[OLD] Open Setup Ideas and Discussion

[Ircher]

Day Vig Gambit

11-Shot Lynchproof Survivor

Town 2-Shot Day Vigilante

1-Shot Lynchproof Townie

Vanilla Townie

1-Shot Lynchproof Townie

Vanilla Townie

Vanilla Townie

Vanilla Townie

1-Shot Bulletproof Townie

Town Wins: If the Survivor is day-vigged.
Survivor Wins: If the Day Vigilante uses up all their shots and miss or the Day Vigilante is lynched.
End-game Scenarios: If only the day vig and the survivor remain, the survivor wins (so that route is not a broken strategy).

The game is by definition night-less.

[callforjudgement]

First, that's not Mafia.

Second, it's broken (100% town EV). BP townie claims. (If they're counterclaimed, you lynch both claims and dayvig the survivor. Or dayvig them both, either works.) Assuming no counterclaims, dayvig claims (and counterclaims, if necessary, with a bullet), then you lynch every unclaimed player twice. Anyone who survives must be the Survivor and so gets dayvigged, and there's no chance of town losing as there are at least two townies (the BP townie and the dayvig) alive, so you have to end up lynching the Survivor eventually.

[mith]

If a townie is lynched D1, scum get a "free shot" at the vig overnight (automatically winning if it hits, and going to a 50% EV endgame otherwise).

Maybe I'm missing something in the setup, but if townie is lynched D1, the Vig has a 1/3 shot of hitting both scum if he shoots, while letting scum shoot has an EV of 1/4.

Also, Vig shooting in the scum lynch case has the same EV - 1/3 hit, plus 2/3*1/2 lynch. Doesn't matter if Vig is outed or not, or if the lynch is scum or town, Vig can shoot. EV is exactly 50%. I doubt they can improve on this.

Ah right, I missed that the vig would shoot after a townie lynch (which is weird, because I considered that case correctly in my previous analysis).
After a scum lynch, though, the vig dies if they shoot and miss, leading to a 1/3 rather than 1/2 chance of lynching correctly, so the EV in the "lynch scum then vig someone" case is 1/3 + (2/3*1/3) or 4/9. (Unless I've missed something again, which is quite possible.)

Yeah, you're right (well, except that it's 5/9, not 4/9). I had this right in a previous version and then forgot the Vig would die I guess. So it matters whether Vig is outed for that case, and total EV is:

1/10*5/9 (Vig outed, scum lynch) + 2/5*2/3 (Vig not outed, scum lynch) + 1/2*1/3 (town lynch) = 44/90, just barely under 50%.

[mith]

I am enjoying the discussion.

I am just assuming in a setup like this that playing things by the numbers is the right play without considering overall Optimal play? What I mean by Optimal is taking into consideration the psychology of the game as well as the numbers. Obviously depending on the setup the Optimal play is going to change. Take for example a Vanilla game where most of the game is itt. Is there a point where weighing in on the psychological components outweighs the EV?

The EV is basically the "baseline" play that town use if they don't have anything better. You can normally assume that town do better than the EV in practice. (For example, if you're in 2:1 lylo with one confirmed town, EV says that town have a 50% chance of winning, but in practice the confirmed townie gets to choose who to lynch and thus (you'd hope) town actually have a better than 50% chance.)

When you have a breaking strategy present, the simplest thing you can do is to follow the strategy, but use scumhunting to decide which choice of player you make to lynch/vig/investigate/etc. when you the strategy gives you a free choice of player. This is a pretty common play (and leads to town scoring well above EV in Nightless games; oddly, this doesn't seem to happen to so much of an extent in games with a normal day/night cycle). Much riskier is deviating from the strategy because your reads are strong enough that a normally low-percentage play becomes a good one. It's rare for players to be this confident in their scumhunting ability, and even players who are that confident are often incorrect to be, so it doesn't happen very much and doesn't succeed all that much when it does.

In your example of a vanilla/mountainous game, EV theory just says "lynch any player", which in practice becomes "lynch the scummiest player", and thus theoretically allows town to win above EV. (In practice, town do well below EV in vanilla-heavy setups with a normal day/night cycle such as 11:2 Mountainous and (as of the most recent statistics, although I suspect they're out of date) White Flag, but that may be the result of a small sample size.)

A quote on this from way back in 2009:

Anyway, the EV is calculated for some theoretical "optimal play" by both sides. If there *were* a clear advantage to be gained by the scum in playing a certain way, the town can always counter it by lynching in a truly random manner (by "random" here I mean "lynch independent of argumentation", not "lynch any living player with equal odds", since clearly there will be some situations where we want power roles to out themselves before being lynched, or we want to lynch from a subset of the living players, or whatever).

And the assumption that the scum are playing optimally ensures that the town can never do better than random, either.

In practice, it doesn't actually work out this way; but that's because players don't play optimally. In other words, balance = EV, deviation from EV = skill.

So, yes, random lynches and NKs (depending on optimal strategies which depend only on the information that we the outside observers have, and not on in-game tells and so forth), justified by the above hand-wavy pseudo-math.

Emphasis added. I think there's a temptation to argue that with optimal play, town can do better than random, but this neglects the fact that EV assumes

both

sides are playing optimally.

[Ircher]

First, that's not Mafia.

Second, it's broken (100% town EV). BP townie claims. (If they're counterclaimed, you lynch both claims and dayvig the survivor. Or dayvig them both, either works.) Assuming no counterclaims, dayvig claims (and counterclaims, if necessary, with a bullet), then you lynch every unclaimed player twice. Anyone who survives must be the Survivor and so gets dayvigged, and there's no chance of town losing as there are at least two townies (the BP townie and the dayvig) alive, so you have to end up lynching the Survivor eventually.

It's not brokem

If the Dayvig runs out of shots, town autoloses.

Still, you could get rid of the BP and make it vanilla if that makes it better.

Finally, even though I called it survivor here, I could very well just call it a Mafia Goon in a nightless game and then it would be considered mafia.

[JasonWazza]

First, that's not Mafia.

Second, it's broken (100% town EV). BP townie claims. (If they're counterclaimed, you lynch both claims and dayvig the survivor. Or dayvig them both, either works.) Assuming no counterclaims, dayvig claims (and counterclaims, if necessary, with a bullet), then you lynch every unclaimed player twice. Anyone who survives must be the Survivor and so gets dayvigged, and there's no chance of town losing as there are at least two townies (the BP townie and the dayvig) alive, so you have to end up lynching the Survivor eventually.

It's not brokem

If the Dayvig runs out of shots, town autoloses.

Still, you could get rid of the BP and make it vanilla if that makes it better.

Finally, even though I called it survivor here, I could very well just call it a Mafia Goon in a nightless game and then it would be considered mafia.

DAY VIG DOESN'T SHOOT UNTIL SOMEONE LIVES THROUGH 2 LYNCHES.

You gave the survivor a confirmed way to be given away.

[callforjudgement]

Finally, even though I called it survivor here, I could very well just call it a Mafia Goon in a nightless game and then it would be considered mafia.

No it wouldn't.

When people say "not Mafia" in this thread, that normally means "there isn't a scumteam consisting of 2 or more members". (It can also mean "town isn't the largest faction", but that's much rarer and mostly happens with AitP variants.) What the roles are

called

is irrelevant. (In particular, the town is typically considered to be the faction with the least information. This is why town/scum tend to reverse roles in 1:1:1 endgames; the scum don't necessarily know which of the other players is the townie, but the townie knows both the other players are scum, and thus knows more.)

[callforjudgement]

I think there's a temptation to argue that with optimal play, town can do better than random, but this neglects the fact that EV assumes

both

sides are playing optimally.

That is indeed a good point. I guess the counterpoint is "if town think they're going to play below EV, they can just agree to random-lynch" (which is where IIRC the commonly seen rule against provable randomness comes form), so if you assume that the players are perfect

strategists

, but not necessarily perfect

scumhunters

, then you'd expect town to play at EV or better. (Or in other words, the argument is just a disconnect about what "optimal play" means. You're working from the assumption that players are perfect at strategy, perfect at hiding as scum, and perfect at scumhunting. I think the more commonly seen assumption in EV theory is that players are perfect at strategy but have no idea how to scumhunt, and thus it doesn't matter how good the scum are at hiding. The two assumptions give the same EV, and thus it normally doesn't matter which set of assumptions you're talking about, but plausible small deviations from the first scenario leave town's win rate untouched, whereas plausible small deviations from the second scenario increase it.)

In practice, of course, players often suck at strategy in addition to sucking at scumhunting, and scum have counterplay in practice that can make town's strategy worse (for example, many players (correctly or not) believe theory discussion to be a scumtell, and thus you can sometimes argue towns out of agreeing to follow a breaking strategy). It's rare for towns to random-lynch even when that would be their best option, which is one common reason for towns to play below EV.

[mith]

The counterpoint assumes town can evaluate whether or not they will play below random-EV, which is not a valid assumption.

I'm working under the assumption that optimal means optimal. "Plausible small deviations" from optimal are non-optimal and could absolutely change the town's win rate, depending on what they are. (But yes, it's equivalent to assume either that the scum are perfect at blending in or that town are perfectly incapable of scumhunting.)

I agree that in practice players are sometimes terrible at strategy, and this can cause towns to play below EV. (Conversely, scum are often terrible at not being scummy, and this commonly leads to towns playing above EV. If that weren't the case, Mafia wouldn't be a very interesting game.)

The rule against provable randomness has more to do with not allowing players to make provably random votes, which would be impenetrable to reads. (And probably some other weird specific situations that came up a long time ago, but I'm not latching onto any in my memory at the moment.) But yes, it does have the added benefit of preventing agreed-on truly random lynches.

[drmyshottyizsik]

2 Mafia Lynchers

4 1 Shot Vigs
3 VTs

Mafia have no NK, vigs and vts can be lynchers target. Mafia have no NK. Each Lynchers has a different target. Town win when mafia is lynched or killed, or they kill the two targets nd still hold a majority.

[mith]

Why would town lynch at all in that game? A massclaim and everyone-shoot strategy is winning in all cases. (The trickiest is the 1-1 split claim case, with 5 vig claims and 4 VT claims. Assign a Vig to each VT and have them shoot; the remaining doesn't shoot. Scum among the Vig claims is outed by the shooting, and the other is hit unless his buddy is assigned to him - in this worst case, it's still 2:3 so town wins)

Probably solvable even if town must lynch day 1.

[drmyshottyizsik]

2 Mafia Lynchers

6 1 Shot Vigs

[JasonWazza]

2 Mafia Lynchers

6 1 Shot Vigs

Shoot the person under you, only mafia win case is if they are one after another on the player list, and that's only assuming that Mafia win if they are 1:1

[callforjudgement]

Seriously, if you want to make this setup work, you have to go the other way. Something like 6 VT, 2 Mafia Lynchers, nightless, scum win if

both

their lynch targets are lynched has an EV of slightly below 50% (which is where you want it) and isn't breakable. (Lynch targets should be unaware but should probably

flip

as lyncher targets, so that the town knows how well they're doing.)

I'd be pretty curious as to what the win rates in practice would look like in this setup.

[mith]

I think you can do better:

No lynch. Split the town into groups of 2 and 6. Have the group of 6 shoot in a circle.

Case 1: 2 scum in group of 2 - Scum win, probability 1/28.
Case 2: 1 scum in each group - The target of the group of 6 scum survives, so 3 players left. No lynch again, and the remaining vig who hasn't shot can kill the scum.
Case 3: 2 scum in group of 6 - If they aren't next to each other, they both die. If they are, one survives along with his target and the group of 2, and the surviving scum is caught.

EV 27/28.

Games with too many Vigs are usually breakable, it's just a matter of finding the optimal way to do it (and I'm not certain we can't get to 100% in this one, just don't see it right now).

[callforjudgement]

Nominate three players to shoot, and give them each a target who's outside the set of three shooters.

If any of the targets survive, the shooter is confirmed scum. For any target who dies, the shooter is confirmed town. So even if all three targets die, you have five players, of which three are confirmed. Three confirmed townies and two confirmed scum are both an instant town win. The remaining situation has 2 confirmed townies, 1 confirmed scum, and three unconfirmed players: lynch the scum, and get the unconfirmed players (who each have their shot left if town) to vig each other in a cycle for the win.

100% town EV.

[drmyshottyizsik]

2 Lovers
2 Lovers
2 Lovers
2 Lovers
2 Lovers
1 Doctor

2 Goons

[LicketyQuickety]

I agree that in practice players are sometimes terrible at strategy, and this can cause towns to play below EV. (Conversely, scum are often terrible at not being scummy, and this commonly leads to towns playing above EV. If that weren't the case, Mafia wouldn't be a very interesting game.)

This is gold right here. I have noticed myself doing this, where I am not really playing strategically as Town. I have played as a mentor in a game and noticed it much much easier to evaluate things from a strategic vantage point. There is also something to be said for Scum getting too caught up in pushing agendas and not Scum hunting, which I again notice in my own game.

[LicketyQuickety]

9 Players

Cop
Insane Cop
Hidden Cop Trigger
VT
VT
VT
VT

Neapolitan
Goon

Roles:
Town:
Cop: Gets a true investigation on people at night. Receives Cop Role.
Insane Cop: gets a false investigation on people at night. Receives Cop Role.
Cop Trigger: Switches the Cop and Insane Cop upon death. This could be any random VT. There is only one in the game. Receives VT Role.
VT: No special abilities. Receives VT Role.
Mafia:
Neapolitan: Can investigate a player at night to find out if they are VT or not. Can Execute the Night Kill
Goon: Can execute the Night Kill

Cops are not told if they are sane or not, they will have to figure that out themselves.
Cops Trigger Role is not told they are Cop trigger. Upon death, this role shows up as VT.

Order of Night Actions:
Cop
Neapolitan
Night Kill

Win Conditions:

Town: Eliminate all members of the Mafia.
Mafia: Eliminate all members of the Town or nothing can prevent this.

[JasonWazza]

Cops Trigger Role is not told they are Cop trigger. Upon death, this role shows up as Citizen.

This is terrible in my mind, not the part where they aren't told, but the part where no one knows that they have died, it makes the cops virtually useless because it's basically impossible to work out what sanity they are and whether they switch unless someone is copping the same target multiple times.

[Not_Mafia]

When people say "not Mafia" in this thread

Summon me and I will appear

[LicketyQuickety]

Cops Trigger Role is not told they are Cop trigger. Upon death, this role shows up as Citizen.

This is terrible in my mind, not the part where they aren't told, but the part where no one knows that they have died, it makes the cops virtually useless because it's basically impossible to work out what sanity they are and whether they switch unless someone is copping the same target multiple times.

The idea is for Cops to live long enough to piece together who is Scum and who is Town. It is Optimal strategy for the Cop(s) to Investigate their strongest reads. In this way, when it is Day 3 and there have been 2 mislynches and it is now MyLo the cops will claim and give their feedback on people, if there is a common denominator meaning they have both investigated the same person, this can clear/confirm several people at once.

[Edit] Also, I have posted this setup on another site and the feedback I got was to actually take out Townies, not add them.

[JasonWazza]

Fact is due to the fact that lynches occur, the game isn't going to be as simple as "Piece it together" at best, you work out your sanity for one night, but that doesn't confirm any other night's alignment checks.

EG. Your N2 check is on a dead townie and is guilty, therefore you know that on N2 you were insane, however, you don't know if you were Sane or Insane on N1, or N3 because you could have started as either and could be either the next day.

[LicketyQuickety]

Fact is due to the fact that lynches occur, the game isn't going to be as simple as "Piece it together" at best, you work out your sanity for one night, but that doesn't confirm any other night's alignment checks.

EG. Your N2 check is on a dead townie and is guilty, therefore you know that on N2 you were insane, however, you don't know if you were Sane or Insane on N1, or N3 because you could have started as either and could be either the next day.

Optimal strategy for this game is to actually investigate you strongest reads. This can be different from person to person because some people get better Scum reads while others get better Town reads. If there is not switching mechanic, it is just too town sided.

There is ofc a chance of adding VT to this game. If you add both VT and Goon(s) then you could add a millar as well.

[mith]

"If there is not a switching mechanic, it is just too town sided" is not equivalent to "it is a good idea to have a switching mechanic".

If you get to day 3 with both Cops alive, and you haven't already lynched scum, that means there is only one Townie left. It's certainly possible that the Cops will be able to piece together whether they have been switched or not (investigating the same player on different nights would do it),

if

there is no counterclaim, but if you are in this situation obviously one of the scum will claim Cop and muddy the results further.

If you don't get to day 3 with both Cops alive, as Jason points out there is not enough information for the remaining Cop to go on.

When you say "investigate your strongest reads", what you seem to be implying is that you should rely on those reads to determine what your sanity is, rather than relying on your results to determine what your target's alignment is. Which you should be doing anyway, so what is the Cop role adding?

[edit]Also, if what you're after is "Cops should try to stay alive so they can solve the game day 3", just make that their role:

2 Masons
5 Townies
1 Mafia Rolecop
1 Mafia Goon

If both Masons are alive when there are 5 players remaining, town wins.
[/edit]