envelope.py

import random
import numpy.random

total_gain_from_swapping = 0
number_of_rounds = 0
while True:
  # small_envelope = random.uniform(0, 1000) # this is well-behaved - the running mean eventually converges to 0
  small_envelope = 2 ** numpy.random.geometric(0.5, 1)[0] # P($2^i) = 1/(2^i) - this is not well-behaved - the running mean wanders around forever
  large_envelope = 2 * small_envelope
  my_envelope, other_envelope = random.sample([small_envelope, large_envelope], 2)
  total_gain_from_swapping += other_envelope - my_envelope
  number_of_rounds += 1
  if number_of_rounds % 10000 == 0:
      print 'running mean gain from swapping is', float(total_gain_from_swapping) / number_of_rounds