Consider three urns, A, B, C containing a, b, and c balls respectively. You play a game by picking an urn at random, each being equally likely and move a ball from it to one of the other two urns, each being equally likely. The game ends when one of the three urns becomes empty.

(A) Write a Python code that simulates this game and compute its mean duration. (B) Verify the value found in (A) by identifying an appropriate one dimensional random walk model.