Numbers will depend on game size, but history shows that games with instant-win conditions shouldn't be too large. As such, a good place to start might be 6:3 (with a resulting EV of 51.4%); that gives town a mislynch (thus a guarantee of at least two chances to hit the lynchpin, and of course they could just lynch scum instead, although an instant-win is likely easier). Note that associative tells are likely to make the lynchpin look scummy and/or the scum guarding them look scummy, and it's in scum's interests to give themselves up to save the lynchpin, so I'd imagine that there'll be a lot of bussing, distancing, and the like involved. It may well be, though, that scum have a large advantage compared to EV in this sort of setup, so perhaps 8:3 (with an EV of 61.6%) would work better. (As usual, the larger the setup is, the less useful an extra mislynch is, because the more likely it is that you'll just end up lynching a random VT.)
Oddly, if run with an even number of players and a compulsive lynch, the EVs appear to be identical to those of a nightless game with the same player count and faction sizes. I assume there's a mathematical reason for this, but it's an interesting coincidence that make the EVs easy to look up. (The correspondence doesn't hold if the total number of players is odd, with the EVs generally much higher; the main reason for this is that there are two different ways for town to win a 2:1 lylo.)
I'm curious as to what the best lynchpin selection strategy for scum is. Strong players are unlikely to get lynched, but putting a strong player into a position where they can't be nightkilled and they can't be "mis"lynched without scum automatically losing seems counterproductive. On the other hand, making the lynchpin a weak player is more likely to have them unintentionally do something scummy and end up getting lynched for it, and/or having them become a compromise lynch.
Well, the lynchpin can't matter any less in 8:3 than in 6:3, because an 8:3 becomes a 6:3 after a mislynch and the lynchpin is still there.
I'm kind-of assuming that scum will play this setup a bit like a White Flag, and try to avoid the 2:1 endgame because it's so nasty for them. Playing on evens normally sucks, but I can see the merit of wanting the "final lylo" to be 3:1, so perhaps evens is a better choice here? (In that case, you'd need to make both kills and lynches compulsive.)
I'm also assuming that the lynchpin mechanic mostly shows up in making scumhunting more accurate. The mechanic has too much of an influence on the game for scum to ignore, so they pretty much have to try to manipulate the lynches. That should be something that shows up and that the other players can detect. (I can sort-of see the lynchpin winning via self-vote, too; it may well be possible to realise that scum are trying to keep you alive. Possibly the most common way I catch scum is that they have a read on me which doesn't seem like it can possibly be justified from their point of view, whether that's a town read or a scum read.)
work with 1 scum, and that's something that I hadn't considered at all. (Normally 1 scum setups don't work because you don't get associatives, but in this setup there are town/scum associatives.)
I think it'd work better at 3:1, though, otherwise town has too much of an incentive to just guess immediately. I'm going to try that in the Micro Queue right now.
