This implementation of Ultimate Tic Tac Toe is solved.

[rlbond86]

https://www.joachim-breitner.de/blog/604-Ultimate_Tic_Tac_Toe_is_always_won_by_X

With the current rules, it is possible for X to always win. Generally, the accepted rule change to avoid this situation is as follows:

If your opponent's move would force you to move in a board that is full or is already won by either player, then you may move anywhere.

See also http://mathwithbaddrawings.com/2013/06/16/ultimate-tic-tac-toe/ and the original post link at the top.