We had family game night last night, and my 4yo son wanted to play Risk. He likes the little army men, and before we had just played with the army men on the board, but I decided to invent a simplified game for him to play. I just made it up as we went along, but I was pleased with how it turned out.
Each person takes a turn drawing a card from the pile. If a person draws a wild card, then they can place their army on any empty country, or if there are no empty countries, they can pick any inhabited country and do "battle." During a battle each player rolls one die, and the player with the highest number wins (in the case of a tie you roll again). The winner either keeps the country, or kicks out whomever was inhabiting the country.
When a player picks a country card, if the country on the card is empty, then they place an army on the country. If the country is not empty they do battle.
Each player keeps the cards they draw, and during their turn if they have three of a kind, then they get to place an extra army on any empty country they choose, or if there are no empty countries, then they can choose an inhabited country and do battle.
The game ends when the pile of cards is exhausted, and there is an army on every country. My thought was that at the end we would count up the number of countries that each player had, and the one with the most would win. We didn't get to do that last night, though, because my son wanted to drive a cannon through all the countries on the board making all the armies fly everywhere (who can blame him!).
I don't think there is any strategy to this game. You are basically subject to the randomness of the cards you draw, and to the dice in the case of battle. You could assign extra points for holding an entire continent at the end of the game, but I'm not sure there are enough opportunities to choose on which country you'd like to place an army.
So there may be room for improvement, however, it was surprisingly entertaining, and it kept the attention of my son. :)