Ultimate Tic-Tac-Toe takes the game you already know and makes it genuinely hard to think about. Instead of one 3x3 board, there are nine of them arranged in a larger 3x3 grid. You win a small board by getting three in a row. You win the game by getting three small boards in a row. The catch is that every move you make determines which board your opponent must play in next.
That single rule changes everything. Sending your opponent to a board that is almost full gives them a free choice. Sending them somewhere you are close to winning hands them the chance to block you. Every cell on every board has consequences two levels deep.
The game spread online around 2013 and has appeared in maths classrooms and puzzle communities as an example of nested strategy. It is significantly harder to solve than regular tic-tac-toe, and no complete optimal strategy is publicly known.
On your first turn you can play anywhere. After that, the cell you play within a small board determines which small board your opponent must play in next. The position of your cell maps directly to a board in the larger grid. If your opponent sends you to a board that is already won or full, you get to play anywhere.
Win three small boards in a row, horizontally, vertically, or diagonally, to win the match. A small board is won by getting three of your symbols in a row within it, just like regular tic-tac-toe.
The strongest opening is the centre cell of the centre board. It sends your opponent to the centre board, where the middle cell is the most valuable, and you have already taken it. Most beginners ignore this entirely.
Avoid sending your opponent to a board where they can win immediately. Before placing your piece, check where your move will send them and what they can do there. Boards that are nearly full give your opponent a free turn, so avoid filling boards without winning them.
Think two moves ahead: not just what you are doing, but where you are sending your opponent, and where they will send you back.