I have been addicted to this Flash based game Dice Wars this week. It is pretty similar to Risk. Lots of fun but tough to play just one.
I was having a trouble estimating the odds of winning any given battle, so I decided to figure them out. My probability is a little rusty, so I couldn't figure it out mathematically and had to go all Monte Carlo on this biyotch (I can remember all the the stuff with coins or balls and urns but can't figure out how to do dice).
This table shows the odds of winning a battle. The number of dice the attacker has is on top and number of dice for the defender on the side. A tie goes to the defender.
For example, if you have 5 dice taking on someone with 3 you have a 90.56% chance of winning. This table is really handy when trying to figure out your strategy.
Anyway, the game is good stuff, give it a try.
Update: The Kdice Wikispace has probabilities as well, and probably more accurate than the table above.