I'll play at position (2,0) for several strategic reasons:

1. This creates an immediate threat along the left column, as I would now have pieces at (0,0) and (2,0).

2. If my opponent doesn't block at (1,0) in their next move, I can win by completing the left column.

3. This position also helps control the bottom-left corner, which prevents my opponent from creating a potential diagonal threat.

4. Looking at future moves, if my opponent blocks the left column at (1,0), I still maintain good board control and can pivot to other winning strategies.

This move forces my opponent to play defensively while maximizing my chances for a win if they make a suboptimal move.