Live Action Mafia

A game of sneakiness and paranoia
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PostPosted: Thu Apr 14, 2016 10:54 am 
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Roles are out (at least for me). I'm town. Let's brainstorm role strategies, especially for the new and modified roles.

Investigations
Investigators, Desperados, Group Investigators, Priests:
When reporting investigations, use a proxy (or a chain thereof), or, better, multiple proxies if you have multiple results at once. Investigators are hard to hide this game because nothing else investigates the same or in a similar way, so if you're a group investigator or priest, consider (with some probability) reporting each of your innocence results to different people or something like that, with time delay, to hide the roles of some of the pure investigators.

Likewise, priests and group investigators who decide not to masquerade as regular investigators should try to make it ambiguous which one they are to their proxies when possible.

Others should add more here, but obviously don't say exactly how you're planning to trick your proxies :P

More on priests

How do we feel these should be used? The plan I've thought of that seems the most promising is:

1) Ask all priests to select a saint list from a fixed public shortlist, and have them pick their sinners more or less randomly (privately). This allows us to get several bits of info on expectation on the death of any given saint (who are probably the "most-likely-to-die-early" people), without letting one mafia saint sacrifice themselves to deactivate all the priests at once (since only sinners they kill would cause problems).

Alternatively, we can stick with the safe strategy of
2) Put trusted townies on the saint list. In this case perhaps some kind of public GN reveal would be reasonable at some point, since trap-kills on them is actually then bad for mafia? though obviously this should not be done anytime soon.

I think I like the first idea better. I'm also thinking in either case that sinner lists should be close to maximal size, but saint lists should be somewhat smaller.

If we decide to go with 1), we should make another thread coordinating priest saint list choices.

Stalkers
These still seem kind of useless... but I'd suggest having every stalker pick a random target for day 1, and forcing all the targets to claim. This counts stalkers, which doesn't help mafia too much and forces mafia to commit to stalker claims on day 1 and decreases chance of fake stalker claims later. It also allows us a way of indexing (and thus directing) stalkers anonymously on future days, assuming minimal collision levels.

Any other ideas?

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PostPosted: Thu Apr 14, 2016 11:16 am 
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I think group investigations may be exploitable, such that we could potentially brute-force search a kill. I'll probably think about this a lot more.

I don't like the idea of the priests' list being public. If the saints are public, I doubt they'll actually be targeted. That said, I think there should be public discussion of who we think is likely to be targeted.

Your stalker plan sounds pretty good. I like using day 1 to alias stalkers.


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PostPosted: Thu Apr 14, 2016 11:36 am 

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*snaps* to aok; priests should choose their own saints and not tell anyone, so the mafia don't know which saints to avoid. They can err on the side of people more likely to die early. Also, probably relatively few saints, to reduce their chances of losing their powers.


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PostPosted: Thu Apr 14, 2016 11:40 am 
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Oh yeah, I wasn't suggesting that priests make their saint lists public. I was just saying that we should have a public shortlist of possible saints and suggest that priests mostly select from them. To be honest, I don't think some outcome like "Ksedlar is on half the saint lists in expectation, don't kill her" would be bad for town :P

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PostPosted: Thu Apr 14, 2016 11:42 am 
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This is equivalent to "discussing" likely targets, I think? I don't see much of a difference besides explicitly warning priests not to be *entirely* predictable.

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PostPosted: Thu Apr 14, 2016 11:54 am 
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I think priests should put the maximum number of people on both lists. First, without taking into account the loss of powers, remember that a priest telling town that a saint killed a sinner is better for town than no priest telling this to town. The information gained from the priest's statement is more than the investigations lost.

Assuming both lists are maxed, each kill has about a 4% chance of triggering each way. Given priest's choices, let's modify this to 6% and 2%. With an expected priest trigger/12.5 kills and and the average priest lifespan to be about 12.5 kills into game, this is an expected 1 priest trigger/game. "Loss of powers" really isn't that big of a deal for a priest --- they've already achieved a positive use of their powers.

Anything that reduces the priest's chance of triggering (such as shorter lists) significantly increases the chance that the priest never achieves anything before dying, and the benefit of doing so is marginal.


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PostPosted: Thu Apr 14, 2016 12:08 pm 
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Good points, and I do think that maxing out the saint list as well makes sense given these. But I'd like to note that priests don't have to "trigger" to provide important information. For example, if we pick a public shortlist making it so that ~ 2 priests have ksedlar on their saint list, a day 1 kill on ksedlar generates either a set of <=5 people containing the killer, or a set of ~9 people not containing the killer. This is pretty good either way.

I just realized that the expected number of priests is between 2 and 3, so maybe this doesn't work that well, but I stand by my claim that public shortlists (of size ~40% of game?) (at least soft versions, for choosing most saints) are beneficial.

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PostPosted: Thu Apr 14, 2016 12:41 pm 
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I think having an explicit shortlist isn't that helpful for priests (who I expect are capable of picking fine targets on their own). I also think it would increase the number of priest collisions (priests having list overlap), which we don't actually want (once one priest has triggered for a death, extra priest results aren't all that useful), as well as let mafia plan their kills better.

I do think priests should max out their lists on both ends though. 20% of game = 6 people, soon to be 5, and we can expect that roughly half of the people will have alibis / be gay knights / be innocent children. In the sinner-> saint scenario, that's super easy to investigate, and in even in the saint->sinner scenario, we've narrowed down the targets to the point where it might be worth lynching/vig-killing them all.

++ stalker counting. The only issue is if two stalkers pick the same person, then we get an incorrect count. So, I recommend that stalkers actually get a randomizer (e.g. https://www.random.org/lists/) to pick their person, to minimize the chance of this happening. As nice as it is to stalk the historical top killers (e.g. lilychen or fmajluf7), we really value not colliding here.

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PostPosted: Thu Apr 14, 2016 12:48 pm 
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Ok, I'm now less convinced that having an explicit shortlist is best, though I think collisions are good for the extra narrowing down when lists don't trigger.

The main benefit of a list of some sort is to let new players know who is likely to be killed early, so that they can have default picks instead of researching if they're hosed.

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PostPosted: Thu Apr 14, 2016 12:59 pm 

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We can put all public roles on saints list, so if anyone attempts to kill them we'll know. That would make mafia/serial killer less likely to kill elected townies because they would be known then.

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PostPosted: Thu Apr 14, 2016 1:37 pm 

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I fully agree with the day 1 stalker plan. And yeah, stalkers seem very weak. Hopefully there aren't too many.

For the first couple days, I think saint lists should be kept smaller, to reduce the risk of priest-deactivation. After the first couple days, the lists should probably be maximized.

Regardless, priests shouldn't tell anybody who their saints and sinners are.

Also, desperados should remember to use their power! If you're a highly-prominent-likely-to-die-early player you should probably activate in the first day or two, even as early as day 0! If you're a less-likely-to-die-early player, you should probably activate two or three days later.

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PostPosted: Thu Apr 14, 2016 8:19 pm 
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I was also going to suggest the Stalker reveal plan, but I suspect Set a Trap makes it not worth it. Mafia could get free kills on them that refresh. I don't have a good sense though of how hard it would be for Mafia to keep getting their charges back. Thoughts?


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PostPosted: Thu Apr 14, 2016 8:28 pm 
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I'd be in favor of maximum size priest lists every day.

The most valuable thing a priest can do is to get any sort of notification from God - saint killed a sinner or sinner killed a saint. That's worth a huge amount - narrowing down the possible killers to just 5 people is incredible! We want this to happen as much as possible, and it's OK if it comes at the cost of losing your power, because it gains the town so much.

The second most valuable thing for priests is if someone on one of their lists is killed, and they don't get a notification. Then, this can be reported, proving that no one on their other list made the kill. If you use full lists, that could prove the innocence of 5 different people, which is worth up to 5 investigations. In particular, if someone on your saint list dies and you don't get a notification, you get to prove all of your saints are innocent, and keep your power.

The worst outcome for a priest is that they learn nothing. If you learn nothing, you're not helping the town.

Priests can maximize their effectiveness by using as big a list as they can every single day.

tl;dr Priests: You're more helpful to town the bigger your list is! Use as big a saint and sinner list as you can!

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PostPosted: Thu Apr 14, 2016 8:35 pm 
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++Isaac. Strongly in favor of max size priest lists.


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PostPosted: Thu Apr 14, 2016 8:41 pm 
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Quote:
The second most valuable thing for priests is if someone on one of their lists is killed, and they don't get a notification. Then, this can be reported, proving that no one on their other list made the kill. If you use full lists, that could prove the innocence of 5 different people, which is worth up to 5 investigations. In particular, if someone on your saint list dies and you don't get a notification, you get to prove all of your saints are innocent, and keep your power.


Unless I misunderstand the rules of priests, you mean you prove all your sinners are innocent (which is arguable more useful most of the time).

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PostPosted: Thu Apr 14, 2016 8:42 pm 
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Also, ++Isaac/aok. I buy this argument.

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PostPosted: Thu Apr 14, 2016 8:59 pm 

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I agree with Isaac and think this makes Daniel look mildly sketchy for suggesting bad strategy.

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PostPosted: Thu Apr 14, 2016 9:06 pm 
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jakob wrote:
Quote:
The second most valuable thing for priests is if someone on one of their lists is killed, and they don't get a notification. Then, this can be reported, proving that no one on their other list made the kill. If you use full lists, that could prove the innocence of 5 different people, which is worth up to 5 investigations. In particular, if someone on your saint list dies and you don't get a notification, you get to prove all of your saints are innocent, and keep your power.


Unless I misunderstand the rules of priests, you mean you prove all your sinners are innocent (which is arguable more useful most of the time).


You're right, I meant sinners can be proven innocent in that scenario.

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PostPosted: Thu Apr 14, 2016 9:12 pm 
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++ maximizing priest saint lists

Alex wrote:
I was also going to suggest the Stalker reveal plan, but I suspect Set a Trap makes it not worth it. Mafia could get free kills on them that refresh. I don't have a good sense though of how hard it would be for Mafia to keep getting their charges back. Thoughts?


Stalkers don't publicly reveal. All stalkers stalk someone, and the people who are stalked reveal that they are being stalked.

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PostPosted: Thu Apr 14, 2016 9:32 pm 
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Group investigator math:
Let H(p) be the entropy of asking a yes/no question, with a p probability of a "Yes" answer. Information Theory says that H(p)=-plog(p)-(1-p)log(1-p) . If a group investigator's 3-person question has entropy H(p), then they gain us .5*H(p) information per day with that strategy. For a strategy of asking about 6-person groups, those questions would have to earn us H(q)>1.5*H(p) entropy per question.

If p=.1, q>.19 for 'every third day' to be better.
If p=.125, q>.252 for 'every third day' to be better.
If p=.15, q>.33 for 'every third day' to be better.
The pattern continues for larger probabilities, as the values for q get progressively more and more unreasonable.

Things this does not take into account:
If there are no kills with unknown killers available, or if the kill is a likely don kill, group investigators should wait for a better kill. This analysis is done in a vacuum assuming no other investigators, group investigators, or priests, but the math shouldn't be disrupted by their presence.

Conclusion:
Under any reasonable assumptions about the ability of group investigators to figure out likely killers, they gain more information by investigating as often as they possibly can, and not waiting to ask larger questions.


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PostPosted: Thu Apr 14, 2016 11:21 pm 
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++ aok.

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