kikuchiyo wrote:Note to town: Claimed serial killers shouldn't be lynched in those situations.
Mmm, I don't think so. I mean, yeah, in the best-case scenario you lynch a werewolf instead, the SK NK's the other werewolf, then the next day you lynch the SK and win. But I think that's a pretty unlikely scenario.
Consider that the T:W:SK ratio was 5:2:1 at that point. If you don't lynch the SK, you've got a 29% change of lynching a werewolf and a 71% chance of lynching a townie. Either way, we go to night (at 4:2:1 or 5:1:1).
That night, the werewolves will kill a townie (because a.) the SK claimed NK-immune and b.) it's not to their benefit to kill him anyway.) In the 4:2:1 scenario, there's a 17% chance that the SK kills the same townie as the wolves did, a 50% chance he kills a different townie, and a 33% chance he kills one of the werewolves. In the 5:1:1 scenario, there's a 17% chance that he kills the same townie, a 67% chance he kills a different townie, and a 17% chance he kills the remaining werewolf.
So the possible lineups on the next day are, from most to least likely:
(3:1:1) 42%
(2:2:1): 36%
(3:2:1): 12%
(4:1:1): 5%
(4:0:1): 5%
Taking these one by one:
(3:1:1) If you lynch the SK now, and go into night at 3:1:0, the wolf NKs a townie and the next day you're at a classic 2:1 lylo.
If you don't lynch the SK now, you've got a 25% chance of lynching the remaing wolf and eventually winning (night is 3:0:1, next day is 2:0:1), and a 75% chance of lynching a townie and going into night at 2:1:1, which I think is always a town loss. The wolf NKs a townie, and the SK has a 33% chance of NKing the same townie, a 33% chance of NKing the other townie, and a 33% chance of NKing the wolf. So the next day you're at 1:1:1, 0:1:1, or 1:0:1, none of which the town can win.
(2:2:1) Now you CAN'T lynch the SK, because that's an instant win for the wolves. But you can't lynch anybody else either, because then you go into night at 1:2:1 or 2:1:1, and there's no town win coming out of those. Even if you were able to get a No Lynch (and it wouldn't be in either the wolves' or the SK's best interests to vote No Lynch), you'd go into night at 2:2:1, and I don't see any town win scenario there, either. Wolves always NK a townie. SK NK's that same townie (25%), a different townie (25%), or a wolf (50%) and then you're into the next day at 1:2:1, 0:2:1, or 1:0:1.
(3:2:1) Again, you can't lynch the SK without triggering an autowin for the wolves. 60% of the time you lynch a townie and go into night at 2:2:1, which is a town loss. The other 40% of the time you lynch one of the wolves and go into night at 3:1:1. The wolf NKs a townie, and the SK can either NK the same townie (25%), a different townie (50%) or the wolf (25%), sending you into the next day at 2:1:1, 1:1:1, or 2:0:1, only the latter of which is a town win.
(4:1:1) If you lynch the SK, you go into night at 4:1, and the next day you're in a 3:1 lylo. If you don't lynch the SK, 20% of the time you hit scum and go into night at 4:0:1, and the next day you're at 3:0:1 and you know who the SK is so you can lynch him and win. The other 80% of the time, you go into night at 3:1:1, with possible outcomes as described above.
(4:0:1) Lynch the SK and win.
The math here all assumes lynches and NKs are effectively random. Obviously, you can do better than random chance and that will affect the numbers somewhat, but it seems to me the town-loss scenarios will still outnumber the town-win scenarios. Also, the percentages may not add up to 100 due to rounding.
Well done Gwyn, you played very well.
