Let's say that you have an event which happen at each second with probability p, each second is independent on previous and next one. Instead of tossing a coin every second, one can try to toss a coin once and estimate when a next event is going to happen, and then call the function again at a moment of event to get next event time and so on.

brnl_pbb_estimate.py

#!/usr/bin/python

import random

class BernoulliPbb(object):
  def __init__(self, p):
    self.p = p

  def Estimate(self):
    r = random.random()
    i = 0

    pbb = self.p
    pbb_sum = self.p
    while r >= pbb_sum:
      pbb *= self.p
      pbb_sum += pbb
      print pbb, pbb_sum
      i += 1
    return i