Pay-to-Play Tic-Tac-Toe

This is my favorite casual game for two with little equipment. It adds a lot of richness to the tic tac toe game, and eliminates the first-mover advantage.
The rules start with tic-tac-toe, but you have an account of play points. The first player gets one point; every subsequent turn a player gets two points. It costs two points to play on an edge square, three to play on a corner, and four to play in the center (i.e. it costs one point per tic-tac-toe that could be made through that square). You can make a play that makes your account go negative, but you need a positive account to play. Even if you have the points to play, you may pass on your turn and keep the points.
Here's an example game:

1. Alice goes first, gets one point, and plays in the center. That costs four points, so her balance is negative three.
   

   	X

   	Bob's points:	0
   	Alice's points:	-3

   
   
2. Bob gets two points and plays on the left side. That costs two points, so his balance goes back to zero.
   

   O	X

   	Bob's points:	0
   	Alice's points:	-3

   
   
3. Alice gets two points, bringing her balance to negative one; that's not above zero, so she can't play.
   

   O	X

   	Bob's points:	0
   	Alice's points:	-1

   
   
4. Bob plays in the corner, which costs three points, bringing his balance to negative one.
   

   O	X
   O

   	Bob's points:	-1
   	Alice's points:	-1

   
   
5. Alice gets two points, bringing her balance to one, so she can play on the corner (cost three) to block Bob.
   

   X
   O	X
   O

   	Bob's points:	-1
   	Alice's points:	-2

   
   
6. Bob plays in the corner, which costs three points, bringing his balance to negative two.
   

   X
   O	X
   O		O

   	Bob's points:	-2
   	Alice's points:	-2

   
   
7. Alice's balance goes to zero, which isn't positive, so she can't play to block Bob.
   

   X
   O	X
   O		O

   	Bob's points:	-2
   	Alice's points:	0

   
   
8. Lucky for her, Bob also can't play: on his turn, his balance goes to zero.
   

   X
   O	X
   O		O

   	Bob's points:	0
   	Alice's points:	0

   
   
9. Now Alice gets two and plays on the bottom to block Bob, returning her balance to zero.
   

   X
   O	X
   O	X	O

   	Bob's points:	0
   	Alice's points:	0

   
   
10. Bob plays on the top.
    

    X	O
    O	X
    O	X	O

    	Bob's points:	0
    	Alice's points:	0

    
    
11. Alice sees she can't win, so she passes, keeping her two points.
    

    X	O
    O	X
    O	X	O

    	Bob's points:	0
    	Alice's points:	2

    
    
12. Bob plays on the right.
    

    X	O
    O	X	O
    O	X	O

    	Bob's points:	0
    	Alice's points:	2

    
    
13. Alice is forced to play at the top.
    

    X	O	X
    O	X	O
    O	X	O

    	Bob's points:	0
    	Alice's points:	1

    
    
14. That's a cat's game, but with a small differentiator: Alice has a remaining balance of one and Bob has a balance of zero, so Alice wins.