I may be overlooking something but wouldn't the numbers be 1 in 7? We have 8 players and the FBI won't investigate himself and the SK won't kill himself so that means 8-1 = 7. I don't see why we should assume that the FBI will only get 1 chance to investigate. Day 2 will have 2 deaths so we'll be down to 6 players. The SK and FBI only have a 1 in 5 chance to get each other.Which is exactly why I pointed that out.
Keep in mind that you must assume based on the low player count that the FBI Agent essentially gets one chance to find the SK with an investigation - something which should be 1 in 6. With that, there is the chance that the SK will kill the FBI Agent anyways - again, 1 in 6. And there's a further chance that the SK will kill the FBI Agent's target if they get an innocent - 1 in 6.
I definitely need clarification here: If we massclaim how will we find SK? It's still a guessing game as far as I see. It's not as sure a plan as you make it sound. The 1/8 FBI being lynched isn't really an issue either as they would quickly claim.Now, if we massclaim, we not only find the SK, but we find the scum as well - if the FBI Agent claims truthfully and is not counterclaimed, we then have a 3/7 chance of lynching an anti-town role, and a 1 in 7 chance of getting the SK - this is actually better odds than if we weren't to massclaim, when we would have a 3/8 chance of anti-town and 1/8 chance of SK, not to mention the 1/8 chance of the FBI Agent being lynched.
The conclusion I've drawn from this post is that you're trying to scare the town into killing off its best asset. The FBI will likely make it to Day 3.