Tic-Tac-Toe as a Magic Square

Here's a game that looks like a math puzzle, but is really tic-tac-toe in disguise.

In the math game, two players take turns picking a number from one to nine. The numbers can only be picked once each game. The first player who picks three numbers that add up to fifteen wins.
A game board is usually drawn up like this:


1   2   3   4   5   6   7   8   9
The players take turns circling their number picks using different colored markers. The first player that can total fifteen with three of their picks wins. A sample game could go like this:

Player 1 circles 5
Player 2 circles 7
Player 1 circles 6
Player 2 circles 4 (to block 5+6+4)
Player 1 circles 8
Player 2 circles 2 (to block 8+5+2)
Player 1 circles 1 and wins 8+6+1

This is a game that is isomorphic to tic-tac-toe, but on the surface looks completely different. Two players in turn say a number between one and nine. A particular number may not be repeated. The game is won by the player who has circled three numbers whose sum is 15.


 Plotting these numbers on a 3×3 magic square shows that the game exactly corresponds with tic-tac-toe, since three numbers will be arranged in a straight line if and only if they total 15.

You don't have to memorize every square on the magic square, although that isn't too hard to do. Remember that the diagonal is 4-5-6 and the other two corners are 2 and 8. Play your regular game of tic-tac-toe, but pick the numbers that match up with the square you would normally place your X or O.

Just for fun:
Can anyone come up with a name for this game? Put it in the comments.