[SETUP] Desperation Day

[mith]

I like it... The difference between 1:4 (7/15) and 2:3 (2/5) is small enough that scum's main concern should be not both getting lynched the first two days. How they choose to do that is what makes it interesting. (D2 would be be less interesting after a town flip, though.)

One small negative is that town no lynching the first two days doesn't hurt their EV all that much (8/21 = 38.10%), assuming scum are required to kill. Doesn't break the setup, it's still in the town's best interest to go for it, but I wonder if there is ever a point in the generalized setup where no lynching becomes viable:

M Mafia
(M+2N-1) Townies
If scum is lynched on Day N, town automatically win.

(If so, easy enough to put some sort of clause in to handle this case. The most subtle one would be something like "If no scum are lynched Days 1-N, scum win.", which reduces the no lynch EV to M/(M+N-1), 2/7 = 28.57% in the 2:7 setup.)

[mith]

Yeah, easy enough to find a count where town want to mislynch:

3 Mafia
6 Townies
If scum is lynched on Day 2, town automatically win.

Day 1 Lynch:
3/9 -> 2:5; 2/7 + 5/7*2/5*1/3 = EV 8/21
6/9 -> 3:4; EV 3/7 = 9/21
EV 26/63 = 41.27%

And I could see a setup like this being interesting, in some respects - day 1 you'd be trying to pick the most town player, and then day 2 you're trying to find scum. (This particular player count wouldn't be much fun though, since the day 1 result has so little impact.)

No lynch is still worse than trying to lynch, here, but that may be an artifact of using an even Desperation Day; no lynch is still LyLo, with one extra townie and no way to restore parity (another no lynch doesn't lose immediately, but does miss out on the auto win chance).

[mith]

The post-D1 EVs for the 2:7 setup:

Lynch scum: EV 19/35 = 57/105 (54.29%)
Lynch town: EV 44/105 (41.90%)
for Vanilla, that second number is 8/35 (22.86%).

So a D1 lynch in this game has about 40% of the impact on EV vs. a Vanilla game.

[mith]

In 3:6, also no; naive EV theory says it is, but the scum will NK one of their buddies if town mislynches because it gives them a better EV, and so you'll end up at 2:5 on day 2 no matter what happens.

Good point. You'd want to require scum to kill town in a setup like that, but it's not interesting enough on its own to warrant the extra rules.