My if/else function doesn't seem to be behaving like it should? [duplicate]

I'm experimenting with the basic guessing game script that gets shown to you as part of "Automate The Boring Stuff With Python".

I want the game to loop infinitely until someone says anything other than "Yes" or "yes" in response to "Would you like to try again?" at which point I would like the loop to break and the script to die. However, even if someone inputs something else, the script always behaves as if "Yes" has been inputted in response. I have no idea why.

Here's the code:

#Guess the number game

import random

def the_game(): # This is the game itself
    try:
        global secretNumber
        global guessesTaken
        global guess
        global try_again
        secretNumber = random.randint(1,20)
        
        for guessesTaken in range(1, 7):
            print("Take a guess.")
            guess = int(input())

            if guessesTaken - 6 == 0:
                print("You have " + str(6 - guessesTaken) + " attempts remaining. Boo.")
            elif guess < secretNumber:
                print("Try again. Higher this time. You have " + str(6 - guessesTaken) + " attempts remaining.")
            elif guess > secretNumber:
                print("Nope. Less. You have " + str(6 - guessesTaken) + " attempts remaining.")
            else:
                break
    except ValueError:
        print("Please enter a number.")
        the_game()
    if guess == secretNumber:
        if guessesTaken == 1:
            print("You did it in " + str(guessesTaken) + " attempt. I bet you're proud of yourself.")
        else:
            print("You did it in " + str(guessesTaken) + " attempts. I bet you're proud of yourself.")
    else:
        print("It was " + str(secretNumber) + ". You suck " + name + ".")

    print("Would you like to try again? Yes or no.")
    try_again = input()



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


while True:
    the_game()

## I want the game to loop infinitely until someone says anything
## other than "Yes" or "yes" in response to "Would you like to try again?"
## at which point I would like the loop to break and the script to die.

## However, even if someone inputs something else, the script always behaves
## as if "Yes" has been inputted in response. I have no idea why.
    
    if try_again == "Yes" or "yes":
        print("Here we go again.")
        the_game()
    else:
        print("Goodbye!")
        break
        exit()