I read the book 'Tic-Tac-Toe Theory (author : Jozsef Beck)', and saw the author's mention like this.
"we know only two explicit winning strategies in the whole class of $n^d$ Tic-Tac-Toe games: the $3^3$ version, which has an easy winning strategy, and the $4^3$ version, which has an extremely complicated winning strategy."
I think author maybe assume $n \ge 4$, because I think that it is easy to make winning strategy for first player in any $3^d$ Tic-Tac-Toe. But I want to confirm definitely, so post this question. Is it right that author assume $n \ge 4$ without comment?
And I have one more question. Was following proposition proved?
"if first player have winning strategy in $n^d$ Tic-Tac-Tow, then first player also have winning strategy in $n^{d+1}$ Tic-Tac-Toe."