[SETUP] No Limits Mafia

[mith]

It's way worse than that if scum don't counter. 3:8:2 Nightless with ICs has an EV of 13/15 (~87%). ICs are brutal for Mafia in Nightless. For no reveal, you just have the ICs pick the lynch each time, lynch everyone, and as long as they don't pick the last two or three of the last four as Mafia, town wins.

For the CC case, if it is truly Nightless (rather than the OP setup) then you lynch one at a time until you have lynched the fakes. This means you are either in 2:8 Nightless (60%), 2:8:1 Nightless with IC (EV = 7/9, ~78%), or 2:8:2 Nightless with ICs (EV = 14/15, ~93%) with equal probability, for a total EV of ~84% (113/135).

Two fake claims would be 1/2 1:8 Nightless (7/9), 1/3 1:8:1 Nightless (8/9), and 1/6 1:8:2 Nightless (1), for a total EV of 23/27, ~85%, so 1 fake claim is best.

Basically, don't used named townies in Nightless unless you are very careful about it. (It's interesting though that the EVs are so close for the three Mafia claim strategies. 117/135, 113/135, 115/135)

[mith]

For the actual setup with 1 fake claim, it goes to 2:8 after lynches and then 2:4 after kills, EV of 33%. (No fakes has the same problem as Nightless; two fakes is obviously not better than 1, since you're lynching all the claims either way.)

I suspect town's actual best strategy is just to ignore the setup entirely and lynch people until they either lose or get down to two+ town players and win. EV would be the same as 3:10 Nightless, EV = 7/13 (~54%, as Awoo says). Going to night is strictly bad for town, and you can't flush out the fake claims without doing so.

[mith]

What I'm saying is that if it is truly Nightless (Mafia get no kills), then there is no punishment for town stopping their lynch fest and taking them one at a time. That way, you may hit the fake claim D1 without taking out the two real docs.

But I now understand you're saying that the OP setup is still in play, you're just ignoring it by lynching all the claims (if there are fakes), making it Nightless with no flips. So yes, 60%, and ignore my comment about 33% above.

[mith]

Incidentally, if it's 5:8:2 instead of 3:8:2, and there is one fake claim, it is better to pick one of the claims and assume it's an IC. There is a 2/3 chance of being right, making the game 4:8:1 (5/9) for a 10/27 chance overall, vs. 1/3 for 4:8 Nightless.

(It may be slightly better still to pick one of the non-claims to be assumed IC - if you are able to lynch the other 11 without losing, you're down to 1:2:1 (2/3) for a 4/9 overall. But it's possible that the odds of losing before you get to that point are enough the other way. I wouldn't be at all surprised if either way results in the same 10/27.)

At this point we're basically talking about a Nightless Neighborhood setup (with two neighborhoods of [M-1]:[T-2] and 1:2).

[mith]

See, my question on this is what's stopping town (or mafia) from saying "Let's lynch everyone who we feel is scummy till we get to 4 people, end the day and hope that we killed all the mafia or if not, we have at least one mafia left so we can go into a 3p lylo"?

Let's say you aim to go down to 4 players and stop. There are three possibilities:

a. You've lynched all the Mafia - yay, you win
b. You've lynched all but one of the Mafia
c. There are still two or three Mafia - boo, you lose

Now let's say you actually made it to 4 players and haven't won or lost yet (so you know you're in case b.). If you now stop and let the Mafia kill, you have 3p lylo as you said, EV is 1/3. However, if you just keep going, you get two chances to lynch the remaining scum, EV is 1/2.

So it's better to just keep lynching and never let this game go to night, as Awoo suggested (overall EV is 60%).

[mith]

That is kinda the point: If the best strategy for town is to ignore most of the mechanics and treat the game like non-flip nightless, it's not a good setup.

[mith]

Yeah, it'd just be a different type of game. With 3:10, 6 lynches gets you down to 3:4 (scum win after NK), 2:5, 1:6 (1:5 after NK), or 0:7 (town win); if you keep the NK mechanic from OP, 2:5 is also an immediate scum win. There may be some cases here where it's better for town to not use the maximum available lynches, but otherwise it's just a somewhere-between-Vanilla-and-Nightless setup.