A simple lotto game in Python
For your current purposes, the biggest problem is that you are relying on global variables exclusively.  This makes it a lot tougher to understand, maintain, and debug your code.  This question actually has some great answers that discuss why this can cause real problems in code:

https://softwareengineering.stackexchange.com/questions/148108/why-is-global-state-so-evil

As a specific example, this bit of code had me confused for a few minutes:

while number_pool:


Because number_pool wasn't used anywhere in your while loop, and so I had no idea why this wasn't just an infinite loop.  I eventually realized that it is getting modified inside the lotto_choice method which is called within the while loop.  This is pretty much exactly why you don't want to use global state: if any bit of code can modify any variable anywhere, you can quickly lose track of who modifies what and when it happens, and bugs can creep in very quickly.  You also will have your own trouble if you come back to the code after a while and find that you no longer remember exactly what gets modified by what functions.

So, always make sure and keep input into functions and output out of functions clear.  In the case of lotto_choice you could easily do something like this:

def lotto_choice( number_pool ):
    choice = random.choice(number_pool)
    number_pool.remove(choice)
    return ( choice, number_pool )


Then you would call it like this inside your while loop:

( choice, number_pool ) = lotto_choice( number_pool )


Now you can easily see where number_pool gets modified.  Since you are just now getting started, now is the time to establish good habits.  So take the time and understand how variable scope works and (especially in a learning exercise like this) make sure not to use any global state.  My biggest suggestion is to fix that and then post a new code review question with your updated code.

Also, small change. You want to only execute your game if called in the 'main' context, like this:

if __name__ == '__main__':
    the_game()