Ultimate Tic-Tac-Toe

Every move does two jobs

Ordinary tic-tac-toe is solved and dull. Ultimate Tic-Tac-Toe fixes that with a single rule: the cell you play in decides which of the nine small boards your opponent must play in next. Drop your mark in the top-right cell of any board and the computer is sent to the top-right board. So each move you make carries two purposes: trying to win the little board in front of you, and choosing where to strand your opponent. The second job usually matters more than the first.

Beginners chase small-board wins and hand the computer a gift with the same stroke, sending it somewhere it can complete a line or set up a fork. Before you commit, look at where the move points and ask what your opponent gets to do when they arrive there. Read every candidate cell twice: once as territory claimed here, once as a destination handed to the other side.

The self-send and the opening

The cell-to-board mapping has a quirk worth exploiting from move one. Play the cell whose position matches the board you are standing in, the centre cell of the centre board, say, and the opponent is sent right back into that same board. Call it the self-send: it is the closest thing this game has to controlling the tempo. The most popular opening is exactly that move. Centre cell of the centre board claims the strongest cell on the strongest board and forces the computer to answer inside the centre, where each of its nine possible replies ships you off to the matching board holding the first move there. Corner-heavy plans are the main alternative, bouncing play around the four corner boards, whose big-board cells feed three winning lines each against the edges' two. Both approaches beat drifting; pick one and let it organize your first half-dozen moves.

Mind the free move

Here's the tactic that decides close games. When you send the computer to a board that's already been won or completely filled, it doesn't have to play there. It gets a free choice of any open board on the map. That's a big concession. Strong play is largely about avoiding those free gifts and, when you can, forcing the computer to hand one to you instead. The late game turns this into bookkeeping: before any move that wins or fills a board, scan the whole map and ask which boards are one move from falling. A free move is only safe to give when the answer is none.

• The centre small board feeds the most big-board lines, so winning it is worth extra, but be wary of ever sending your opponent there.
• Think one layer up: three small-board wins in a row take the match, so treat each little board as a cell in a larger game you're also playing.
• Sometimes it's right to lose a small board on purpose, if the winning move would send the computer somewhere dangerous.

Sacrifices and the long game

Because every cell is also a command, the exchange rate between boards is strange. A small board is worth one cell of the big grid, but initiative compounds, so trading a board away for two or three turns of favourable destinations is often a bargain. The practical version: when the computer builds two-in-a-row on a board you have been sent to, check where the blocking cell would send it before you block. If the answer is somewhere lovely, consider conceding that little board and playing the cell that strands the computer instead. Games are won by players who track what each move buys on both layers, not by players who win the most skirmishes.

A doodle that went viral

Plain tic-tac-toe is a solved bore, 765 essentially different positions and a guaranteed draw between two people paying attention. The layered version rescues it by making the board too big to exhaust and every move double-edged. It circulated for years as a pencil-and-paper variant under names like meta tic-tac-toe and nine-board before a 2013 blog post by the maths teacher Ben Orlin sent it around the internet, and it has been a favourite of programming courses ever since, because writing a strong player is genuinely hard. Nobody has published a complete solution, and the best bots reason by Monte Carlo tree search, playing out thousands of random futures per move instead of calculating to the end. The depth you feel on your third game is real; the computers feel it too.