[SETUP] Cops' Dilemma

This forum is for discussion of individual Open Setups, including theoretical balance.
User avatar
Hoopla
Hoopla
User avatar
User avatar
Hoopla
Posts: 10788
Joined: October 12, 2008

[SETUP] Cops' Dilemma

Post Post #0 (ISO) » Thu Jun 30, 2016 7:22 pm

Post by Hoopla »

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

Cops' Dilemma2x
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!
User avatar
Realeo
Realeo
Jack of All Trades
User avatar
User avatar
Realeo
Jack of All Trades
Jack of All Trades
Posts: 5238
Joined: February 11, 2016
Location: Indonesia

Post Post #1 (ISO) » Sat Jul 02, 2016 3:00 am

Post by Realeo »

Wouldn't this be easier for town to treat this game as mountainous? I personally as cop find it unreasonable risk to have potential fake report and double death.
"The debate on whether short multi postings or a long wall of post is good or not is like a debate on gun control--we would never understand each other and we have to make peace with it." -Realeo

I'm mabye a serious player, but I'm capable of joke. Ok?
User avatar
Hoopla
Hoopla
User avatar
User avatar
Hoopla
Posts: 10788
Joined: October 12, 2008

Post Post #2 (ISO) » Sat Jul 02, 2016 6:13 pm

Post by Hoopla »

If a cop got a guilty on N1, would you not be tempted to claim that result? I think some would.
User avatar
Realeo
Realeo
Jack of All Trades
User avatar
User avatar
Realeo
Jack of All Trades
Jack of All Trades
Posts: 5238
Joined: February 11, 2016
Location: Indonesia

Post Post #3 (ISO) » Sat Jul 02, 2016 7:34 pm

Post by Realeo »

So it is optimal for cop to check N1, due to power of info for mafia but redirector can't redirect to the scared loner. So the most optimal move for mafia is to mess up with their report, right?

I want to run computer simulation, but I want to confirm my observation first.
"The debate on whether short multi postings or a long wall of post is good or not is like a debate on gun control--we would never understand each other and we have to make peace with it." -Realeo

I'm mabye a serious player, but I'm capable of joke. Ok?
User avatar
Hoopla
Hoopla
User avatar
User avatar
Hoopla
Posts: 10788
Joined: October 12, 2008

Post Post #4 (ISO) » Sat Jul 02, 2016 9:10 pm

Post by 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.
User avatar
Hoopla
Hoopla
User avatar
User avatar
Hoopla
Posts: 10788
Joined: October 12, 2008

Post Post #5 (ISO) » Sat Jul 02, 2016 9:11 pm

Post by Hoopla »

another big variable influencing N1 decisions is whether a townie, cop or mafia is lynched d1.
User avatar
hitogoroshi
hitogoroshi
¯\_(ツ)_/¯
User avatar
User avatar
hitogoroshi
¯\_(ツ)_/¯
¯\_(ツ)_/¯
Posts: 3450
Joined: February 24, 2008
Location: shiftless layabout

Post Post #6 (ISO) » Thu Jul 07, 2016 9:00 am

Post by hitogoroshi »

It's probably optimal for one cop to claim D1 and not investigate until the PGO is de-triggered, while the other cop investigates each night and claims with a result D2 if the first cop is killed D1, and with two results D3 otherwise.
"Don’t buy a dozen eggs if you just want a hardboiled egg. Don’t buy a head of lettuce if you just want a salad. Don’t buy eggs and lettuce if you want egg salad because those are not the right ingredients." -Julius Bloop
User avatar
Hoopla
Hoopla
User avatar
User avatar
Hoopla
Posts: 10788
Joined: October 12, 2008

Post Post #7 (ISO) » Thu Jul 07, 2016 8:48 pm

Post by 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.
User avatar
Realeo
Realeo
Jack of All Trades
User avatar
User avatar
Realeo
Jack of All Trades
Jack of All Trades
Posts: 5238
Joined: February 11, 2016
Location: Indonesia

Post Post #8 (ISO) » Sat Jul 09, 2016 5:00 am

Post by Realeo »

This setup flusters me because there is no equilibrium strategy.

I mean, a good setup should have no or few equilibrium strategy but I just don't know =p

I will try to give this setup another math trial, but at this point, it's a question whether this is a bug or a feature.
"The debate on whether short multi postings or a long wall of post is good or not is like a debate on gun control--we would never understand each other and we have to make peace with it." -Realeo

I'm mabye a serious player, but I'm capable of joke. Ok?
User avatar
callforjudgement
callforjudgement
Microprocessor
User avatar
User avatar
callforjudgement
Microprocessor
Microprocessor
Posts: 3972
Joined: September 1, 2011

Post Post #9 (ISO) » Thu Aug 04, 2016 9:52 pm

Post by callforjudgement »

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.
scum
· scam · seam · team · term · tern · torn ·
town
User avatar
Hoopla
Hoopla
User avatar
User avatar
Hoopla
Posts: 10788
Joined: October 12, 2008

Post Post #10 (ISO) » Sat Aug 06, 2016 9:53 pm

Post by Hoopla »

In post 9, callforjudgement wrote: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.
User avatar
JasonWazza
JasonWazza
Jack of All Trades
User avatar
User avatar
JasonWazza
Jack of All Trades
Jack of All Trades
Posts: 8940
Joined: August 1, 2012

Post Post #11 (ISO) » Sun Aug 07, 2016 11:41 pm

Post by JasonWazza »

Wouldn't the logical strategy for Scum just be to double shot, and hope both cops don't investigate?

that brings it down to an early 3:2.

I mean i guess this only applies in the case a townie is lynched, but it still feels optimal.

And since they have only 3 townies and 2 cops left, they have a decent chance of nailing at least 1 cop regardless.

As for town, they also should probably run based on a similar scenario (and i'd argue lynching the Loner is optimal, because sure the cops can be redirected, but that doesn't mean all that much.)

Lynching loner leaves:

2 Mafia
2 Cops
4 Townies

Double Redirect: Both cops live, claim their Results, (mafia likely counters/claims as well) and go think about the results and try to bust the game open right there (worst case scenario is both get redirected, but is fairly unlikely.)
The one Redirect/one Kill route probably needs you to play smart around it, optimal strategy would probably depend more on who got killed then anything else.
Double Kill: assuming both cops don't get hit, the game is likely broken
1 cop living: Claim cop, don't claim result, if one cop claims, their result is true (Guilty is 100% a mafia lynch, going to a 2v1 lylo, Innocent is 66% a mafia lynch, going to a 2v1 lylo with a confirmed innocent)
2 cops living: Claim cops, don't claim results as before, this varies based on the amount of cops claiming, but your generally in a massive win scenario, Also always make an order for Cops to claim in (unless 2 claim), as this increases the chance of a possible mafia screw up.
Returning win rate: 4/1, 80%
In the process of creating a game to mod, we will see what it holds.
User avatar
LicketyQuickety
LicketyQuickety
Survivor
User avatar
User avatar
LicketyQuickety
Survivor
Survivor
Posts: 12785
Joined: May 14, 2015
Location: Where the moon and the sea meet.

Post Post #12 (ISO) » Mon Aug 15, 2016 8:51 pm

Post by LicketyQuickety »

IDK, was thinking something similar to hitogoroshi.

None of the cops claim and both investigate N1 and don't investigate again. Was thinking cops have best chance NOT to trigger PGO since the numbers are in their favor (Most people alive). This leaves Mafia with no extra info. Each person (Townies) give cop cover?

Anyways, what's wrong with this? I am not good at this setup stuff so I am asking.
I was anything worse than you! Anything worse than you was I!

You was doided teh aposit_tisopa het dedoid saw em.
Post Reply

Return to “Open Setup Discussion”