Tic-tac-toe is usually treated as the game you teach a child five minutes before the child discovers that competent play makes it boring. Math Lair looked at that and found an entire mathematics lesson hiding underneath.
Read Math Lair’s tic-tac-toe page
The page explains standard play, then quickly moves into variants: magic-square tic-tac-toe, avoidance or misère play, movable markers, multiplayer versions, 3-D tic-tac-toe, Ultimate Tic-Tac-Toe, and other rule changes that turn the familiar grid into something less trivial.
From there it gets more interesting.
Math Lair uses the game as an introduction to combinatorial game theory and generalized tic-tac-toe. One section discusses Frank Harary’s idea of choosing polyomino shapes as the winning objective and asks which shapes can actually be forced by the first player.
That leads to “winning” and “losing” animals, smallest board sizes, move counts, and the observation that once a target contains a smaller impossible shape, the larger target is impossible too.
The page even gives a clean strategy argument for why the second player cannot have a guaranteed winning strategy in generalized tic-tac-toe: if such a strategy existed, the first player could make an irrelevant opening move and then copy it.
This is what educational hobby pages do well
The page was last updated in March 2020, but its design and structure feel much older in the best possible way. It is one long, patient explanation with links, diagrams, questions, references, and almost no interface between the reader and the idea.
That matters because mathematics pages age unusually well when they are built around reasoning instead of presentation tricks.
A flashy interactive demo may break. A clearly written argument about strategy usually does not.
Math Lair also shows how an old-fashioned personal educational site can outperform a search result. Searching “tic-tac-toe” gives you millions of playable boards. This page asks why the game behaves the way it does, what happens when the rules change, and how one simple game connects to larger mathematical ideas.
CacheRat’s 1,967 Ancient Web Domains research list has many pages like this: narrow subjects explored far past the point a commercial site would bother.
The Web is good at breadth. Pages like Math Lair remind us that individuals were often better at depth.