I think I might be the Goblin - EVIL WIN

Forum Games Completed
,
#128

you two are same-minded now

#129

We’ve always been a hivemind
–May

1 Like
#130

hey ash you have 13 minutes

#131

i think you can’t eat paneer for an hour no matter how good it is

1 Like
#132

OH I FORGOT

#133

ahahaha

BotF XXXV: Her Royal Highness Register -- GOOD WINS
#134

If there’s a single village idiot, their info is sober. One of the extras is drunk, not the original.

1/3 chance of one cop [one sober, zero drunk] = 100% correct info
1/3 chance of two cops [one sober, one drunk] = 50% correct info
1/3 chance of three cops [two sober, one drunk] = 66.6666% correct info

Overall 72.2% base chance of correct info. IF AND ONLY IF you take all drunk info to be wrong (not true!) and all numbers of cops to be equally probable (not true!)

–May

#135

Oh jarek do you wanna whisper

#136

yeah

#137

/wjisper jarek

#138

/accept

#139

2 Likes
#140

UNVOTE

1 Like
#141

3 minutes…

2 Likes
#142

Public statement from the executives and shareholders of Chomp’s:

We blundered and will keep a more positive eye on the hydra

2 Likes
#143

/nominate Ash @Zugbot

send numbers

#144

carbonated has nominated Ash.

#145

damn. sleepy.

#146

sword nimi remains impatient

perhaps tomorrow will bring things into more light

#147

So the way I’m approaching this is:

Major Assumption

Socially, I believe that the host is always going to give you a good check on D1 if they can because the lack of information we have outside of that means we always act on a redcheck minus insane socials, especially given that you were targeting a slot who will inevitably have an enormous impact upon the game (spent far too much time trying to find the Madoka Magica term for this). This is a major assumption, but I believe in it strong enough to run with it.

I’m also assuming you’re town and not made mad by a Cerenovus, but that feels like less of a jump.

Probability Calculation

We are calculating the probability you got a bluecheck given that BetterMittens is a redcheck. The formula for conditional probability is P(A and B) / P(B).
In this case, A is the scenario where you get a bluecheck, and B is the scenario where BetterMittens is mafia.

P(B) is easy: assuming you’re town, BetterMittens has a 2/8 = 25% chance of being a Minion or Demon.

P(A and B) - the probability you both get a bluecheck and where BetterMittens is mafia - is harder, but we can simplify it. There are four possibilities:

  1. Bluecheck + Town
  2. Redcheck + Town
  3. Bluecheck + Mafia ← What we’re solving for
  4. Redcheck + Mafia

Because of our major assumption, we strike out #2.
Additionally, we assume that for #1, the Storytellers would leave your check untainted. Thus, it equals the base probability that BetterMittens is town: 6/8 = 75%.
We know that the probability of all four options will add to 100%. We have that the probability of Option 1 is 75% and that the probability of Option 2 is 0%. Therefore, the probabilities of Option 3 and 4 add to 25%.

In a more intuitive sense, this mirrors the base probabilities of being town and mafia: we’re looking at subsections of those probabilities.

So our goal is simple: find the probability that your redcheck could not be messed with in any way (as per our major assumption, if your redcheck could be messed with, the Storytellers would mess with it), subtract that from 25%, then divide that by 25% to get our final probability.

More Assumptions, Weeeeeee

This is the part where we need to make some giant assumptions. That said, if you disagree with the numbers I use, you’re free to change them accordingly.

  • Equal probability of being a sober Village Idiot:
    • 1 Village Idiot - Guaranteed to be sober
    • 2 Village Idiots - 1/2 chance to be sober
    • 3 Village Idiots - 1/3 chance to be sober
  • Equal probability of which Demon and Minion is in play, removing Kazali-Xaan (1/14 for each pairing)
  • Equal probability of Demon location (1/4 chance for the Demon to be your neighbor)
  • The Xaan: By far my biggest leap, but I imagine the GMs will lean towards having a different number of Outsiders if they added this in. Given that 9 of us gives 2 Outsiders, I suspect they will either lean towards 1 Outsider or 3 Outsiders. I’m guessing the probability distribution would look like 50%-20%-30% because I do not think the Storytellers would add 4+ Outsiders to a game this small.
    • 1 Outsider: 50% chance
    • More than 1 Outsiders: 50% chance

Everything else should be accounted for: Boffin can’t trigger unless you are literally the Demon (see Major Assumption), and Sweetheart only triggers on death.

The Actual Math

DrunkVillageIdiot
DrunkVillageIdiot1920×1801 267 KB

Result

Given our numerous assumptions, there is a 48.32% chance that BetterMittens is mafia given that you got a bluecheck.

2 Likes