[EV] M Mafia, 1 Vigilante, T Townies

[Mathdino]

but my point is that if said vig is at a point where they can confirm someone as scum

the town was likely to win anyway

i have seen many games where i've thought
"wow town would've lost without the cop"
or
"wow town would've lost without the doc/JK/RB stopping that kill"

it is rare that i see games thinking "wow town would've lost without those vig shots"

in fact i see more games thinking "wow town would've won that if not for the vig"

[mith]

It's not hard to see that having a Vig is better than not having a Vig, at least if the remainder of the game is Vanilla. Having a Vig gives 2 Town-controlled kills for every 1 Mafia-controlled kill. Mafia-controlled kills always hit town, so you want as few of those over the course of a game as possible. (A Vig kill is actually slightly better than a lynch, as has already been pointed out - the Vig kill is choosing from a smaller pool with the same number of Mafia, and so is more likely to hit Mafia if chosen randomly.)

The math is different if there are other town roles. But unless the game can be broken through claims or information roles, I am firmly in the "Vig should always shoot" camp.

[callforjudgement]

A simple way to see how having the vig is better is that instead of not vigging, you can just get town to vote on the vig kill. That makes it more or less equivalent to a lynch (except that if the vig themself is voted as the vig target, they can shoot someone else, thus giving town a bit more of an edge).

[mith]

Yeah, that's another good way of looking at it (though that plan is actually demonstrably worse than letting the Vig make the decision randomly, if it's followed strictly; it tells Mafia who is likely to be killed, so they can kill someone else and avoid doubling up on a townie, and it also tells Mafia who the Vig is as soon as they don't die).

(If I weren't so busy, I'd put something together to calculate the EV of that. Actually might be an interesting setup to run, just having that as a weakened Vig role.)