Guessing game

import random

print("What is your name?")
name = input()
print("Well,", name + ".  I'm thinking of a number between 1 and 20.")

# ask to guess 6 times.

def guessGame():
    secretNumber = random.randint(1,20)
    attempts = 0
    guessed = False

    while attempts <= 6:
        print("Take a guess..")
        guess = int(input())

        if guess < secretNumber:
            print("Your guess is too low.")

        elif guess > secretNumber:
            print("Your guess is too high")
        elif guess == secretNumber:
            print("Great job!")
            attempts = 7
            guessed = True


        attempts += 1

    if guessed == False and attempts == 7:
        print("Nope.  The number I was thinking of was", secretNumber)

    print("Would you like to play again?")

    response = input()

    if response.lower() in ["yes", "yeah", "yep", "affirmative"]:
        guessGame()
    elif response.lower() in ["no", "nope", "piss off"]:
        print("Goodbye")


guessGame()