I played against myself in a way where I chose only the best options. The result was a game where, you could claim any square you wanted in any turn, but your opponent could do the same, and you both could choose anywhere on the board. In other words, it came down to basically a normal tic tac toe game.
Add a mode where it's a three by three of three by threes of three by threes. In other words, where as there are 9 tic tac toes in strategic tic tac toe, there would be 9 strategic tic tac toes, each worth a spot on the much larger tic tac toe game. call it something like super strategic tic tac toe or something
 "Strategic Tic-Tac-Toe"){kind=icon}