I just made a test in real time without savestate or any luck manipulation and I managed to win against all colors in 8 turns on expert difficulty.
[edit] Someone suggested yesterday to edit my posts instead of making new ones. So here goes..
I played the game again today, for fun since I really love this game. :)
Managed to beat all computers in only 5 turns!
http://133an.sytes.net/~highness/risk-5turns.jpg
No manipulation involved. I had very good luck with defeating colors and getting their cards though. But now I really beleive someone could do a sub 5 turns run.
The game seems to be strange to manipulate. If you try to attack a country, and then load a state and attack it again you will get the same result, no matter what you press. However, if you attack another country before attacking your planned target, the result is very likley to change.
Therefor it can be good to loose some battles in order to not loose as much in a more important battle. Some times you can have 7 troops and attack a country with only 2 troops and still loose. So if you have a country with two troops and attack someone with 13 troops you are very likley to win without any losses on your planned target.