Live Action Mafia
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Strategy!
http://mafia.mit.edu/viewtopic.php?f=174&t=4387		 Page 1 of 1
Author:  jamb [ Wed Mar 16, 2016 3:37 pm ]
Post subject:  Strategy!
A few comments:
1) Please tell me if you think my strategy ideas are mistaken in any way; I could easily be overlooking things. (I will post more here in the future.)
2) Please refrain from posting your strategy ideas right now, when they could help the mafia plan. In particular, if you have a brilliant idea for catching a mafia in a lie, I recommend waiting until AFTER everyone has role-claimed so that mafia can’t adjust their role claims to avoid your plan.


ROLE CLAIMING

Everyone should claim a role as soon as you get it. (If you already have one, please tell us so :P)

Mafia already know your role, so there is *no* advantage to lying. Townies should not lie about their roles because this will only hurt town. If we discover that you lied about your role we will assume you are mafia.
Author:  ksedlar [ Wed Mar 16, 2016 6:21 pm ]
Post subject:  Re: Strategy!
Agreed. Especially with respect to waiting on strategy discussion until role claims happen in order to reduce how much mafia can plan.
Author:  pravinas [ Thu Mar 24, 2016 12:20 am ]
Post subject:  Re: Strategy!
If you want me to raise your paranoia, PM me. I want to prove my conspiracy-theory-ness.

Also, it's nice that there are so many psychologists. It makes this game a lot more logic puzzly. We need to get psychologist goodwill up as a priority. Might not be a bad idea to concentrate on a few psychologists and have a DA banana bread them on a late day.

And I kind of want to execute a Key Person on D3, so we can verify claims, but only if multiple people claim it. Otherwise, it's probably safe to say Jackie's telling the truth. I kind of doubt that there will be more KP claims.
Author:  pravinas [ Thu Mar 24, 2016 9:22 am ]
Post subject:  Re: Strategy!
I have been informed that I can "Boo!" myself. Well that's happening.

We should pile on Paranoia onto as few people as possible initially, so that we can narrow down the list of who can trigger each incident.
Author:  jamb [ Thu Mar 24, 2016 9:27 am ]
Post subject:  Re: Strategy!
Pravina,

Good ideas. I have comments on them, but won't share yet. PLEASE wait until everyone has role claimed; the remaining 4 people could be mafia who are waiting to see what our plan is before they decide how to claim.
Author:  ksedlar [ Thu Mar 24, 2016 10:58 pm ]
Post subject:  Re: Strategy!
Everyone MUST do all incants publicly (in front of people, not just claim you did it).

Psychiatrists should probably use early questions to check the numbers of things.
Author:  pravinas [ Thu Mar 24, 2016 11:15 pm ]
Post subject:  Re: Strategy!
It might be reasonable to do Boo! and Banana Bread! not-so-publicly, so that mafia can't necessarily count on events triggering. However, all information should definitely be publicly revealed by loop end.

(ofc I'm thinking a lot about Boo! as CT)
Author:  jamb [ Fri Mar 25, 2016 7:38 am ]
Post subject:  Re: Strategy!
To clarify, all FIRST DAY incants should definitely be public to prove people's roles - is that agreed?

Pravina, you might be able to convince me that later secrecy would be useful. But I think it's more likely to just allow any mafia DA/CTs to get away with privately doing incants on a bunch of people.
Author:  ksedlar [ Fri Mar 25, 2016 2:09 pm ]
Post subject:  Re: Strategy!
Plan for minimizing how much mafia psychiatrists can lie:

First of all, we give all the goodwill to psychiatrists (I think there's probably no reason to give goodwill to anyone else for now). For each day, we have a set of questions (on the order of 3 or 4 questions) that we want psychiatrists to ask. Each psychiatrists individually picks a question to ask. When psychiatrists get their answers, they simultaneously reveal them (or simply reveal in such a way that they couldn't have heard the other psychiatrists' answers first). If mafia psychiatrists (meaning claimed psychiatrists who are mafia) lie, there's a good risk of them ending up in a beef with a town psychiatrist whose answer disagrees with theirs. Beefs give town even more information, so this forces mafia into a position where they're incentivized to tell the truth, and we get mostly accurate information.

Some example numbers with 4 psychiatrists getting goodwill:
1/4 is mafia, set of 3 questions: mafia has 19/27 chance of getting caught in a beef if they lie
1/4 is mafia, set of 4 questions: mafia has 37/64 chance of getting caught in a beef if they lie
2/4 is mafia, set of 3 questions: a single mafia has a 5/9 chance of getting caught in a beef if they lie
2/4 is mafia, set of 4 questions: a single mafia has 7/16 chance of getting caught in a beef if they lie
Author:  aok [ Fri Mar 25, 2016 2:15 pm ]
Post subject:  Re: Strategy!
I need goodwill to be able to protect someone, just saying. Unfortunately, given that we expect the day 1 culprit to trigger, I don't expect to be able to protect anyone on day 2 anyways, and I don't expect day 3 to happen on the first loop.

To prevent us getting information out of who wins the goodwill vote, the mafia want to cast their votes in proportion to the town votes. If we want to make this as difficult as possible for them, we should be casting our votes unpredictably and randomly. Therefore, I suggest that we each vote for a random psychiatrist. We can get information out of who claims to have won the goodwill vote.
Author:  aok [ Fri Mar 25, 2016 2:15 pm ]
Post subject:  Re: Strategy!
I need goodwill to be able to protect someone, just saying. Unfortunately, given that we expect the day 1 culprit to trigger, I don't expect to be able to protect anyone on day 2 anyways, and I don't expect day 3 to happen on the first loop.

To prevent us getting information out of who wins the goodwill vote, the mafia want to cast their votes in proportion to the town votes. If we want to make this as difficult as possible for them, we should be casting our votes unpredictably and randomly. Therefore, I suggest that we each vote for a random psychiatrist. We can get information out of who claims to have won the goodwill vote.
Author:  dylanhen [ Fri Mar 25, 2016 2:20 pm ]
Post subject:  Re: Strategy!
"No provable randomness, simultaneity, dead-man switches, cryptography, or anonymous communication."

So if we use Katie's plan, the Psychiatrists can't reveal simultaneously.
Author:  ksedlar [ Fri Mar 25, 2016 3:17 pm ]
Post subject:  Re: Strategy!
Aok, you only need goodwill if you get paranoia. Anyone who boos you without a REALLY good / previously discussed reason is outed as mafia.

Psychiatrists don't need to be exactly simultaneous. For example:
There are a bunch of players in Front Room. The psychiatrists who got goodwill stay in the kitchen (or somewhere where they can't hear), and one by one enter Front Room to tell the players there what the result was. They then go back to the kitchen and send the next psychiatrist in. Each psychiatrist is watched the whole time to make sure they don't use electronic communication.
Author:  jamb [ Fri Mar 25, 2016 3:18 pm ]
Post subject:  Re: Strategy!
Josh and I just had a discussion in which we concluded the following:

- (IF Luke and jamb are both KPs AND there exists at least one mafia killer) then there are at most 6 mafia
Pf: if >=7 mafia, the mafia killer kills town's DA (assuming aok is town, or kill a random townie otherwise) so town has 7 votes. If Luke and jamb are both KPs and a mafia killer exists, then there must be at least 2 DAs, one of whom is mafia. Thus even if town's <=1 killer kills one mafia, mafia will have 7 votes - 1 person + 1 DA = 7 votes, to tie and lynch a KP.

- in order to keep the game tight, it will probably at some point come down to town voting perfectly to win the lynch vote, and that's why the day 2 culprit matters: they have to know who they are so they don't accidentally give minus votes to town's lynch choice. (If the d2c is a DA then it would be -2, otherwise -1.) This means the day 2 culprit is almost certainly a townie, and presumably someone that the mafia would want to leave alive. (Probably not a DA then.) Also note that the d2c, even if they know who they are, can't necessarily vote for the mafia's lynch target to put negative votes on them, because the mafia could be trying to lynch either one of the two KPs and it's impossible to know which one (assuming both KP claims are true).
Author:  jamb [ Fri Mar 25, 2016 3:18 pm ]
Post subject:  Re: Strategy!
Katie - aren't the goodwill voting results announced at day start, aka 8am? I don't think anyone feels like gathering in the kitchen then.
Author:  ksedlar [ Fri Mar 25, 2016 3:32 pm ]
Post subject:  Re: Strategy!
Jackie; people can gather later in the day and just not reveal goodwill results until then. Psychiatrists aren't high on the mafia's to-kill list, and even if they were, I think a delay is worth getting more accurate information.

Also, I think that we should try to maximize the number of psychiatrists asking a question for the same value of n, e.g. :
Day 1: P1, P2, P3, P4 (banana breaded)
Day 2: P1, P2, P3, P5 (banana breaded)
Day 3: P1, P2, P3, P4 (banana breaded)
Day 4: P1, P2, P3, P5 (banana breaded)

A proposed set of questions (open to suggestions) for psychiatrists' first question:
(mafia AND killer) , +-1 paranoia
(mafia AND conspiracy theorist) , +-1 paranoia
(mafia AND double agent) , +-1 paranoia
(mafia AND psychiatrist) , +-1 paranoia
The question uses +1 paranoia if the day 1 incident happened and -1 paranoia if the day 1 incident didn't happen. These questions give us some information about the day 1 culprit, but are mostly useful for figuring out role numbers for mafia. I think mafia are unlikely to have 2 or more key people, which is why I didn't add that associated question to the set.

On another note, I'm becoming increasingly convinced that it is REALLY bad to boo / banana bread non-publicly. It seems like it gives mafia a lot of plausible deniability for triggering incidents, confuses psychiatrist results, and makes determining the culprit of events harder. The only thing I can see it doing for mafia is causing incidents to happen that mafia don't expect, which doesn't even seem significantly bad for mafia. I am personally going to send any conspiracy theorist who privately boos someone straight to the top of my sketch list (only below proven mafia).
Author:  jamb [ Fri Mar 25, 2016 3:33 pm ]
Post subject:  Re: Strategy!
continued posts from my discussion with Josh:

- probably most of the psychiatrists are Mafia; there isn't really much reason for Mafia not to claim psychiatrist (jamb disagreed slightly here because it makes non-psychiatrists look good if there are more claimed psychiatrists, but agreed with the general idea)

- we could possibly use the goodwill distribution conditions to prove people town. In particular, DAs and CTs-who-have-booed-once should get 2x votes; assuming all our claimed CTs and DAs are town, then if we created a cycle, the 4 people voted for by these 4 would be the ones who got the goodwill. If they don't all get goodwill, or if someone else gets goodwill, then beefs exist! (In particular, we should make the expected targets of these goodwill votes people who are likely to be good.) A problem with this is that tiebreakers are in favor of mafia getting goodwill which is sad, but hopefully we can still get some trust chains OR beefs going.

- if we find at least one killer who's not Troy, then Troy is provably good.
Author:  jamb [ Fri Mar 25, 2016 3:40 pm ]
Post subject:  Re: Strategy!
Katie, I thought the entire point of the simulated simultaneity was to make sure mafia couldn't communicate with each other before revealing their results?

Also, you're making some really big assumptions with your 4-day plan, such as (A) aok will be alive to banana bread people every day (B) the game will last 4 days (C) you can ask questions from the last day's goodwill. (A) and (B) are unlikely and (C) is a rules question that I'm not sure about.

The first question has n=1 and a question contains at most n terms. "Mafia AND killer" has 2 terms.
Author:  ksedlar [ Fri Mar 25, 2016 4:01 pm ]
Post subject:  Re: Strategy!
Jackie,

The point of simulated simultaneity is to make sure that mafia don't know what questions town psychiatrists asked before revealing their results. Lacking this knowledge makes it so mafia either have to tell the truth or risk beef. Mafia can communicate with each other to decide on what they say their results are anyway.

4 day plan is just a sample. The important point is "maximize number of psychiatrists asking a question for the same value of n." You can't ask questions from the previous days' goodwill; banana breaded psychiatrists get two goodwill questions at once.

I had not noticed the "n terms" stipulation. :( That makes the questions a lot less useful, because we can't get as much information from "too big" as I thought.
Author:  ksedlar [ Fri Mar 25, 2016 4:18 pm ]
Post subject:  Re: Strategy!
++ using the goodwill distribution to prove people town. It also works regardless of whether CTs boo once or twice. Something like the following would be excellent:

aok - psychiatrist 1
Pravina - psychiatrist 2
Dgrazian - psychiatrist 3
Lotta - psychiatrist 4
p1 - aok
p2 - Pravina
p3 - Dgrazian
p4 - Lotta
everyone else - themself

Anyone who doesn't vote like this is proven mafia. If psychiatrist n claims to have received goodwill, then they effectively vouch that their voter is innocent (and if they claim to not have received goodwill, they are claiming that their voter is guilty). If aok/Pravina/Dgrazian/Lotta is mafia and their respective psychiatrist is town, then the voter in question will receive the goodwill. However, if both parties are mafia, then the tiebreak would go to one of Luke or Jackie (the key people, who win alphabetically by role) if one of them was a mafia or culprit for some day.

Psychiatrists 1-4, if they get goodwill, prove their voter innocent. If they don't get goodwill, they prove their voter guilty. If any of aok/Pravina/Dgrazian/Lotta is mafia and their respective psychiatrist is town, then the mafia will get goodwill
Author:  aok [ Fri Mar 25, 2016 4:58 pm ]
Post subject:  Re: Strategy!
I think loops will probably end on day 2 until we figure out who the mafia killers are.

I still advocate the plan of "everyone vote for a random psychiatrist."
Author:  ksedlar [ Fri Mar 25, 2016 5:18 pm ]
Post subject:  Re: Strategy!
Aok,

Yeah, but there are no more than two killers, and they get outed as mafia the loop after they make a kill. So we only lose a max of two loops to mafia killers.

Why do you think that people voting randomly will give more information than my proposed voting arrangement? Mine should give 4 role-checks, plus maybe being able to out a lying mafia pair (if one of Luke/Jackie is culprit or mafia). That seems like a lot.
Author:  ksedlar [ Fri Mar 25, 2016 5:20 pm ]
Post subject:  Re: Strategy!
Also, regardless of what voting scheme we decide, aok should vote ASAP because he'll probably get shanked.
Author:  aok [ Sat Mar 26, 2016 3:03 pm ]
Post subject:  Re: Strategy!
We only learn who mafia are if we trust that their victim is town, which isn't necessarily the case with the Key Persons.
Author:  ksedlar [ Sat Mar 26, 2016 3:54 pm ]
Post subject:  Re: Strategy!
Oh yeah, that's an important point. Mafia KP are really strong. :(
Author:  ksedlar [ Sat Mar 26, 2016 6:16 pm ]
Post subject:  Re: Strategy!
I forget if this was said, but town's pattern needs to be:
D1: lynch mafia killer
D2: lynch C3
D3: lynch C4

If mafia have a CT and a DA, then on day 1 the mafia DA can banana bread C4, and the CT can boo C1 and C3. So unless there is no mafia CT or DA (unlikely), town MUST kill the day 3 and 4 culprits. There may be extra kills needs via Troy / KP with guns, but this is the minimum.
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