I coded a simple tic-tac-toe "from scratch" (haven't included a GUI or anything of that sophistication). I would like to know about any improvements that can be made to this game. Thank you.

import random

board_lst = [] 


class board: 
    def __init__(self, rows, columns):
        self.rows = rows
        self.columns = columns


    def draw(self):
        global board_lst
        for number in range(self.rows):
            board_lst.append([])
        for number in range(self.columns):
            for i in range(len(board_lst)):
                board_lst[i].append('')
        

    def add(self, move, x, y):
        global board_lst
        board_lst[x][y] = move
        for i in range(len(board_lst)):
            print board_lst[i],"\n"
        
        
        
tic_tac_toe = board(3,3)
tic_tac_toe.draw() #Draws the tic-tac-toe board



def is_empty(x, y): #Checks if a cell on the board is empty
    return board_lst[x][y] == ''

def is_valid_move(move, x, y):#Checks if a move is valid
    return (move == 'x' or move == 'o') and (x in range(3) and y in range(3))\
           and is_empty(x,y)

def player_move(move, x, y): #Places an 'x' or an 'o' on the board
    if is_valid_move(move, x, y):
        tic_tac_toe.add(move, x, y)
    else:
        print "Move is not possible."

def vertical(): #Checks each column for a human move and makes a move in that column
    if board_lst[0][0] == 'x' or board_lst[1][0] == 'x' or board_lst[2][0]:
        if is_valid_move('o',0,0):
            tic_tac_toe.add('o',0,0)
        elif is_valid_move('o',1,0):
            tic_tac_toe.add('o',1,0)
        elif is_valid_move('o',2,0):
            tic_tac_toe.add('o',2,0)
        else:
            vertical()
    elif board_lst[0][1] == 'x' or board_lst[1][1] == 'x' or board_lst[2][1]:
        if is_valid_move('o',0,1):
            tic_tac_toe.add('o',0,1)
        elif is_valid_move('o',1,1):
            tic_tac_toe.add('o',1,1)
        elif is_valid_move('o',2,1):
            tic_tac_toe.add('o',2,1)
        else:
            vertical()
    elif board_lst[0][2] == 'x' or board_lst[1][2] == 'x' or board_lst[2][2]:
        if is_valid_move('o',0,2):
            tic_tac_toe.add('o',0,2)
        elif is_valid_move('o',1,2):
            tic_tac_toe.add('o',1,2)
        elif is_valid_move('o',2,2):
            tic_tac_toe.add('o',2,2)
        else:
            vertical()
    else:
        player_move('o', random.randint(0,2), random.randint(0,2))
        
        
def computer_move(): #Allows the computer to make a move based on the human moves
    if board_lst[0].count('') == 1:
        board_lst[0][board_lst[0].index('')] = 'o'
        for i in range(len(board_lst)):
            print board_lst[i],"\n"
    elif board_lst[1].count('') == 1:
        board_lst[1][board_lst[1].index('')] = 'o'
        for i in range(len(board_lst)):
            print board_lst[i],"\n"
    elif board_lst[2].count('') == 1:
        board_lst[2][board_lst[2].index('')] = 'o'
        for i in range(len(board_lst)):
            print board_lst[i],"\n"
    else:
        vertical()
        
        
    
def human_move(): #Allows the user to make a move of his/her own choice
    x = raw_input("Enter the row number: ")
    x = int(x)
    y = raw_input("Enter the column number: ")
    y = int(y)
    player_move('x', x-1, y-1)


def every(lst, el): #Checks if all the elements in a list are the second parameter
    counter = 0
    for i in range(len(lst)):
        if lst[i] == el:
            counter = counter
        else:
            counter += 1
    return counter == 0
        

def turn():
    #Allows one to choose which player gets the first turn
    #and directs the game accordingly
    def play():
        print "Human's turn to move."
        human_move()
        if all_in_row():
            print "Human wins."
            print "\n"
            game()
        elif is_draw():
            print "The game is a draw."
            print "\n"
            game()
        else:
            print "\nComputer's turn to move."
            computer_move()
            if all_in_row1():
                print "Computer wins."
                print "\n"
                game()
            elif is_draw():
                print "The game is a draw."
                print "\n"
                game()
            else:
                print "\n"
                play()
                
    def play1():
        print "Computer's turn to move."
        computer_move()
        if all_in_row1():
            print "Computer wins."
            print "\n"
            game()
        elif is_draw():
            print "The game is a draw."
            print "\n"
            game()
        else:
            print "\n"
            print "Human's turn to move."
            human_move()
            if all_in_row():
                print "Human wins."
                print "\n"
                game()
            elif is_draw():
                print "The game is a draw."
                print "\n"
                game()
            else:
                print "\n"
                play1()
                
    turn_op = raw_input("Who do you want to go first (1 for computer or 2 for human): ")
    if turn_op == '1':
        play1()
    elif turn_op == '2':
        play()
    else:
        print "Invalid selection."
        print "\n\n"
        turn()
        
def is_draw(): #Determines if there is a draw
    counter = 0
    for i in range(len(board_lst)):
        if not '' in board_lst[i] and not (board_lst[i] == ['x','x','x'] or board_lst[i] == ['o','o','o']):
            counter = counter
        else:
            counter += 1
    if counter == 0:
        return True
    else:
        return False
        
            

def all_in_row(): #Checks if there is a tic-tac-toe all-in-a-row by human
    for i in range(len(board_lst)):
        if board_lst[i] == ['x','x','x']:
            return True
        else:
            lst = [x[0] for x in board_lst]
            lst1 = [x[1] for x in board_lst]
            lst2 = [x[2] for x in board_lst]
            if every(lst, 'x'):
                return True
            elif every(lst1, 'x'):
                return True
            elif every(lst2, 'x'):
                return True
            else:
                chk = [board_lst[0][0], board_lst[1][1], board_lst[2][2]]
                chk1 = [board_lst[2][0], board_lst[1][1], board_lst[0][2]]
                if every(chk, 'x'):
                    return True
                elif every(chk1, 'x'):
                    return True
                else:
                    return False

def all_in_row1(): #Checks for all-in-a-row by computer
    for i in range(len(board_lst)):
        if every(board_lst[i], 'o'):
            return True
        else:
            lst = [x[0] for x in board_lst]
            lst1 = [x[1] for x in board_lst]
            lst2 = [x[2] for x in board_lst]
            if every(lst, 'o'):
                return True
            elif every(lst1, 'o'):
                return True
            elif every(lst2, 'o'):
                return True
            else:
                chk = [board_lst[0][0], board_lst[1][1], board_lst[2][2]]
                chk1 = [board_lst[2][0], board_lst[1][1], board_lst[0][2]]
                if every(chk, 'o'):
                    return True
                elif every(chk1, 'o'):
                    return True
                else:
                    return False
    


def game(): #The actual game 
            
    print "==== TIC-TAC-TOE oxox ===="
    print "\n"
    for i in range(len(board_lst)):
        print board_lst[i],"\n"
    print "\n"
    print "To start the game enter 1; to exit, enter 0."
    choice = raw_input("Enter choice here: ")
    if choice == '1':
        turn()
    elif choice == '0':
        return
    else:
        print "Invalid entry. Try again."
        print "\n"
        game()
    
game()
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