Scum will fake-claim doctor some fraction of the time if they get run up to lynch. Doctor will counterclaim in this case, and things follow.
Doctor choosing to protect between CI and someone else is also a game theory problem. In reality, doctors will probably choose to protect the CI only some fraction of the time.
Scum will also only shoot the CI some fraction of the time, obviously.
The assumptions are not perfect, but I hoped that they wouldn't throw the simulation off too much.
You could well be right that it doesn't matter, too. But I'd somehow expect that correct doctor strategy would push the town's EV above 50%. Could easily be wrong about that, of course.
(It occurs to me that you might want to drop one of the VTs anyway -- isn't it better to have the random-lynching EV be in the low 40% range to really discourage follow-the-clear strategies? This would also make a successful doctor-protection must more of a plus for town, since it would win back an extra lynch. But maybe that makes the game too much about town night actions for your purposes. Not sure.)
Anyway, game theory!
Spoiler: Just to check the low-level stuff
If there are only four people alive at night (1 CI, 1 doctor, 1 VT, 1 goon), I make it that town wins 50% of the time, whatever the doctor does (including protecting nobody).
Less trivially [and probably less correctly], if there's 1 CI, 1 doctor, 2 VTs and 1 goon alive at night, I get the following:
the doctor should try to protect the CI (1/15) of the time
the strategy "protect nobody" is dominated by "protect not-the-CI"
so the doctor should protect one of the non-CI players (14/15) of the time
the goon should try to shoot the CI (7/15) of the time
the goon should shoot somebody other than the CI (8/15) of the time
Protecting the CI so rarely even though the scum will try to shoot him half the time seems a bit odd, but I think is correct given the (town) pay-off matrix I came up with:
SHOOT CI
SHOOT not-CI
PROTECT CI
66.7%
27.8%
PROTECT not-CI
44.4%
47.2%
Can't promise this matrix is right though.
Posted: Mon Dec 23, 2013 2:21 pm
by FakeGod
Biggest problem is that successfully protecting someone else doesn't give the town much.
First, doctor have to consider whether the mafia decided to no-kill, or he actually did block a kill.
Second, town is at either 8, 6, or 4 players total remaining after a no kill, town needs to no lynch to maximize their chances of lynching mafia.
Posted: Mon Dec 23, 2013 3:06 pm
by agi102
Blood Night (3p)
1 Vigilante
1 Werewolf
1 SK
Night start. All kills are COMPULSIVE. If everyone dies, WEREWOLF wins. If no action occurs, they kill themselves. If there are two people left at day, Vig wins over WW, WW wins over SK, SK wins over Vig.
This is obviously Night Start, but Mafia can't kill because they want to watch Santa the Miller's reindeer and plan to murder him.
Posted: Mon Dec 23, 2013 10:18 pm
by Empking
Blood Night:
The game is just No Lynch. Random kill, Smoke clears. Celebrate\congratulate. I'd probably play it.
Shot in the Dark:
Probably leads to a D1 Mass Claim, likely very town-biased.
One Muderer:
Probably just a slog; also town favoured.
Outnumbered:
Is there a lynch? If so, town can't win, can they?
Santa:
I like the idea somewhat. I can't grasp the balance of it.
Posted: Mon Dec 23, 2013 10:49 pm
by penguin_alien
I was playing around with this set-up inspired by a game Hanasawa ran on Skype Mafia, and I would appreciate any feedback.
Night start. All kills are COMPULSIVE. If everyone dies, WEREWOLF wins. If no action occurs, they kill themselves. If there are two people left at day, Vig wins over WW, WW wins over SK, SK wins over Vig.
Since you say what happens if everybody dies, I'm guessing that the SK isn't any sort of bulletproof. And if the SK isn't bulletproof, I don't understand why you specified what happens with two people alive, since that can only happen if somebody plays against their wincon. (If only one player dies, who did that player try to kill?)
It looks like the werewolf wins 50% of games, which doesn't seem fair/fun for the people who draw the other roles. (Not to mention that a game that starts at and ends during a single night and has no uninformed majority isn't mafia?)
Everyone's uninformed, so there's some strategy going on.
Night start. If no one survives a certain night phase, WW wins. If two players survive a night phase, Vig wins over WW, WW wins over SK, and SK wins over Vig.
Posted: Thu Dec 26, 2013 8:57 am
by agi102
In post 6654, Empking wrote:Blood Night:
The game is just No Lynch. Random kill, Smoke clears. Celebrate\congratulate. I'd probably play it.
It's Night Start. I fixed it.
Shot in the Dark:
Probably leads to a D1 Mass Claim, likely very town-biased.
One Muderer:
Probably just a slog; also town favoured.
What about everything I gave the JK? T_T
Outnumbered:
Is there a lynch? If so, town can't win, can they?
There's a lynch. Maybe give town some type of Lynchproof?
Santa:
I like the idea somewhat. I can't grasp the balance of it.
Me neither. Someone simulate it?
Posted: Thu Dec 26, 2013 9:47 am
by BBmolla
In post 6655, penguin_alien wrote:I was playing around with this set-up inspired by a game Hanasawa ran on Skype Mafia, and I would appreciate any feedback.
This sounds cool, I just have no idea how balanced it would be. I'd play it.
I'll think more in depth about strategy behind it when I get home
Posted: Thu Dec 26, 2013 3:47 pm
by LlamaFluff
I would be worried about a D1 massclaim as scum there.
Posted: Thu Dec 26, 2013 3:54 pm
by penguin_alien
Which role(s) do you think would amount to scum claims? Roleblocker would be my thought, and I was originally thinking this could be offset by the part where scum choose one role that won't be in the game at all and so function as a safeclaim. I'm not sure which other ones would be dead giveaways.
Posted: Thu Dec 26, 2013 4:31 pm
by LlamaFluff
In post 6661, penguin_alien wrote:Which role(s) do you think would amount to scum claims? Roleblocker would be my thought, and I was originally thinking this could be offset by the part where scum choose one role that won't be in the game at all and so function as a safeclaim. I'm not sure which other ones would be dead giveaways.
Well its WIFOM, but you are basically going to lock scum into either trying to get lucky or going for one of the claims they grabbed. So if the were taking what they grabbed you need to have a role that isn't going to just be proven false, which is not the same as the best roles to keep out of the hands of scum.
It might be balanced, but it will swing depending on what town drafts and if scum doesn't just use their "safeclaims" it creates a situation where it can be unbalanced.
Maybe even doing something as simple as guaranteeing a variable amount of VT (2 or 3) could help as scum at least have a door number three to use. Right now its something like: Scum remove, JK and RB, must use JK/RB vs Scum remove JK/RB, claim Hider and Commuter, hope they get lucky. This way they could also have "drawn" VT as there will at least be a few of those in the game.
Posted: Thu Dec 26, 2013 4:42 pm
by penguin_alien
Do you think it works better replacing the RB, investigator, and detective with VTs? My original plan was for it to be a set-up where everyone would have something to do at night, but if that's not possible to make equitable, better a useable set-up. Alternatively, what about replacing the giveaway roles with less swingy roles?
Posted: Thu Dec 26, 2013 4:53 pm
by LlamaFluff
I don't think your choice of roles are wrong, but when there are a lot of roles you tend to make the game next to impossible for scum. In this one I just see that immediate massclaim creating a situation where scum are going to be cornered even before having to worry about how they play. When you add VT roles, it gives scum an extra spot to hide in. Its like C9++ to an extent. The early claim is a good tactic for town, but due to there being VTs even in the most power heavy of setups, there are places for scum to hide if they don't feel like they have enough of a grip on the game to claim a PR.
With the current setup you are forcing them to claim a PR which is going to be pro-town in the long run since scum can be caught by claiming something town drew, by a town PR, or by not being able to prove their role.
Posted: Mon Dec 30, 2013 4:29 am
by Oversoul
Coroner is useless in 9p.
Posted: Mon Dec 30, 2013 6:16 am
by RedCoyote
What do y'all think about something like this? The offense option may not have enough incentive, but maybe because I'm more of a conservative player. I think maybe there are those that would relish that option.
EDIT: Here is a link to a completed game for anyone who happens to stumble upon this post and is interested.
What do y'all think about something like this? The offense option may not have enough incentive, but maybe because I'm more of a conservative player. I think maybe there are those that would relish that option.
Pfft offense all the way.
Posted: Tue Dec 31, 2013 4:51 am
by RedCoyote
Well, I'm going to /in it in the Micro queue and we'll see what happens.
Posted: Tue Dec 31, 2013 5:01 am
by JasonWazza
Actually question, is the decision announced or kept secret?
Posted: Tue Dec 31, 2013 5:04 am
by RedCoyote
Secret.
Posted: Tue Dec 31, 2013 10:10 am
by agi102
Transit Mafia (9p)
5 Bus Driver
1 Role Cop
1 Vigilante
1 Mafia Bus Driver
1 Mafia Doctor
The SEUSS (Super Extremely Unbalanced Stupid Setup) (3p)
1 Doublevoter
2 Mafia Goon
Mafia have NO SCUMCHAT. Mafia do NOT know each other. Yes, I know it isn't mafia. 3 votes to lynch D1.
Jester Mania (9p)
5 Jesters
2 VT
2 Mafia Goon
The AMUSE (Arguably Most Unbalanced Setup Ever) (11p)
6 Doublevoters
5 Mafia Goons
Day Start. No massclaims allowed. Mafia have scumchat, but they must post under alteregos and post restrictions, and they do not know who each other are. If any rules are broken or there is a no-lynch, mod will modkill a scum and 2 town.
Enforcer Outpost (5p)
2 Cops
1 VT
2 Mafia Goon
The FUSSY (Fiendishly Unbalanced Silly Setup Yay) (3p)
2 Doublevoting Vigilantes
1 Mafia Goon
Night Start, if no one survives the night, Mafia Goon wins.
Tick Tock (7p)
1 Cop
1 Doctor
1 VT
1 2-shot Deathproof Power Role Enabler (if jailkept, all power roles are shut down for that night)
1 Suicidal Mafia Goon
1 Suicidal Mafia 2-shot JK
1 Suicidal Mafia Doctor
Goon dies after Night 2, JK dies after Night 3, Doctor dies after Night 4.
The USUAL (Unbalanced Setup: Ultimately Arduous lol) (9p)