How to make this random number game better? I'm a newbie trying to teach myself Python. Could somebody tell me if there is a better way to write this?  I am also curious as to whether or not there is anything I should not do.  This code does work, but some indentation may have been lost when I pasted it.

import random

def game():
    yes = ['y', 'Y', 'Yes', 'yes']
    number = random.randint(1, 20)
    numAttempts = 0
    print('')
    name = input('What is your name? ')

    print('')
    print('Nice to meet you', name, '! I am going to guess a random number! You will have 3 tries to guess it. '
                                'Good luck!')


    while numAttempts &lt; 3:
        print('')
        guess = int(input('Guess the number I have chosen between 1 and 20. '))
        numAttempts += 1
        if guess == number:
            print('')
            print('You guessed correctly! The number was', number, "!", 'Great Job', name, '!')
            break
        elif guess &gt; number:
            print('')
            print('The number is lower than', guess, "!")
        elif guess &lt; number:
            print('')
            print('The number is Higher than', guess, "!")
    else:
        print('')
        print('Sorry, the number I chose was', number, 'but you have used all 3 tries', name, '!')

    print('')
    gameover = input("Would you like to play again? Yes or No? ")
    while gameover in yes:
        game()
    else:
        print('')
        print('You should have chose yes. You computer will now explode!')

game()
A few observations:


In place of the while loop with you managing the numAttempts index,  why not use a for loop with the in keyword? i.e. for numAttempts in range(3):
Note that with the above, you can still use your else block (for supports the else clause! :)  )
Multiple games keep asking for your name. Unless your code has Alzheimer's, consider avoiding that :) 
Related to the above : Structurally, you've chosen to recurse to play another game. Why not keep your game atomic and keep the whole offer another game choice/logic external to your function? 
Your second elif does not make sense. Why not just else (guess can only be &lt; number now!)