[QUOTE=Sitnam]
I’ve been thinking about a person claiming a power role to avoid a band wagon kill (one especially uninformed as our first lynch). It’s my understanding that roles are rare, baring any mason’s (I know what they are, just not how they play out), we’ll have just one doctor and detective (or about two similar roles), if we’re unfortunate enough to lynch one of those the first turn town is serious trouble. What precautions does town usually take so this doesn’t happen? If it does, how can we make the best of it? Granted it looks like a 1/8 chance of lynching a town power role, the odds being twice as likely that we’ve picked scum that’s then claiming to be a power role for town. The reason we’d even lend any credence to his/her claim at all is we think such a power role might exist, we still just don’t know. I see these as the five likely outcomes of a power claim to avoid a lynch:
The person about to be lynched says they are in a pro town power role and are either telling the truth (12.5% of that I guessing, yet will still then not outlast the night) or:
1.) Someone else stands up and says no, because THEY are the role and are not lying.
2.) Someone else stands up and says no, because THEY say they are the role and are lying. (a ballsy strategy that only pays off if both are scum, which will ultimately provide a massive tell in later days)
3.) No one else stands up because person actually in said role is scared of being night killed.
4.) No one else stands up because the role claimed doesn't actually exist and so no one can honestly counter claim.
The odds for #4 cannot be determined but I see them as unlikely (this game was claimed to be pretty vanilla), the chance #3 happens is very very good in the beginning (and since its the best outcome for town, the essence of my conclusion), and if #1 happens and we lynch the first guy (town or no, killing all liars seems like a solid policy) we’ll then know if the person lynched is the actual power role that was claimed. If so, the counter claimer is a dead man, a town power role for one early scum (I’m including lying townies) is a high casualty rate but I believe near acceptable.
The odds of picking scum or a townie that’s lying is so much greater than actually lynching someone whose honest in claiming a power role that can’t actually be proven that I see no rational alternative.
We have to lynch in spite of power role claim, if only to keep the good guys honest and the bad guys shitting their pants.
[/QUOTE]
These situations, while intuitive, do not reflect reality. The probability of a person claiming a power role being truthful is not equal to the distribution of that role through the town as a whole. There’s three posibilities:
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The person is telling the truth: The truth value here is obvious. Let’s say n[sub]0[/sub] is the number of players, n[sub]r[/sub] is the number of role r that actually exist in the game, c[sub]r[/sub] is a claim of role r, and i is the player. Thus, while p(r[sub]i[/sub]) = n[sub]r[/sub] / n[sub]0[/sub], the truth value is actually T(c[sub]r[/sub] | r[sub]i[/sub]) = 1 because we know that c[sub]r[/sub] = r[sub]i[/sub].
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The person is lying scum: The truth value is also obvious here, the probability is the same, but T(c[sub]r[/sub] | r[sub]i[/sub]) = 0 because we know that c[sub]r[/sub] != r[sub]i[/sub].
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The person is lying, but is pro-town: This is just monumentally stupid. FOA, he’ll convince the person ACTUALLY having that role that he’s scum, which will make the real role either claim, or just mark him up as scum. It will also potentially get the real roll to out himself by expressing doubt of the claim. And it will CERTAINLY get him lynched when the real role dies. There is a case to be made for a more valuable role possibly pretending to be a lesser role to try to protect himself, but a vanilla doing this is so harmful to the town that it either won’t be done, or it’s so damaging, that it throws out the modelling anyway, so I’ll ignore it as a possibility.
Thus, we can model the truthiness of a claim as follows: T(c[sub]r[/sub]) = Σ(i=1, n, T(c[sub]r[/sub] | r[sub]i[/sub])) which reduces to T(c[sub]r[/sub]) = n[sub]r[/sub] / (n[sub]r[/sub] + n[sub]s[/sub]). This is demonstratably larger than p(r[sub]i[/sub]) = n[sub]r[/sub] / n[sub]0[/sub] because the denominator is the number of players minus the vanilla townies, which is necessarily smaller than the total number of players.
Further, this doesn’t take into account the simple fact that a pro-town role has greater motivation to claim that particular role to save his life, while a scum has a lesser motivation because it will likely lead to him losing cover, thus a better model would be T(c[sub]r[/sub]) = n[sub]r[/sub] / (m[sub]r[/sub]n[sub]r[/sub] + m[sub]s[/sub]n[sub]s[/sub]), where m is the motivation. Thus, because m[sub]r[/sub] >> m[sub]s[/sub], it follows that T(c[sub]r[/sub]) –> 1.
For the non-mathematically inclined, basically, the chance that a major power role claim is a lie is low because there’s little motivation for scum to claim it because it gains them little, and is cover easily blown.
