Why directional rounding is odd. Try with python2 (rounds ties away from zero, which is bad) and python3 (rounds ties to nearest even number).

rounding.py

from random import randint as rand

max = 10000000
sum = 0
sumR = 0
for i in range(0, max):
  x = rand(1, 1000) / 2.0
  sum += x
  sumR += round(x)
print((sumR - sum) / max)