What is the problem with my reverse number game?

import random

def main():
    guesses_left = 4

    help = """If I guess too low write "higher".
If I guess too high write "lower".
If I'm correct write "correct"
"""

    current_guess = random.randint(1, 10)

    higher_or_lower = input("My guess is {} ".format(current_guess))

    while True:
        if higher_or_lower.lower() == "higher":
            current_guess = random.randint(current_guess + 1, 10)
            higher_or_lower = input("How about {} ".format(current_guess))

        elif higher_or_lower.lower() == "lower":
            current_guess = random.randint(1, current_guess - 1)
            higher_or_lower = input("How about {} ".format(current_guess))

        elif higher_or_lower.lower() == "correct":
            again = input("Yay. Shall we go again Y/n: ")

            if again.lower() != "n" or "no" or "no.":
                main()
            else:
                break
        else:
            print(help)
            higher_or_lower = input("Now tell me. Was I correct or should I guess lower or higher? ")
            continue
        guesses_left -= 1
        if guesses_left == 0:
            again = input("I'm out of guesses. Shall we go again Y/n: ")
            if again.lower() != "n" or "no" or "no.":
                main()


print("""Here's a fun game. Think of any integer between 1 and 10 and I'll try to guess it.
I have 4 guesses.
If I guess too low write "higher".
If I guess too high write "lower".
If I'm correct write "correct"
If you write anything that isn't a recognizable command I will show these messages again.
    """.format(help))

play = input("Do you have a number and are you ready to play? Y/n ")

if play.lower() != "n" or "no" or "no.":
    main()
else:
    print("bye")