Want to play a game of Tic-Tac-Toe that's genuinely challenging and hard? Try "Ultimate Tic-Tac-Toe," in which each square is made up of another, smaller Tic-Tac-Toe board, and to win the square you have to win its mini-game. Ben Orlin says he discovered the game on a mathematicians' picnic, and he explains a wrinkle on the rules:
You don’t get to pick which of the nine boards to play on. That’s determined by your opponent’s previous move. Whichever square he picks, that’s the board you must play in next. (And whichever square you pick will determine which board he plays on next.)...
This lends the game a strategic element. You can’t just focus on the little board. You’ve got to consider where your move will send your opponent, and where his next move will send you, and so on.
The resulting scenarios look bizarre. Players seem to move randomly, missing easy two- and three-in-a-rows. But there’s a method to the madness – they’re thinking ahead to future moves, wary of setting up their opponent on prime real estate. It is, in short, vastly more interesting than regular tic-tac-toe.