In post 9, mykonian wrote:in the first 2 nights, they have one roleblock, 2 kills. If they kill one of the 3 key pr's, you are still not safe from a game broken by massclaim. If they just block one, still have 5 potential innos in a 13p game. You are asking for scum to have a perfect game, or accept that your game could very well suck in the later stages as nobody has to scumhunt anymore.
And I just don't think it's asking the scum to play a perfect game. It's asking them to play a reasonably plausible game.
The scum, on D1, have 10/13 unknowns. For 3 nights, that's 3/10 chances just off of D1 stats alone to hit a PR.
A D1 mislynch on a VT makes it 3/9 chances to hit a PR.
A D2 mislynch on a VT makes it 3/8 chances to hit a PR.
The worst-case scenario of the roleblocker lynched (which making the RB full wouldn't fix anyway) still makes that 2/10 and then 2/9 chances.
And keep in mind there's multiple PRs to hit.
On N1, the mafia have one/two methods of hitting a PR.
If a VT mislynch,
-They have a 3/9 chance of blocking a PR. (One third.)
-They have a 3/9 chance of killing a PR. (One third.)
-Combined, they have a 6/9 chance of preventing a PR from getting a result.
If a Goon mislynch,
-They have a 3/10 chance of blocking a PR. (Still almost one-third.)
-They have a 3/10 chance of killing a PR.
-Combined, they have a 6/10 chance of preventing a PR from getting a result. (3/5ths. Still a majority.)
On N2, the mafia have one method of hitting a PR.
-If the mafia hit a PR with the nightkill after a D1 VT lynch, then...
*If a VT mislynch, they have a 2/8 chance of hitting a second PR. (One fourth.)
*If a Goon lynch, they have a 2/9 chance of hitting a second PR.
-If the mafia hit a VT with the nightkill after a D1 VT lynch, then...
*If a VT mislynch, they have a 3/7 chance of hitting a PR. (Almost half.)
*If a Goon lynch, they have a 3/8 chance of hitting a PR. (3/8ths.)
-If the mafia hit a PR with the nightkill after a D1 Goon lynch, then...
*If a VT mislynch (placing game at 2-6-2 relevant roles-irrelevant roles-mafia), they have a 2/6 chance of hitting a second PR. (One third.)
*If a second goon lynch (in which case the mafia's playing a terrible game?), they have a 2/7 chance of hitting a second PR.
-If the mafia hit a VT with the nightkill after a D1 Goon lynch then...
*If a VT mislynch (placing game at 3-6-2 relevant roles-irrelevant roles-mafia), they have a 3/6 chance of hitting a PR. (One half.)
*If a second goon lynch (in which case the mafia's playing a terrible game?), they have a 3/7 chance of hitting a PR.
Hitting a PR N2 prevents them from getting a result.
The total math there is if perfect (VT mislynch both days),
-6/9 (N1) + 2/8 (N2; hit a PR N1);
-6/9 (N1) + 3/7 (N2) as results. (I'm ignoring the very-realistic scenario of a PR lynch for the purposes of this math. Also ignoring the mafia PR being lynched since making the roleblocker full doesn't stop that math-wise.)
66% chance of stopping at least one PR N1 with a chance of stopping two. (I know I'm simplifying here a bit so I need to do it in more detail but for this post this'll have to do since my mind's too scatterbrained to crunch the absolute most in-depth version of these numbers.) 25% of stopping a second PR N2; 42% of stopping a PR N2 if the NK missed.
At least 16% chance of stopping two of the three PRs in the first two nights if a PR is killed N1. (The actual odds I believe are higher than this.)
At least 29% chance of stopping two of the three PRs in the first two nights if a PR isn't killed N1. (The odds may or may not be higher than this.)
That's assuming purely random play and not taking into account how the mafia won't be roleblocking their nightkill, how the ascetic if claimed is not a valid target for the block (and probably not kill either), and the mafia as the informed minority and possessing daychat will have an active ability to bounce off of buddies the ability to search for breadcrumbs. (Not to mention the obvious chance of town players claiming their role, which slants odds in the scum's favor significantly as they can kill OR block the doctor and can block the cop/neapolitan.) And I'm reasonably sure that's within the realms of normal math.
If a VT lynch D1 and a Goon lynch D2:
-6/9 (N1) + 2/9 (N2; hit a PR N1);
-6/9 (N1) + 3/8 (N2) as results.
At least 14%; At least 25%. Same caveats as above, same assumptions as above.
If a Goon lynch D1 and a VT lynch D2:
-6/10 (N1) + 2/6 (N2; hit a PR N1);
-6/10 (N1) + 3/6 (N2) as results.
At least 20% of hitting TWO of the three PRs that are a threat; At least 30% of hitting at least one. Same caveats as above, same assumptions as above. (I may need to crunch the full math numbers on this one in particular since this would imply that mafia's chances of winning actually vastly improve upon a D1 goon lynch...though in hindsight I can kinda buy that anyway since that matches what my personal experience has been anyway.)
Those are all the combinations in which the mafia don't play a terrible game. (Mafia lynches both D1 and D2; mafia losing their PR D1 or D2 with them not using it N1.)
Admittedly: this is the math from the mafia point of view.
Not the town point of view.
And not the combined point of view.
And as I mentioned already, not going into all of the combinations which can happen with their odds and numbers properly interacting. (I'm beginning to understand why you can get a degree and make a living off of just pure simple math.
)
But while I'm sure math nerds/statisticians may cry a little at my shortcuts/math failures here, it doesn't need to be exactly precise numbers-wise to convey the general point.
If the mafia are lynched two days in a row, they played a bad game.
If the mafia failed to stop any of the three power roles two days in a row, they played a bad game.
If the mafia failed to stop any of the roles N1, they played a sub-optimal (borderline-bad) game in of itself. (This is slightly more excusable than the other two, but still.)
When you also take into account how the town can't get hard guilties (short of the weak doctor death WITH a second nightkill, which by the way places the game on evens with no way to get off of them unless the doctor previously stopped a kill), the mafia have a lot of freedom in movement. They can't be caught. They have some soft-guilties on them, sure. Neapolitan, and No Result. But these aren't hard guilties, because it can be reasonably expected for the No Result to be a roleblock (especially with a roleblocker actually on the fucking mafia roster); it can be reasonably expected of a mastina game to have a duplicate ascetic (albeit unlikely); it can be reasonably expected of a mastina game to have a rolestopper as EITHER alignment; it can be reasonable for it to be a jailkeeper; it can be reasonable for it to be a commuter; it can be reasonable for me to use my non-standard role on a Hider. All of these are things I can and mostly already HAVE done.
And all the mafia player has to do to dodge the Neapolitan result is claim a non-vanilla role. Literally any role, at all, whatsoever. They have no way of being caught in a fakeclaim unless they fakeclaim VT. I don't think you're properly weighing the amount of strength impunity to freely claim whatever the fuck they want to gives the scumteam. (Admittedly it is often poorly utilized, but it's still something they have as an option.)
Yes
, there is the risk of an innocent build-up. The weak doctor's innocents however are indefinite. The cop/neapolitan may get hard innocents, but overlapping targets (especially with the nightkill) can and will lessen their numbers. Yes, there is the theoretical risk of getting three innocents N1, and three more N2. Theoretically.
But I just don't think it's going to be a likely scenario. I think that the town's natural lack of advantages, and the mafia's natural advantages, will serve to even further enhance the stats against a town lockdown, and make it so that even as-is the mafia have a strong ability to remove the town's few strengths from them.
Again. I can compromise: I can make the mafia's non-consecutive roleblocker be a full-roleblocker if that would make you happy. (I still hold that'd make the game go from even to landslide scum victory, but I'm not omniscient nor am I perfect so I'm willing to take the gamble on me being wrong and you being right there.)
But the mafia don't need a second PR here. That'd push things from "mafia have a reasonably tough game, but winnable by both" to "mafia are just going to fucking dominate no matter what".