (opt_open) and optional close parens (opt_close).