Game theory? Optimal play in a social deduction game (Werewolf/Mafia)

Anyone interested in helping me with a problem I've got?

It relates to the group social deduction game "Werewolf" (a variant on 'Mafia'), specifically proper play with a specific important role in the game ("Bloody Mary").

I can figure out how to brute force analyze it by making random choices and simulating a half million games on the computer, but I'd like to know if there is anything more effective I can do.

If anyone is interested in the details, I can lay it out here, but didn't want to waste time if no one would be interested. I've taken several Stats courses (for a computer degree), but nothing serious and deep.

- Nick