How to Maintain the Balance of Power on Risk?
Hold a medium-to-small sized continent (like South America or Africa) and avoid aggression while you build up.  Attempting to take Asia, Europe, or North America will raise a lot of red flags, and Australia's defensibility makes it suspicious too.

RISK is defined in the later game by the ridiculous armies you get when trading in cards, so your main task is to be in the position to trade in for a lot, then bust out of your home and take another continent.