Mafia Grey Flag
Mafia Black Flag
Normal day/night cycle.
If the first mafia member to be lynched is the white flag, then town wins immediately (like the godfather in a vengeful game, but not just on day one).
If the first mafia member to be lynched is the grey flag, then the town wins if they lynch a second mafia member (the game becomes white flag).
If the first mafia member to be lynched is the black flag, then the town wins if they lynch all three mafia (the game becomes mountainous).
The mafia win if they reach parity with the town.
EV-wise, we can assume all three mafia are equally likely to be lynched first given that there is a mafia lynch at all. Ergo, the EV is the average of three EVs:
-White flag lynched first: town's odds of losing are their odds of not mislynching every single day, which is (1 - (10/13)(8/11)(6/9)(4/7)) = 78.7%
-Grey flag lynched first: white flag, known 47.8%
-Black flag lynched first: 10:3 mountainous, known 20.8%
Overall EV is the average, a lovely 49.1%. Actually remarkably close both to 50% and to a normal white flag game. Pardon the somewhat overloaded terminology/the fact that "white flag", "grey flag" and "black flag" are all already names for other setups :p
In practice, this is likely to be incredibly skewed and vary a lot from game to game; the mafia black flag may have incentive to play as a jester early on, but that could backfire horribly if the grey flag is lynched. Different mafia members would have different incentives to avoid being lynched and different incentives to bus in different ways, and since mafia members would flip with the color of their flag interactions would be very interesting.
Also pardon me if someone has come up with this before, as it wouldn't surprise me too much.