Dots and Boxes
The pencil classic โ close a box, go again. Chains decide everything.
About this game
Click between dots to draw an edge; complete a box's fourth side to claim it and move AGAIN โ the rule the whole game turns on. The AI takes offered boxes and avoids giving any away while safe moves last; the endgame is where you can outplay it.
The chain game hiding in a kids' game
รdouard Lucas (Tower of Hanoi's inventor) published this in 1889, and it runs deeper than its pencil-and-paper looks. Phase one is avoidance: never draw a box's third side. When safe moves exhaust, someone must open a chain โ and the extra-turn rule cascades, so whoever opens SHORT chains while keeping long ones wins big. The expert move the AI doesn't know: the double-cross โ decline the LAST TWO boxes of a chain (draw the closing edge instead), sacrificing two boxes to force your opponent to open the next chain. Control every chain-opening this way and the endgame is a harvest. Counting chains before the first sacrifice is the entire high-level game โ arithmetic as combat. Tic-tac-toe and Connect Four teach the shallower cousins.
Frequently asked questions
Why do I get another turn for a box?
It's the core rule โ completing a box grants an immediate extra move, which lets whole chains fall in one turn. Everything strategic flows from this cascade.
What's the double-cross strategy?
When gifted a chain, take all but the last two boxes, then close the chain with a non-capturing edge โ sacrificing two boxes but forcing your opponent to open the NEXT chain. Chain control beats box greed.
When does the real game start?
When safe edges run out โ every remaining move opens some chain. Strong players count chain lengths BEFORE that moment: an odd or even chain count decides who should be forcing whom.
How does the computer play?
Honestly but shallowly: it completes boxes, never volunteers a third side while safe moves exist, and picks randomly otherwise. It doesn't know the double-cross โ that's your edge.