I'm trying to write an AI player for Risk. For placing armies and reinforcing borders, I've started with a heuristic approach that weighs the least number of fronts, the least continental fronts, the continent value, and maybe a continental affinity in the event of a tie. Depending on how you weigh the continent value against the number of continental borders, this always picks Japan or Argentina first, assuming the theatre is the original map.

I'm thinking there must be a "one true" next correct territory to put a unit, regardless of how many ready units there are, what the current state of the map is, etc. Likewise for attacking. Right now my AIPlayer attacks anywhere he has 3 or mor troop strength regardless of the opposition (very stupid, I know :-)

Trying to figure out this troop placement thing made me realize I don't actually have a working strategy as a human player. I've always basically just tried to get a connected map wherever my opponents weren't, or else just placed units randomly. But the more I look at it, the more I think the best early strategy is to take and hold South America. Trying to generalize the reasons for that strategy into something that would work for any map.