I'll play in the bottom-right corner (2,2) for several strategic reasons:

1. It blocks the opponent's potential diagonal threat from top-left (0,0) through my center (1,1) to bottom-right (2,2)
2. It creates two potential winning lines for me:
   - A horizontal line across the bottom row (if I can later play at 2,0 and 2,1)
   - A vertical line down the right column (if I can later play at 0,2 and 1,2)
3. This move forces my opponent to play defensively rather than building their own attack

By controlling a corner that connects with my center position, I'm setting up multiple winning paths while blocking the opponent's most direct threat.