538_count_ttt.py

def threes(board):
    for x in [0, 1, 2]:
        yield [board[x][0], board[x][1], board[x][2]]
        yield [board[0][x], board[1][x], board[2][x]]
    yield [board[0][0], board[1][1], board[2][2]]
    yield [board[0][2], board[1][1], board[2][0]]

def is_done(board):
    for th in threes(board):
        if th[0] is not None and th[0] == th[1] and th[1] == th[2]:
            return True
    return False

def count_games(board, player):
    if is_done(board):
        return 1
    next_player = 0 if player == 1 else 1
    total = 0
    for r in [0, 1, 2]:
        for c in [0, 1, 2]:
            if board[r][c] is None:
                board[r][c] = player
                total += count_games(board, next_player)
                board[r][c] = None
    return total

start_board = [
    [None, None, None],
    [None, None, None],
    [None, None, None]
]

print(count_games(start_board, 0))