The computer AI is not very complex nor smart at these early stages, but are surprisingly fun and challenging, given their crudeness.
The computer can;
Look for viable opponents, and chooses one at random.
Chooses a path to the enemy, and attacks any enemy unit it crosses.
Buys upgrades if it has enough gold.
The only dynamic choose the AI makes is checking if the opponent is alive, it does so before deciding who and where to attack. The rest is either random or static choices.
It is currently three types of computers; Neutral, Aggressive or Defensive. Paths, upgrades and the timing of attacks varies depending on what type it is.
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