You should never have to use more than 9 moves for 3x3. Hitting the same square twice has no net effect, even if the two moves on the same square are separated by other moves.
There is a lot of math involved in this game and you can quite quickly note some less obvious rules like this one. Maybe there are some very nontrivial, but interesting things out there. I'm not good enough in combinatorics to tell... :D