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Author Topic: M123: Doomsday Mafia (Town and Survivor win!)  (Read 11295 times)

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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #725 on: June 16, 2019, 08:39:41 am »

I would suspect that scum probably did choose 4 PRs, because if you're going to make one of your scum buddies a neighbor, then you want a lot of town neighbors. In that world, there are 4 roles chosen and one of them is a neighbor. The probbiality of that is 57.1%. The most likely case. This sounds like a reasonable guess.
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #726 on: June 16, 2019, 08:44:47 am »

I think I want a (partial) massclaim regardless, however. If we can pin down how many PRs there are, then we get another group where we know how much scum is among them. For example, if we get 5 claims, one of them is guaranteed scum.

I suggest we have everyone claim PR and non-PR. I think this will be more helpful for town than for scum. Remember that town could have a PGO, so scum can't safely NK anyone.
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MiX

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Re: M123: Doomsday Mafia (Day 2)
« Reply #727 on: June 16, 2019, 08:45:12 am »

Short probabilities post. Let's assume no 3d party neighbor. What is the probability p of having two additional town members? It depends on how many PRs scum picked. If it's ...

... 4, then p = 28.6%  (6 * 2/7 * 1/6)
... 3, then p = 14.3%  (3 * 2/7 * 1/6)
... 2, then p = 04.8%  (1 * 2/7 * 1/6)
... 1, then p = 00.0%

Did you factor the fact that third-party removes one of the roles and/or third-party's most likely traitor so there's 1 more PR?

We could verify this via massclaim. That would give us additional information about how many PRs there are. But I don't think there's a world in which I don't want to lynch out of the neighborhood. Probably ash or DatSwan. Probably DatSwan.

If we do this, I sugest a mere "I am PR" or "I am not PR" given there's a bunch that don't mind dying.

I would suspect that scum probably did choose 4 PRs, because if you're going to make one of your scum buddies a neighbor, then you want a lot of town neighbors. In that world, there are 4 roles chosen and one of them is a neighbor. The probbiality of that is 57.1%. The most likely case. This sounds like a reasonable guess.

I wouldn't pick 4 powers, sounds overkill and I don't think there's those many good powers. But I can see why increasing the chances of neighbors is good if you choose to be scum neighbor.

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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #728 on: June 16, 2019, 08:48:20 am »

Did you factor the fact that third-party removes one of the roles and/or third-party's most likely traitor so there's 1 more PR?

I did not. It always gets more complicated  :( Hold on.
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Glooble

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Re: M123: Doomsday Mafia (Day 2)
« Reply #729 on: June 16, 2019, 08:49:17 am »

I guess I see the benefit of a mass PR/ not PR claim, and the possibility of the PGO certainly helps, but don’t forget it’s a 1-shot active PGO. So it probably only protects the other roles for one night. And don’t forget scum could fake claim and mess up our numbers.
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I think town!Glooble pointing to something as a scum tell and then shortly thereafter doing that thing is a lot more likely than scum!Glooble doing that.

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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #730 on: June 16, 2019, 09:02:03 am »

Disregard the first post. I had forgotten about the extra modifications. That means we need to differentiate between the different picks of the third party member, and then between how many PRs scum picked. But it's still very doable.

Third Party Picked Traitor (+1 PR)
4 scum PRs -> p = 47.6%  (10 * 2/7 * 1/6)
3 scum PRs -> p = 28.6%  (6 * 2/7 * 1/6)
2 scum PRs -> p = 14.3%  (3 * 2/7 * 1/6)
1 scum PRs -> p = 04.8%  (1 * 2/7 * 1/6)

Third Party Picked SK or Reporter (-1 possible town role)
4 scum PRs -> p = 40.0%  (6 * 2/6 * 1/5)
3 scum PRs -> p = 20.0%  (3 * 2/6 * 1/5)
2 scum PRs -> p = 06.7%  (1 * 2/6 * 1/5)
1 scum PRs -> p = 00.0%
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #731 on: June 16, 2019, 09:06:03 am »

Reasonably certain these are correct. Anyone want to verify?

Unfortunately, this makes the case less strong and I'm now no longer certain I want to lynch between ash and DatSwan. Probably still like a PR / non PR claim.
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #732 on: June 16, 2019, 09:08:11 am »

I guess I see the benefit of a mass PR/ not PR claim, and the possibility of the PGO certainly helps, but don’t forget it’s a 1-shot active PGO. So it probably only protects the other roles for one night. And don’t forget scum could fake claim and mess up our numbers.

Yeah, there'll probably do that. It's still very useful. I don't want to talk too much about what scum can and can't do, though...
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jotheonah

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Re: M123: Doomsday Mafia (Day 2)
« Reply #733 on: June 16, 2019, 09:29:34 am »

So it's EFHW/ash/Swan... most likely they're 3 town, since I don't think any of them would pick survivor. Of these 3...yes, I suppose Swan's the scummiest, but I would sooner lynch EFHW...which revealed this information at my request. I think we just outed 3 town. Thank you EFHW.

I need to get a Glooble case ASAP.

This is a scummy reaction to EFHW’s claim and reveal. Once again, MiX is trying to proactively derail a town plan that might put his partners. Who jumps to “they’re obviously all town” like that? Like, that fast. He doesn’t even consider there’s scum there.

vote: MiX
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EFHW

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Re: M123: Doomsday Mafia (Day 2)
« Reply #734 on: June 16, 2019, 09:56:07 am »

Short probabilities post. Let's assume no 3d party neighbor. What is the probability p of having two additional town members? It depends on how many PRs scum picked. If it's ...

... 4, then p = 28.6%  (6 * 2/7 * 1/6)
... 3, then p = 14.3%  (3 * 2/7 * 1/6)
... 2, then p = 04.8%  (1 * 2/7 * 1/6)
... 1, then p = 00.0%
What do each of the 3 numbers being multiplied represent?
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MiX

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Re: M123: Doomsday Mafia (Day 2)
« Reply #735 on: June 16, 2019, 10:34:44 am »

So it's EFHW/ash/Swan... most likely they're 3 town, since I don't think any of them would pick survivor. Of these 3...yes, I suppose Swan's the scummiest, but I would sooner lynch EFHW...which revealed this information at my request. I think we just outed 3 town. Thank you EFHW.

I need to get a Glooble case ASAP.

This is a scummy reaction to EFHW’s claim and reveal. Once again, MiX is trying to proactively derail a town plan that might put his partners. Who jumps to “they’re obviously all town” like that? Like, that fast. He doesn’t even consider there’s scum there.

vote: MiX

I'm waiting for scum to push one of them, ssshhhhh don't tell anyone.

On the other hand feel free to kill me, I built a very minor case for Glooble based solely on his Swan interaction which is probably really weak but I can't see anything better. I'll post it when it's complete.
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MiX

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Re: M123: Doomsday Mafia (Day 2)
« Reply #736 on: June 16, 2019, 10:39:01 am »

Once again, MiX is trying to proactively derail a town plan that might put his partners.

What do you mean by "once again"? I pushed for the claim and everything!
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #737 on: June 16, 2019, 10:51:21 am »

What do each of the 3 numbers being multiplied represent?

The way you compute the percentage, in case anyone wanted to check.
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EFHW

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Re: M123: Doomsday Mafia (Day 2)
« Reply #738 on: June 16, 2019, 10:54:28 am »

Is this wrong?

Probability of 3 town neighbors with 4 scum modifications and 7 possible town prs= (chance of no scum pr being neighbor) × (2/7 + 2/6 + 2/5) × 1/4.

Chance of scum not picking neighbor in 4 choices, if it were random = 1 - (0 + 1/7 + 1/6 + 1/5). The 0 is because they can't pick 4 modifications that are prs.
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EFHW

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Re: M123: Doomsday Mafia (Day 2)
« Reply #739 on: June 16, 2019, 11:08:18 am »

Or just prob. of 3 town neighbors with 4 mods = (2/7 + 2/6 + 2/5) × 1/4 = 25%.

My question was about how you chose those numbers to be in the equation with those relationships, not what the equation was for.

I promise to do at most only one more post about math.
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #740 on: June 16, 2019, 11:12:36 am »

I don't get how you're getting your numbers. Explain?

Here's how I did it. We draw 4 times from a pool of 7 roles. To hit 2 neighbors, we have to hit neighbor twice and non-neighbor twice. The chance to hit the first neighbor is 2/7, because they are two. the chance to hit the second is 1/6. The chance to hit non-neighbors is then 5/5 and 4/4, i.e. guaranteed. So the probability for neighbor-neighbor-notneighbor-notneighbor is 2/7 * 1/6 * 5/5 * 4/4 or just 2/7 * 1/6. Now there are 6 possible ways to order the two neighbors and the two non-neighbors, so we multiply the thing with 6. (That's n choose k with n = 4 and k = 2.) That's the first probability in my first post. Everything else works with the same principle, just different numbers.
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #741 on: June 16, 2019, 11:19:37 am »

My question was about how you chose those numbers to be in the equation with those relationships, not what the equation was for.

That makes sense, I hope the previous post answers that.
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EFHW

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Re: M123: Doomsday Mafia (Day 2)
« Reply #742 on: June 16, 2019, 11:30:18 am »

2/7×1/6 is for the combination with lowest prob of picking neighbor twice. The max is 5/5 × 4/4 × 2/5 × 1/4, right? Multiplying the lowest x 6 seems somewhat underestimating, but thank you for explaining.
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #743 on: June 16, 2019, 11:37:42 am »

No, they're actually all equally likely. if you pick notneighbor-notneighbor-neighbor-neighbor, you get 5/7 * 4/6 * 2/5 * 1/4. That's the same numbers in the nominator and denominator as 2/7 * 1/6 * 5/5 * 4/4, just in a different order. The result should be exact.

Whatever you draw first is out of 7, so the denominator has to be 7.
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EFHW

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Re: M123: Doomsday Mafia (Day 2)
« Reply #744 on: June 16, 2019, 11:40:23 am »

No, they're actually all equally likely. if you pick notneighbor-notneighbor-neighbor-neighbor, you get 5/7 * 4/6 * 2/5 * 1/4. That's the same numbers in the nominator and denominator as 2/7 * 1/6 * 5/5 * 4/4, just in a different order. The result should be exact.

Whatever you draw first is out of 7, so the denominator has to be 7.
ok, neat. Sorry for the distraction.
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #745 on: June 16, 2019, 11:53:35 am »

Ok, I think we should figure out who is in favor or VT / non-VT claim.

*raises hand*

Mix and Glooble have already kind of agreed to it, but obv you can withdraw that if you change your mind.
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #746 on: June 16, 2019, 11:56:59 am »

The main benefit is that we create buckets with a certain number of scum in and outside. These buckets are super neat because they narrow down the lynch pool and can lead to the creation of a bunch of ICs. The drawback is that scum can target PRs but this is mitigated by the one-shot PGO.
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pingpongsam

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Re: M123: Doomsday Mafia (Day 2)
« Reply #747 on: June 16, 2019, 01:22:54 pm »

Am I parsing the setup correctly that Mafia has to have selected a minimum of 1 modifications in order for there to be 3 neighbors in the neighborhood? That would require one modification to be converting a goon to neighbor and the corresponding town upgrade being neighbor.

I am just now getting the probability discussion because I was weighing how likely it was that Mafia picked only 2 modifications but the result was 2 town neighbors in addition to the original town neighbor. I was wavering that in order for the neighborhood to be all town mafia picked potentially 4 (with a weight towards the higher end of modifications) modifications and none was neighbor goon.

I guess, in short, it seems if there is a strong likelihood of a neighbor goon then lynching a neighbor is a decent option and a fantastic limit for reread analysis.
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silverspawn

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Re: M123: Doomsday Mafia (Day 2)
« Reply #748 on: June 16, 2019, 01:37:59 pm »

Am I parsing the setup correctly that Mafia has to have selected a minimum of 1 modifications in order for there to be 3 neighbors in the neighborhood?

Ye.

That would require one modification to be converting a goon to neighbor and the corresponding town upgrade being neighbor.

Yeah. But this is very unlikely.

I am just now getting the probability discussion because I was weighing how likely it was that Mafia picked only 2 modifications but the result was 2 town neighbors in addition to the original town neighbor. I was wavering that in order for the neighborhood to be all town mafia picked potentially 4 (with a weight towards the higher end of modifications) modifications and none was neighbor goon.

Yeah, exactly. THat's the scenario where the 3 towns scenario has a prior probability of 47.6%, which is high enough to be somewhat plausible.

What's your take on the VT/non-VT claim?
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pingpongsam

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Re: M123: Doomsday Mafia (Day 2)
« Reply #749 on: June 16, 2019, 02:21:53 pm »

What's your take on the VT/non-VT claim?

I’m not opposed. I can’t really grasp the utility of it with no revealed scum to date because they should be able to manipulate the information to make it sufficiently useless today but I think it becomes increasingly useful as scum begin to flip.
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