(bug report) I think I found a winning strategy for the first player in the 3x3 round-based variant.
First, the player starts at the corner with a circle, and after the opponent moves, put a square near the marked circle orthogonally, in a row/column which doesn't have the opponent's circle. This prepares for a win while simultaneously attacking any blocking piece. After that, there are multiple scenarios:
- If the opponent doesn't block the winning square, mark the square and win. It doesn't matter if the opponent defends by attacking or not.
- If the opponent does block the winning square, but using a non-circle piece, it will be immediately attacked by the player's square piece. The player then marks the square and wins.
- If the opponent blocks the winning square using a circle piece, simply wait. Mark any piece to pass the turn or block any potential losses. Note that the opponent has no attacking pieces on the board yet. Then wait for the opponent's move and mark on the winning square. It also doesn't matter if the opponent defends by attacking or not.
Assuming this strategy is valid, I suggest attacking first before checking the winning condition.