The base problem with regfan's plan is he's missing the lynch, I think. It's the only surefire kill people have, and plans of crosskilling tend to get ruined by scum commuting, leaving you with a 50% shot afterwards, which isn't a terrible improvement of a usual day, and runs the risk of hitting two townies at which point town gets set back majorly.
Lets see. If you extend regfans idea to three people shooting groups you get a 100% information return. If all die, too bad, they were townies who all shot. If someone commutes, that means two survive, of which one has to be a townie who didn't get shot because scum commuted, and the commuting scum.
You can't lynch day one and then make two circles of three, that wins the game for scum.
If you make one group, if all are town, you lost the game (20% chance).
If one is scum, you lose one townie there, and have a 100% lynch day 2 if scum chooses to commute (60% chance)
If there are two scum, same as the above, 100% lynch day 2. (20% again)
All other townies which aren't in that group of 3 commute, leaving day 2 with a 80% chance to lynch scum and 20% of insta lose. I think that's in town's favor, as losing by lynches is easier then that 20%, I think.
I could go on telling you in that case night two wouldn't be bad for town with just one scum kill there and 3 townies left, bringing the game to a 3p lylo with scum's commute still in and the one of the confirmed townie as well, but knowing all this from reading this post,
scum won't commute when he knows he's being shot
Which means in that same scheme, you lose in 20% of the cases, in about 60% of the cases three people die night 1, 1 scum and 2 townies and in about 20% of the cases one person dies and scum is trying to wifom you (hence the "about" 20% and the "about" 60%, as wifom tells you scum will have to choose suboptimal in the 60% scenario sometimes to make it in the 20% case, which would otherwise always lose them the game since you'd know both scum without wifom)
In the 60% case, which is all that changed because of scum's response, day 2 is a 3p lylo, with scum still having both one shots and town having two vig shots, meaning it has to be a straight up lynch as you can't beat the scum at night with any certainty. 33% win ratio is still better then doing nothing as town, as a mountainous 7p with a mislynch day one only gives you a 13% chance of winning.
If you did lynch scum day one, and you do the same, you have a 50% chance of victory, and a 50% chance of a 3p lylo (which adds to 66% for town). If you let scum shoot you once (which he could do at any night, which he wants to do the night when he wins, affected by WIFOM since town saves it commute for that night.) that leads to a best case scenario (where he shoots right away) of 60% and a worst case (where he shoots the night he wins) of 50%. If town manages to commute his shot you are back at 66%, making the breaking strategy slightly better then the strategy of simply not shooting as town.
You improve a little on the not shooting strategy by shooting controlledly as town at night, as a vigs chances are a little higher if the game was truely random (since he won't shoot himself), but tbh, I think that's a point where the assumption of randomness isn't good enough anymore to show a difference between strategies, and I don't know if it would pull up the chances of winning above 66% anyway.
Surrender, imagine and of course wear something nice.
