All right.

It looks like there are a certain number of indefensible positions. If you can get to one of these, you're good. If not, just make a move that doesn't allow your opponent to saddle you with one. Taking one off of the longest row that wouldn't allow him to put you in one seems to be a good move.

The ones I've found so far are 0-2-4-6, 0-1-4-5, 0-1-1-1, 0-1-2-3, 2-3-4-5, 1-1-3-3, 0-1-1-3, 0-1-3-4, 0-0-a-b (where a+b is even), 1-1-5-5, 2-2-5-5. (I'm not sure about those last two.) Oh, and, obviously, 0-0-0-1.

The computer is a pretty bad first move player. Most of the time, you can get him into one of these predicaments in your first move.