Army encirclement

The last time I did this was on CivBE. AI had a small group of units headed for my capital which was behind two cities and so after they all ran into the space between three cities, I purchased all the hexes to block off their retreat. They sat there for like 20 turns shuffling units around until they dow'd on me but by then I had them surrounded on all sides with infantry. >.> Combined with ranged support, it was ugly for the AI.

Surprisingly enough they tried to retreat, but my land rovers made it pointless for them to retreat because the enemy infantry couldn't outrun the land rovers.
 
I can think of better uses for gold than to just buy tiles to encircle a soon-to-be invasion force. And if the AI intends to DOW you anyway, your borders will soon become open, whether you like it or not. Might as well buy a few archers for defense than to encircle the units by buying potentially mediocre tiles.
 
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