script to run simulations of settlers of catan board tile setups to find the average number of games played before encountering a duplicate arrangement.

catan_boards.py

import sys, random

# board is defined as list of 19 land tiles: Forest (4), Sheep (4), Wheat (4), Brick (3), Rocks (3), Desert (1)
def new_board(board=''):
  available = list('ffffsssswwwwbbbrrrd')
  for i in range(19):
    random.shuffle(available)
    board += available.pop()
  return board

def rotate(board):
  return board[7] + board[3] + board[0] + board[12] + board[8] + board[4] + board[1] + board[16] + board[13] + board[9] + board[5] + board[2] + board[17] + board[14] + board[10] + board[6] + board[18] + board[15] + board[11]

results = []
for test in range(int(sys.argv[1])):
  boards = {}
  while len(results) == test:
    permutations = [new_board()]
    for _ in range(5):
      permutations.append(rotate(permutations[-1]))
    if any(permutation in boards for permutation in permutations):
      results.append(len(boards)+1)
    boards[permutations[-1]] = 1
  print 'test %s: duplicate board found after %s games. average: %s' % (test+1, len(boards), sum(results)/len(results))