A buddy in another community shared this undergraduate paper on Mafia optimization and probabilities.

The paper just talks about mountainous games with single-opportunity-at-EoD voting and ERIT (Elim Random In Tie)

The relatively intuitive proof of increase of mafia win probability on odd total player numbers, as well as the final optimal ratio equations are both very interesting IMO. e.g. 11/2 is not what people would expect to be optimal for a 13er.

The fact that they specify the recurrence equation on players makes for a good formula IMO, though. Makes it easier to adapt to games with roles too.