Why use a list's length to count the number of attempts?

import random
def game():
    secret_num = random.randint(1,10)
    counter = 5
    while counter > 0:
        try:
            guess = int(input("You have {} chances. Guess a number between 1 and 10: ".format(counter)))
        except ValueError:
            print("{} is not a number".format(guess))
            break
        else:
            if guess == secret_num:
                print("You got it! My number was {}".format(secret_num))
                break
            elif guess < secret_num:
                print("Too small")
            else:
                print("Too big")
        counter -=1
    else:
        print("The number was {}".format(secret_num))

    play_again = input("Enter 'y' to play again " ).lower()
    if play_again != 'y':
        print("Bye!")       
    else:
        game()           
game()