[SETUP] Cops' Dilemma

[Hoopla]

To celebrate this shiny new subforum, I will get the ball rolling for the NEW SETUP type of threads...

Cops' Dilemma

2x

Mafia 1-Shot Redirectors

(with special factional ability)
1x

Scared Loner

(Innocent Child 1-Shot PGO*)
2x

Cops

4x

Townies

Daystart

~~

- Scared Loner gets announced as innocent at the start of D1
- At the end of N2, the Scared Loner receives information of the amount of Cop investigations that occurred on the first two nights
- If zero, he freaks out that the Cops aren't doing their jobs and commits suicide
- If one or more, he relaxes and disarms his PGO shot (if he still has it)

- The mafia team has a factional nightkill as standard, but also a factional double-nightkill they can use any night in lieu of all other actions, HOWEVER it only succeeds if both of the targets are Cops
- Each mafia member cannot perform two actions in one night - they have to choose one or the other (one can kill and one can redirect, or both can redirect if they wish)
- The exception to this rule is if there is only one mafia left, then he can kill AND redirect in one night if he wishes.
- The double-kill can still be attempted by the solo mafia, but not redirect at the same time

- If a Cop is redirected to the Scared Loner, he dies, and the Scared Loner loses his bullet.
- If a Cop is redirected to a mafia member, he will be given a guilty result, but won't be told he has been redirected
- And vice versa if redirected to an innocent player

The game is centered around wifom for when the mafia should use their redirects and when Cops should investigate (if at all). The N2 suicide in the event of no Cop investigations is there as a way to break the no investigate at all strategy (which might probably be best) and spur the Cops into tentative action. The double-kill rule is there to prevent the game from being broken via massclaim and also give the Cops a dilemma about when/how to roleclaim (if at all), as it may setup a double-kill. This rule also allows mafia to potentially fakeclaim Cop while both are alive.

Personally I think it's likely that 1 or 2 Cops will/should investigate N1, so I think mafia's best play is to redirect twice on N1 and to put town in even numbers on D2 and/or hopefully use up the PGO shot/frame someone. It's risky for Cops to not investigate on N1, because if the other Cop doesn't investigate also and either is NK'ed, the last Cop is forced to investigate on N2 at the risk of the Scared Loner suiciding. This prevents the Cop from claiming D2 to be innocent/force a 50-50, as being mislynched in a 50/50 creates a Scared Loner suicide OR being forced to investigate N2 while mafia know who the Cop is, is very bad if they actually do still have a redirect left.

However, if the Cops think redirecting N1 is a likely mafia play, investigating N2 is a better strategy despite being forced to investigate then. And so on and so forth with the wifom.

The "solo-mafia can redirect AND kill in one night rule" is there in the event of a D1 mafia lynch, and gives him an opportunity to get back in the game on N1 with a potential for 2 kills OR a clever frame, assuming Cops will claim a guilty and town will be convinced enough it's not tainted evidence.

Whether or not a Cop actually comes forward and claims information will be an interesting dynamic as mafia can conceivably fakeclaim Cop with impunity on D2 if no Cops are dead by then. If a town Cop claims on D2, they risk opening up the double-NK possibility for scum, so what Cops' do with their information will be crucial.

I don't

think

I've overlooked any obvious breaking strategies, but you never know!

[Hoopla]

If a cop got a guilty on N1, would you not be tempted to claim that result? I think some would.

[Hoopla]

i don't think what's optimal for a cop N1 is static. it depends on what they think the mafia (and the other cop) is going to do. i think the frequency of investigation also depends on how usable the cop believes its information will be - which depends on if he thinks the town will actually believe/use that information. there needs to be at least one investigation overall, so does cop A think the cop B will investigate either night, meaning cop A can get away with zero investigations?

when/how often he thinks the mafia will try to redirect (and who they will redirect) should also influence a cop's investigation choices.

i think there are certain scenarios where investigating both nights could be correct.

[Hoopla]

another big variable influencing N1 decisions is whether a townie, cop or mafia is lynched d1.

[Hoopla]

Then couldn't mafia both redirect N1? If a townie is lynched D1, mafia has a 50% chance of altering the second Cops' result. So, if the second Cop claims a guilty D2, should it be followed by the town after no-kill on N1? This strategy also outs both cops by D2 giving scum a double-kill on N2. There is also a chance of lynching the other Cop D1 (if it doesn't claim), which forces the first Cop to investigate N1 otherwise the Scared Loner suicides N2. If the other Cop claims on D1 to prevent their lynch, mafia get a double-kill N1.

[Hoopla]

What about lynching the Scared Loner D1 so that scum have no way to kill the Cops via redirection? Then the cops can safely investigate every night, and although their results won't be reliable, you're going to get four investigations by lylo unless a cop gets lynched (and they can probably save themself from lynching via claiming). Given that the results aren't fully reliable, the investigation results are best treated like reads rather than like modconfirmed information.

A key facet of why an Innocent Child is such a good role for town is that they improve lynching odds on every day they're alive which helps town PoE more of the game. The Scared Loner can conceivably be alive until D3, so trading in that equity for safe but untrustworthy investigations seems suboptimal. You're costing the town one of their three mislynches (could actually be just two mislynches if the scum double-NK the Cops). If the town does lynch the Scared Loner D1, scum should counter by double-redirecting on N1 to taint the investigation results. Then what happens if a Cop claims a guilty at the start of D2? Do you go with it? Does the other Cop/Cops now not claim? Scum can fakeclaim Cop safely without being counterclaimed, as the threat of the double-NK on the cops looms large if scum find out both their identities.

Now that I think about it, a redirect/NK on N1 might be better than a double-redirect. If they hit a Cop, the remaining Cop should claim to prevent info going to grave on N2, so the town only gets one investigation for the game in this scenario, with a 1 in 5 chance of a redirection tainting that investigation. If they hit a townie, the same dilemma occurs for the Cops. The town cannot let scum know who both the Cops are, as a double-NK on N2 can win the game on a D2 mislynch. So again, what happens when a Cop claims info on D2? Should they be believed? Should the other Cop/Cops remain silent? If both Cops remain silent, should they claim upon being wagoned to L-1 and should that claim reprieve them? If so, and both Cops remain silent until then, how does town ever expect to lynch scum D2, if scum can safeclaim Cop upon being wagoned? Both Cops claiming isn't a viable strategy, so how should town determine which Cop gets to claim information, as both Cops remaining silent seems pointless too if the goal of lynching the Scared Loner is to get more investigations.

I think potential hypocopping strategies run the risk of scum PoE'ing who the Cops are before the town can use the information, although I haven't thought about that indepth too much.