Let there be a gas particle in a box. Now cut the box in half and if the gas particle can exist in all remaining space in the box, the box has had an ergodic transformation.

Non ergodic: Let there be a car on a major highway in a city. Now cut the roads on the highway in half (say for construction). Congestion results and consequently the cars never again move as fast as before. (equivalent to your house of cards)

  def ergodic(f(),x):
      return f(avg(x)) == avg(f(x))