title: Probability exercise returning different result that expected
body: <p>As an exercise I'm writing a program to calculate the odds of rolling 5 die with the same number.  The idea is to get the result via simulation as opposed to simple math though.  My program is this:</p>
  
  <pre><code># rollFive.py
  
  from random import *
  
  def main():
      n = input("Please enter the number of sims to run: ")
      hits = simNRolls(n)
      hits = float(hits)
      n = float(n)
      prob = hits/n
      print "The odds of rolling 5 of the same number are", prob
  
  def simNRolls(n):
      hits = 0
      for i in range(n):
          hits = hits + diceRoll()
      return hits
  
  
  def diceRoll():
      firstDie = randrange(1,7,1)
      for i in range(4):
          nextDie = randrange(1,7,1)
          if nextDie!=firstDie:
              success = 0
              break
          else:
              success = 1
      return success
  </code></pre>
  
  <p>The problem is that running this program with a value for n of 1 000 000 gives me a probability usually between 0.0006 and 0.0008 while my math makes me believe I should be getting an answer closer to 0.0001286 (aka (1/6)^5).</p>
  
  <p>Is there something wrong with my program?  Or am I making some basic mistake with the math here?  Or would I find my result revert closer to the right answer if I were able to run the program over larger iterations?</p>