No thought went into picking random.random in the test -- it was just a
random ;-) choice.  Amaury's analysis of the source of non-determinism
is on target, and the easiest fix is to pick a coded-in-Python function
to pickle instead.  I suggest, e.g., changing the sporadically failing
doctest to:

>>> import pickletools
>>> dis(pickle.dumps(pickletools.dis, 0))
    0: c    GLOBAL     'pickletools dis'
   17: p    PUT        0
   20: .    STOP
highest protocol among opcodes = 0