[SETUP] Hospital Hijackers

[biancospino]

What happens in a 2/1/1 endgame? Draw? Town is actually the only faction incapable of losing at that point so maybe they should win, after all at that point there are no more threaths to the town.

3/2/1 after a circleprotect wouldn't actually be that bad for Town from an EV point of view. The SK and one Mafia is known.

• If town lims the Mafia, it's 3/1/1 entering night, they circleprotect excluding the SK. If the SK kills that's 2/1/1 or 2/1/0 entering day, with all scums known and all townies essentially bulletproof, so it's either an happily ever after or a town win; if SK does not kill (or their victim is saved) and maf kills SK (they can't kill town or they get caught), it's 3/1. Now, that isn't actually MeLo; if there's a mislim, town can still win if the two doctors circleprotect; so town wins iff they can find a group of two players containing the scum, which has a probability of 1/2 if it's done at random.
  (I think the scum in 3/2/1 would try to kill the SK and try to win instead of risking an unavoidable draw; I have no idea what the SK would do since they would have pretty much lost already.)
  
• If town lims the SK, it's 3/2 entering night. circleprotecting here obviously doesn't work; if the docs protect at random (except that they don't protect the known scum), town has a 5/9 probability of not dying during the night, at which point it goes to 3/1/0 which like above has an EV of 1/2

Assuming Mafia would try to avoid the branch that could result in a 2/1/1 draw, town still has a 1/2*1/2+1/2*5/9*1/2=7/18~39% EV (about the EV of 11:2 mountaneous for reference)

after one miselimination

and if pretty much the worst thing possible happens N1.

[biancospino]

Oh, yeah, I was operating under mandatory lims for some unfantomable reason. However, this does leave the door open for a pretty nasty strategy for town thou. Consider the following strategy:

• no-lim D1.
  
• circleprotect at night. N1, each doc protects the player one position down the playerlist (the last protects the first), N2 two positions, N3 three etc (the scaling isn't strictly necessary, but it does allow more occasions to have the sk possibly be able to kill a mafia which would be very theatrical. The EV doesn't actually change if the cycle is fixed thou, as long as it is actually random)*
  
• keep no-limming until someone dies at night.
  
• If exactly one player dies at night, lim their "protector". If two players die, lim one of their "protectors" at random. When either of those events happen, abandon this strategy.

In addition, use the following strategies for situations that may occur:

• If the game, at some twilight, goes to 4/1/1 with a known sk or 4/2/0 with a known mafia, circleprotect excluding the known antitown.
  
• If the games gets to a point where only one antitown faction remains and all of its members are unknown, circleprotect around everyone.
  
• If the games gets to 5/1/1 with no known antitown,
  cease all lims again until a death occurs
  , an circleprotect until that happens.
  
• If at any point there is a known antitown and town has a majority, lim them (if there are two choose at random).

I ran a simulation of 10,000,000 games using these rules (with very shoddy programming, so I guess I may be off by a smidge), with the added assumption that antitown will never attempt to perform a kill that would reduce their EV but would always attempt a kill that would increase their EV, and that scum does not want an Happily Ever After, so will attempt a kill if not doing so would result in a draw and doing so would not result in an autoloss.
Town won around 52,8% of the time, no dayplay required (whereas one would want a ~33% winrate per faction I suppose). And notably the strategy explicitly requires nolimming

a lot

, which is quite undesirable

*It's actually possible to choose the offset in a (almost) truly random fashion without using provable randomness in the thread explicitly and without requiring faith in other players. Whether or not this is against the spirit of the rule on randomness is unclear

Spoiler:

Just have all players agree to check the Dow Jones at a very specific moment in time during the Night, convert it in base N-1 where N is the number of living players, and use the

last

digit as the offset.

I've actually done pretty much this very thing once in a Real Time meatword Mafia game.