I think I fucked up the math but I'll check it tomorrow. The EV for the game before Omniscient selection should be townsided, but 20% chance of victory in a random shot might swing victory likelihood towards scum?
Come see me in the Great American Melodrama in Oceano
What happens if the Omniscient is lynched? They keep selecting while dead?
I have a feeling that it'd be possible to arrange a code which allows the Omniscient to indicate both members of scum to the town via their selection of nominated players. The scum's nomination would make things a bit more complex, but given the extra information from the D2 flip, it's quite probable that this setup has an 80% EV (i.e. town have a 100% breaking strategy that gives away no information about who the Omniscient is, and thus scum are on a pure guess to steal the win).
6 players alive is one of the worst numbers for this sort of breaking strategy, though, so it's possible it can't be broken. I'll have fun trying to figure such a strategy out, though!
OK, yes, this is trivially breakable: the town arrange a plan in which the Omniscient always chooses a Mafioso and townie that are adjacent in the player list, with the Mafioso first (potentially wrapping round the player list, e.g. the Omniscient can choose a Mafioso at the end and a townie at the start).
No matter who the scum choose, there'll be at most two possible picks that the Omniscient could have made (the most ambiguous possible situation is three adjacent players in the player list, at which point the Omniscient must have picked the first two or the last two). That means you know for certain that of two specific players, one of them is scum. You just lynch them both D2 and D3, putting you back into the same situation with one less townie and one less scum. Then the Omniscient chooses the same way again (we're now in a 3:1 setup assuming a mislynch D1). Again, there are only two possibilities for who the scum is, so you lynch them both D4 and D5 and get an 80% town win.
In order to hide who the Omniscient is, it's important to do no scumhunting at all; so D1 you just lynch the first player on the player list, and then you follow the Omniscient's signals (via the lynch choices) from there. You have a guaranteed 80% win no matter what choices you make so you may as well not give away anything as you're making them.
There's an occasional fail in your breaking scenario, assume playerlist is A B C d E f G, lowercase being mafia. A lynched first, Mafia pick B, Omni picks C d. Town go with the first two (aka B and C), and then lose after 2 MLs.
Oh, yeah, I missed that the maf pick is first, so even in f G B or C d E, you're most definitely still lynching one of the first two because it's either the top slot or the middle slot, and cannot be the bottom slot.
