import random

def initialize_game():
    return [[0 for _ in range(4)] for _ in range(4)]

def add_new_tile(board):
    empty_cells = [(i, j) for i in range(4) for j in range(4) if board[i][j] == 0]
    if empty_cells:
        i, j = random.choice(empty_cells)
        board[i][j] = 2 if random.random() < 0.9 else 4

def print_board(board):
