[SETUP] Desperation Day

[callforjudgement]

• 7 Vanilla Townies
  
• 2 Mafia Goons (with a compulsive factional nightkill)
  
• If scum is lynched on Day 3, town automatically win. Otherwise, factions win or lose as normal.

The factional nightkill is compulsive to stop scum no-killing on N2 to push town onto evens.

EV is calculated as follows:

• There's a 2/9*1/7 = 2/63 chance of lynching scum D1 and D2, town win.
  
• There's a 7/9*5/7 = 35/63 chance of lynching town D1 and D2. You have a 40% chance of triggering the instant win, and a 60% chance of mislynching and losing.
  
• The remaining 26/63, there's a 4:1 situation going into D3, which has a (1/5 + 4/5 * 1/3) = 7/15 chance of a town win.

Total EV is (30 + 210 + 182) / (63 × 15) = 422 / 945, or about 44.66%.

Strategy here is fairly interesting, given that town may want to lynch a less likely scum candidate D2 (or even D1) in order to save a likely scumflip for their "desperation day" on D3, at the cost of scum getting a nightkill which they can use to influence how easily that player gets lynched (or spout WIFOM everywhere). It also makes bussing more viable early and less viable late than is usual in a 9p; I'm not sure whether people consider that a good thing or not.

Thanks to xyzzy, whose setups got me thinking along these lines.

[callforjudgement]

In general, in a setup like this I'd prefer to give town a better EV for lynching scum early than for mislynching early, and that should discourage no-lynching. I guess the best way to look at it is: lynching a townie is always better than no-lynching (because it gives you a smaller lynchpool on desperation day), so the only reason to no-lynch would be fear of lynching scum. You can avoid this by ensuring that lynching scum is always preferable to lynching town.

I guess the most unusual feature of this setup is that it has considerably less swing than a mountainous/white flag setup, whereas most setups have more. There's a point at which swing being too low basically makes the early game uninteresting because it has very little impact. I don't think that's happened here yet, but could potentially happen in a generalized version, and negative swing (where town benefits from mislynches) leads to huge problems outside a Nightless, as it implies that scum should probably be NKing each other rather than townies.

[callforjudgement]

In 2:7, no (see mith's numbers in #4).

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.

[callforjudgement]

I think you need to make scum feel like they're in danger of being lynched, specifically so that the associative tells happen. I agree with you that it's reasonable to not be too sad if you miss, though.

[callforjudgement]

Just as a note: I put a trial run of this setup into the Micro queue, but it's having trouble filling (only a couple of days left now). So here's a setup advert so that players who are interested in this setup and feel like playing it can check it out.

(It's possible that it won't fill anyway, of course. This might be bad timing for running the setup, but it might also be a sign that this sort of setup is unpopular.)