Happily Ever After Policy

[Mathdino]

So I've been running some EV calculations on the Newbie Setup, and I've run into a few situations where it would either be essentially throwing the game for mafia to kill, or would be suboptimal for either side to do anything.

I'm not talking about situations like 1:3 vanilla. In practice, mafia DOES kill in those situations to remove a strong townie. So I've made the assumption that in that scenario, town no lynches and mafia kills. In most scenarios I've actually made the assumption that mafia kills, as more nights usually give town more information (Cop/Neapolitan).

I'm talking about things like the following:

A. Tracker + Doctor + 2 VTs vs Mafia Goon (claims VT). VT gets lynched.

Town massclaimed, and the doc is on the Tracker. Tracker is checking remaining VT claims.

Killing will immediately lose the game due to the tracker's result. So killing would legitimately be 100% throwing the game here, and can never improve EV.

If the burden is on town to lynch however, they have a 50/50 shot the next day of lynching correctly.

So who is the burden on in this situation? Who wins if mafia (optimally) no-kills forever, while town (optimally) no-lynches forever? And if one group is FORCED to do something, which group is it?

B. Tracker (with an inno on the Doctor) + Unclaimed Doctor + 2 VTs vs 2 Mafia Goons, going into night.

This is more complicated. I worked out the odds for if mafia kills in this situation, and later no-kills when it would be throwing otherwise (putting the burden on town).

If mafia kills, town EV is 38.9%.

If mafia stops killing altogether, however, the next day (MyLo), town has a 50% chance of losing immediately. If they do lynch correctly, it goes into Tracker + Unclaimed Doc + 2 VTs vs Mafia Goon at night, and unless this scenario has a 78% or higher town EV no matter what mafia does, this EV is lower. (if mafia specifically NEVER kills and town is forced to lynch, that scenario has a 66.7% EV for town, putting the entire "mafia stops killing" scenario at town EV = 33.3%)

Mafia is benefited by not killing at all.

And of course, because of this, if mafia no-kill, town will no-lynch to throw the choice back to them and increase their own EV.

So who is the burden on in these situations?

I'm specifically interested in the official Newbie Queue policy on this, because that would be what affects my EV calculations.

That said, feel free to discuss your own thoughts/opinions on Happily Ever After situations.

[Lycanfire]

it's a draw. get them to do a tiebreaker on a monday to decide

[Toomai]

The way you described it, I'd look at it like this.

A.

The remaining goon does not have a choice in the matter - assuming no town blunders, if he makes a kill, he loses guaranteed. By contrast, the town does have a choice whether to lynch or no-lynch. Assuming no scum blunders, choosing to no-lynch does not advance the gamestate at all. By contrast, choosing to lynch is not only an attempt to win but a fairly good chance at winning (50/50 at random, which is likely to be better in a practical "3:1 with 2 conftown" situation). So in the end, I'd say the onus is on town to lynch, because it is them who are choosing to not advance the gamestate (because for scum, "do this or lose" is not a choice).

B.

This is 4:2, so the Doctor already has a protect and therefore a possible town result. In the face of a possible "4:2 with 3 conftown", this is pretty strong incentive for scum to look for him. In addition, there is no way for the Tracker to know for sure his buddy is a Doctor - he could be a Jailkeeper, or even a Cop and the scum no-killed that night. Finally, having a Doctor means that it's not MyLo, because the nightkill can still be stopped. I think this is too complex a situation for either side to consider holding to a no-killing loop.

[Mathdino]

@Toomai: Good take, and that's along the lines of what I've been working with.

A. Along the lines of "advancing the gamestate":
- What if scum killing gives them, for example, a 1% EV? Is the burden still on scum? I say yes, because it's > 0, but getting that close makes things fuzzy.

- What if, due to a doc protection or a vig kill earlier in the game, town ends up in even numbers (where it's optimal to no lynch)? Would you argue it's town choosing not to advance the gamestate?

And to bring in

Lycanfire

(thanks for meming), what if the mod kills someone for being conftown because their hydra buddy posted their role PM, and town begins a no-lynch/no-kill cycle?

B. A couple clarifications:
- It's 2:4

going into night

. Town just lynched a VT the previous day, I didn't make that clear.
- Tracker knows that their target is the Doc because of setup shenanigans. A hypothetical jailkeeper would be on the tracker, and a hypothetical cop just means the claimed tracker would be dead already.
- You might be right about not-being-MyLo raising the town's EV. I'd have to work out the equilibrium for who doc protects and who scum shoots tbh.

[implosion]

Spoiler: A vignette

Scenario A actually reminds me of something that happened on epicmafia many years ago. I was the last scum alive, and the setup was me + a vanilla townie + an oracle (targets someone at night, if they die that person's role is revealed) + a bomb (if shot at night, kills the shooter). I'd claimed vanilla so you can see there was nothing I could do but endlessly no-kill, but on EM after 3 cycles you get rocks fall everyone dies, which is actually meaningful since they have a points system and nobody got points. The system displayed a message on the last possible day or night before it would happen, and it was common wisdom that it was that side's responsibility to do something, so the town repeatedly no-lynched to force me to kill, and I couldn't very well argue against them doing that without outing myself as mafia... so I decided to no-kill to force everyone to lose rather than give town the win, and I got reported for it, which I found amusing. Don't think anything happened with the report.

I think scenario 1 is effectively the town's choice over whether they want to take the 50/50, or force a draw. They can't force scum to kill. But it's much, much more subtle when it's simply suboptimal for scum to kill. I mean, you're missing the very simplest scenario in which this arises:

C. 3 VT versus 1 Goon, two dead power roles with no remaining information from them on people alive, going into night.

This will basically always be a thing in every single game in pretty much every queue.

Scum no-killing gives them better odds if town is willing to lynch at 4p. What if it's 3:1 going into

day

first? The way EM did it, the first side to no-act was obligated to act in situations like this, but clearly this doesn't work as a catch-all as can be seen by my spoiler above (or just by scenario A).

[Mathdino]

In cases of all-vanilla, I'm adopting The EV Project's standard of assuming that town no-lynches at evens (forcing scum to kill). I don't know what precedent that's set on.

I agree re: first side to no-act. But that leads to shaky situations.

- What if the first "no-act" is caused by a doc protection?
- Or a jailkeeper block?

Example newbie scenario. 4p with a jailkeeper, and the jailkeeper keeps jailing the same player.

- If that player is town, what stops scum from no-killing forever to frame that player?
- If that player is scum, do they get confirmed to be scum by the fact that they're not technically "no-act"ing and are genuinely trying to kill?

This isn't a very good example, because regardless of what scum does (if they're not the player getting jailed), there's a 50% EV. But the idea stands.

[popsofctown]

I'm not a setup design guy but I figure bet policy is to pick a side to have Happily Ever after burden based on which one seems to have the tilt of the setup, and then tell the mafia during confirms which side has H.E.A. burden.

I don't really want to think about how you design around awful power roles like doctor and cop.

[callforjudgement]

Innocent Tracker + Innocent Doctor + 2 vs. 1 is an example of a screwy endgame I haven't seen before. So congratulations on finding it, I guess!

It's not a "perfect" screwy endgame, though, because town do have an action other than no-lynch that doesn't immediately lose them the game (and it's hard to define the EV of no-lynch when it won't accomplish anything; mathematically, you discover that the EV of no-lynch is the EV of no-lynch, no more information than that). Some of those do exist, but all examples I know of involve either multiball (2 VT vs. known Mafia vs. known Werewolf is the simplest), or nonstandard victory conditions.

For what it's worth, I think you can make a good flavour argument that if town put scum into a situation in which the scum can't kill, there are no threats left to the town. So calling that ending a town win would not be ridiculous, although it would be nonstandard. The caveat, of course, is that in Nightless games the only threat to the town is typically their own voting…

[Gamma Emerald]

hydra buddy

hydras ain't in newbies pal

[Gamma Emerald]

I'm not a setup design guy but I figure bet policy is to pick a side to have Happily Ever after burden based on which one seems to have the tilt of the setup, and then tell the mafia during confirms which side has H.E.A. burden.

I don't really want to think about how you design around awful power roles like doctor and cop.

I don't like this idea because it feels like potential setup info that shouldn't be given

[Toomai]

In the general case, the mod should step in and say "both sides will lose if this continues" because it forces someone's hand, but no matter when you do it one side has the advantage.

I'm currently of the opinion the mod should warn about this when:

• there's been 4 consecutive deathless cycles (2 no-lynches and 2 no-kills)
  
• the town is obviously no-lynching by choice rather than by failure to lynch

...and then state after the 6th consecutive deathless cycle (3 no-lynches and 3 no-kills) that "someone will die this phase or everyone loses", which in the end puts the onus on whoever started it.

Obviously this isn't foolproof, but it only really falls apart when

1. town is no-lynching on purpose
   
2. one of:
   1. scum cannot kill without being found out guaranteed
      
   2. scum is trying to kill but got blocked by town roles 3 times in a row

If 1, scum killing would be a blunder and so should not be considered a valid choice, and so the onus should be on town - but if the mod explicitly states "the onus is on town", that pretty much mod-confirms whatever massclaim happened to get into the situation.
If 2, that's pretty rude for town not to lynch the scumbutt after 2 days of blocking him, and they may in fact deserve the everyone-loses option.