Analyzing Luck in Risk

Hello everyone I am an undergrad math student and I'm working with a group of friends on a mini project to try and analyze how much of a factor "luck" is in Risk games and how much of it is affected by strategy.

We'd like to start by defining luck in a way that we can denote mathematically. Apart from this, we also want to look at which strategies are more likely to help you win a game (say attacking, defensive, slow, aggressive etc) given that everyone is "equally lucky". Any help or suggestions would be greatly appreciated. Also, is it possible for us to get our hands on any of the game data from the app, in terms of troop placements, dice rolls, win-loss statistics etc?

Thank you again!