Mafiascum.net

• 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.

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.)

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.

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).

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.

Is town victory percentage lower if scum is lynched d1?

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.

interesting setup. d2 could be a lot of fun.

a comment about mountainous setups from a purely anecdotal standpoint: sometimes a D1 scum lynch in two scum mountainous games can be damaging as it removes association tells from the game completely. i've only seen a couple of games go this way, so no real data to back up that claim, but i think lynching scum d1 in mountainous isn't that important, to the point where i'd just use d1 for policy lynching a lurker or the most anti-town/unhelpful player.

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.

In post 6, callforjudgement wrote: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.

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.)

I'm curious what this would look like in a multiball version. I'd think a 9:2:2 would have Day 3 as the Desperation Day. However, scum seem to like killing scum at night. That will probably have to be taken into account.

A better on would be 11:2:2. 9:2:2 would leave town outnumbered Day 3 if only town died with no targeting the same person for nightkills.

In post 11, Gamma Emerald wrote:I'm curious what this would look like in a multiball version. I'd think a 9:2:2 would have Day 3 as the Desperation Day. However, scum seem to like killing scum at night. That will probably have to be taken into account.

Multiball in this would have to have the scum team lynched in d3 losing I think. One scum team lynching the other should not auto = town win IMO.