[SETUP] Common Ground

[TierShift]

I'm gonna run EV on that in a bit BB. I love the setup but it looks really mafiasided.

[TierShift]

Assumptions:
1) mafia don't selfnom (might do it sometimes, but not often, and I doubt it affects EV much)
2) town lynch every day and randomly (lynching from the list has 0 chance of lynching scum, but a higher than average chance to hit SK, therefore I find this reasonable)
3) SK always kills anyone on the list that is not himself (unless it's 3:2:1, in which case killing immediately loses)
4) mafia immediately win at 2:2:1, whether it's day or night (because that wasn't entirely clear)
5) SK still kills on last day mafia is lynched
6) SK doesn't kill if mafia are eliminated
7) 0:1:1 endgame is SK win since he has a kill and the maf doesn't
8) 1:1:1 is a town loss (otherwise town can make lazy plays for the draw)

Spoiler: mith's nightless formula

Calculating EV
EV[M,T] = (T-M)/(T+M)

This means there is always a NK on town unless it's 3:2:1.

Spoiler: boring calculations

Day 1:
town lynch+NK: 6/9-->4:2:1
mafia lynch+NK: 2/9-->5:1:1
SK lynch: 1/9-->6:2 nightless, 50% EV for town/mafia.

Town EV 1/9*1/2=1/18 Scum EV 1/9*1/2=1/18

Day 2:
If 4:2:1 (probability 2/3)
Town lynch+no NK: 6/9*4/7=8/21 -->3:2:1
Scum lynch+NK: 6/9*2/7=4/21-->3:1:1
SK lynch: 6/9*1/7=2/21-->4:2 nightless, 1/3 EV for town, 2/3 for mafia.

Town EV 6/9*1/7*1/3=2/63 Scum EV=6/9*1/7*2/3=4/63

If 5:1:1 (probability 2/9)
Town lynch+NK: 2/9*5/7=10/63-->3:1:1
Scum lynch+NK: 2/9*1/7=2/63-->4:0:1 nightless, 3/5 EV for town, 2/5 for SK

Town EV 2/63*3/5=2/105 SK EV=2/63*2/5=4/315

SK lynch: 2/9*1/7=2/63--> 5:1 nightless, 2/3 EV for town, 1/3 for mafia

Town EV 2/63*2/3=4/189 Scum EV= 2/63*1/3=2/189

Day 3
If 3:2:1 (probability 8/21)
Town lynch: 8/21*3/6=4/21-->mafia win

Scum EV=4/21

Scum lynch+town NK: 8/21*2/6=8/63-->2:1:1
SK lynch: 8/21*1/6=4/63-->3:2 nightless, 1/5 EV for town, 4/5 for mafia

Town EV 4/63*1/5=4/315 Scum EV=4/63*4/5=16/315

If 3:1:1 (probability 4/21+10/63=22/63)
Town lynch +no NK (SK wants to avoid kingmaker since he wins in 3/4 of the cases): 22/63*3/5= 22/105-->2:1:1
Scum lynch +NK: 22/63*1/5=22/315-->2:0:1 1/3 EV for town, 2/3 for SK

Town EV 22/315*1/3=22/945, SK EV=22/315*2/3=44/945

SK lynch: 22/63*1/5=22/315-->3:1 nightless, 1/2 EV for town/maf

Town EV=22/315*1/2=11/315, Scum EV=22/315*1/2=11/315

Day 4
2:1:1 (probability 6/63+22/105=106/315)
Town lynch+NK: 106/315*2/4=53/315-->SK win

SK EV 53/315

Scum lynch+NK:106/315*1/4=53/630-->SK win

SK EV 53/630

SK lynch: 106/315*1/4=53/630-->2:1 1/3 EV for town, 2/3 for mafia

Town EV=53/630*1/3=53/1890 Scum EV=53/630*2/3=53/945

Total town EV: 1/18+2/63+2/105+4/189+4/315+22/945+11/315+53/1890=214/945=0.226
Total scum EV: 1/18+4/63+2/189+4/21+16/315+11/315+53/945=97/210=0.462
Total SK EV: 4/315+44/945+53/315+53/630=589/1890=0.312

Not as bad as I originally thought. However, town absolutely have to eliminate one scum faction fast or keep facing NKs. Town preferably eliminate SK day 1 or SK day 2 or 3 with 1 mafia removed. Eliminating mafia day 2 also works, doing it on day 3 goes to a difficult 2:1 lylo since SK has limited associative tells. Removing SK post day 1 without a mafia removed makes it extremely hard. Not removing any faction until day 4 gives town a probability of only 1/12 of winning.

Looks like an extremely interesting set-up. Send me a message if you ever decide to run it.