[Setup]Accuser and Investigator

[Not Known 15]

I am re- using an old concept of mine for this Micro Open setup... which is also somehow bastard-y
Setup:

6 Scared Townies

Scared Townie

You have no special powers.

Do not get elected for Accuser and accuse two Townies, do not lynch the Investigator, and get rid of the Mafia or ensure that the Investigator lives Day 4.

2 Mafia Goons

Mafia Goon

Factional Communication: You can talk with your partner here: LINK
Compulsive Factional Kill: Every night, one person of your team must kill someone who isn't jailkept.

Lynch the Investigator or reach parity with the town. Do not leave the Investigator alive till day 4.

1 Town (Activated Innocent) (Day 4 Investigator)

Town (Activated Innocent) (Day 4 Investigator)

You may, at any time, reveal yourself as Town. You can be forced to reveal yourself on Day 3.
If you are alive at Day 4 town wins.
Do not get lynched, and get rid of the Mafia or survive to Day 4.

Lynches and Nightkills are compulsive.
Day 1 has two stages: Selection and Accusation.
In Selection, the Town votes upon someone to be the Accuser.
If the Accuser is Mafia, the Accuser is lynched and the game proceeds to Night.
If the Accuser is Town, the Accuser selects 2 Accused. If they are both Mafia, town wins. If not, the Accuser gets lynched.
Then the game proceeds to Night with the Accused being jailkept.
On Day 2, the Accused are gladiated. After that lynch the game proceeds to Night 2 with the remaining Accused being jailkept.
On Day 3, if the Day 2 Lynch was an Accused, and Town, the Investigator is forced to reveal themselves if they are alive.
On Night 3, the last remaining Mafia must select someone to gladiate for the next day if the Accuser was Mafia.
On Day 4, town wins if the Investigator is alive, and the final lynch happens.

[mith]

Almost certainly too scumsided. A town Accuser losing the game (as opposed to just being lynched) if they don't pick both scum incentivizes town to claim investigator, so a day 1 investigator claim is meaningless. That means a 1/9 chance of picking the investigator day 1, and only a 1/28 chance of town winning in that case.

The town Accuser case is a mess to calculate EV for, but EV for scum Accuser is 229/315 (~72.70%); if we assume EV for town Accuser is same as Vanilla 2:5 (8/35, 22.86%) but accounting for the 1/28 chance of instantly winning, overall EV is around 25%. Town will do a bit better than that because of the investigator, but not much.

Without the loss condition on the town Accuser, it's probably closer to balanced - scum can force the investigator out to get a 1:6 (19/35), but investigator Accuser isn't a thing any more which helps.

[Sukima]

Well, even if town claimed investigator under threat of lynch, wouldn't lynching them anyways if they don't activate IC mean that you'll pick someone else and just deal with a shot investigator in that scenario?

IE 6/9 chance of town accuser, 2/9 mafia accuser, and 1/9 of the other two but a known investigator?

[Creature]

Without the loss condition on the town Accuser, it's probably closer to balanced

Wouldn't town sistematically accuse the investigator to keep him alive through jailkeep?

[Not Known 15]

Without the loss condition on the town Accuser, it's probably closer to balanced

Wouldn't town sistematically accuse the investigator to keep him alive through jailkeep?

I changed the win condition of the Accuser to let town win and to not accuse two townies. This has several effects:
It's easier to win for the Accuser, but they still need to perform well which means that they will do everything to ensure a Mafia pick(or better:two)
There is still an incentive for town not to get Accuser...
Town will NOT systematically accuse the Investigator because it is a good way to lose.
I also changed something else: If Mafia is chosen for Accuser Day 1 the remaining Mafia will be forced to gladiate someone Night 3- for Day 4.
This helps town a bit by ensuring a 1v1, although mafia chosen.

[mith]

Well, even if town claimed investigator under threat of lynch, wouldn't lynching them anyways if they don't activate IC mean that you'll pick someone else and just deal with a shot investigator in that scenario?

IE 6/9 chance of town accuser, 2/9 mafia accuser, and 1/9 of the other two but a known investigator?

You’re right, I spaced on reveal meaning mod confirmed. That does change things.

[Not Known 15]

Well, even if town claimed investigator under threat of lynch, wouldn't lynching them anyways if they don't activate IC mean that you'll pick someone else and just deal with a shot investigator in that scenario?

IE 6/9 chance of town accuser, 2/9 mafia accuser, and 1/9 of the other two but a known investigator?

You’re right, I spaced on reveal meaning mod confirmed. That does change things.

No, reveal means mod confirmed. Which means that Mafia cannot really claim Investigator(they will be told to activate IC and if they can't they are an impostor). I think the changes now make the game more town-sided... too much?

[mith]

I suspect it is still a bit scum-sided, but I don't have time to work through everything to confirm that...

[Sukima]

What's the EV if we assume random selection for everything except if investigator is chosen to be lynched, ever, in which case they'll activate IC and the other person gets lynched.

[mith]

I mean, that's basically exactly what the EV would be. I don't think there is any possible breaking strategy for this beyond investigator revealing when necessary.

The challenge in calculating this is (vs. a Vanilla variant) is in keeping track of the status of the investigator. It's not hard, exactly, just tedious.