What are the flaws in this setup?

[LicketyQuickety]

Town:
Doctor X2
VT X7
Mafia:
Goon X2 with a 1-shot strongman
Werewolf:
Werewolf X2 with a 1-shot strongman

Could someone analyze this setup and tell me what you think?

[LicketyQuickety]

looks like a fire and ice semi-clone

Is it the exact same setup?

Let me check.

It's not.

How does this compare to Fire and Ice?

[LicketyQuickety]

only town power is protective
two scum factions
there's some unique-ness but that's the one I'd compare to
honestly this seems a bit townsided, I can see the checks put in place but I'm worried about what happens if they fail.

Mafia has to play with the werewolves and vise versa. They have to play a meta game within the game, which is why I think this is interesting.

I have no clue what the EV would be for Town, nor do I know how one would calculate it. Would be interesting if someone did take the time to do this.

Game is solved through Game Theory.

[LicketyQuickety]

EV for Multiball setups gets difficult in a hurry even for Vanilla games, never mind with abilities. See [EV] Vanilla Multiball if you want to break your brain again.

I noticed you simplified the calculations to only where it matters in that thread. If your 2:1:1 is changed to 9:2:2 this changes the dynamic completely. I assume the equivalent of 2:1:1 with 2:2 would be 4:2:2, but I can't even be sure if that is correct since it very well could be 8:2:2 or 6:2:2 as the equivalent. This makes breaking down the setup I proposed into only simplest terms beyond my understanding.

I guess you answered what was "wrong" with the setup, lol.

Ironically enough, I prefer mountainous games for their predictability. This is felt as more focussed on Scumhunting in practice because you don't have roles like cop to pick up the slack.

What has happened to the mafia landscape since its inception? Is it even the same game anymore?

[LicketyQuickety]

This answers the question of what the equivalent of 2:1:1 would be for X:2:2:

(Interestingly, X:X:cX has roughly the same balance for X=1 to 4; 40% exactly at 1:1:4, up to 40.7% at 4:4:16, for c=4. I suspect X:X:cX setups will converge to the 2X:cX Nightless value for large X., so X:X:4X would converge to 50% exactly. Far too lazy to prove that right now, though.)

So it would be an inverse type of calculation with something like 8:2:2 with 2 Doctors. It gets ridiculously complicated adding the Strong Man's though.

I think it would be more appropriate to calculate for 4:2:2 with 2 Docs. No idea how many Town would be needed for 2 Doc's and 1 Strongman a piece for bother Scum factions with a x:2:2 setup though.

[LicketyQuickety]

not really imo? basically the strongmans create this process
does scumteam X use their strongman?
if yes strongman is expended, target always dies
if not it remains there and doc protection is factored in
Honestly I kinda want to create a code for determining EV of vanilla setups in Java or smth

You are only taking into account that there is one Scum Team. If there are 2 Scum teams, then if Doc claims then we get a prisoners dilemma and this is just the beginning stage of the first occurance where it matters to calculate EV (I think). Mafia and Werewolves have to out guess each other on whether to use their strongman on the Doc claim or not. Obviously the only people who are not going to claim Doc are going to be VT which then confirms them as Town, which then regresses into Scum occasionally not claiming Doc. Then the coup de gras is that Scum don't have to even NK the would be Lynchie. Effectively, you could operate in this game as though it was mountainous, since claims then really make no difference at all in practice.

I think I would like to run a setup like the one I proposed at some point.

[LicketyQuickety]

A test run would be very helpful imo, yeah

Done!

Taking pre-ins

[LicketyQuickety]

Also keep in mind that the Doctors don’t only affect EV by preventing kills (which actually matters less in Multiball, and already doesn’t matter much in single faction). The bigger effect is that they are a named role that can be claimed. In this particular setup, both Doctors claiming and protecting each other is very powerful, and scum counterclaiming puts them at a significant disadvantage relative to the other group. I would guess best strategy for both groups is to try to take out the other and save the strongman to break the Docs when the other group is gone. I expect this is very townsided with optimal play by all sides (though bad play by one scum group could bump up the other significantly).

So... Both docs claim and Mafia/Werewolves can all claim.. basically. You could end up with 6 people claiming Doc. It ends up being kind of a crapshoot in how I am envisioning this. If Town gets lucky and lynches Scum, then that Scum team is at a huge disadvantage. I don't see how Town prevents a Mass claim of Docs.

In the setup I am running in the Micro queue, there are 3 VT instead of 2 or 4. This gives Mafia the option to let one of their members NOT claim Doc...

[LicketyQuickety]

You misunderstand what I'm saying - it is not optimal for any scum to claim in that situation (at least, that's my intuition). It's a Prisoner's Dilemma situation (as is multiball in general); just as scum want to shoot other scum first (if they have a choice they want to eliminate the other group before killing town at all - in a perfect knowledge situation, this leads to a town win), they also don't want to be the group that counters Doc (it only helps the other group).

In particular, if *all* scum claimed Doc, there are three confirmed VT and town should win easily (they'd have to be very unlucky for scum to even get close to winning).

The town's EV is likely worst if there is one counter from each group; but from the scum perspective, if I think there will be one counter from the other group, it's better for ours not to counter at all. If both groups reason that way, neither will counter and there are two confirmed Docs protecting each other. (Again, intuition. I could be totally wrong and one counter is best in all cases.)

I see. So, if I have this right, you are saying in the case where all Scum claim Doc, this forces Scum to have to kill confirmed VT first? Sorry for putting it a different way, I am just trying to see more of the angles of this.

In the case with one Scum member claiming Doc and the other claiming VT, this gives 5 VT claims and 4 Doc Claims. So it would be better to lynch in the Doc claims because Town has the best chance of Lynching Scum that way. I guess the way I see it is as a prisoners dilemma, truely, because on the one hand you would have a better chance to lynch Scum lynching in the Doc claims but at the risk of lynching a PR, which makes it a not so easy call IMO. I guess I would go back to what would be the EV for 5 VT claims and 4 Doc claims? IDK how complicated that would be to figure out because the two options are just not synonymous with each other. I guess it really depends on how Scum view their chances of one Scum member claiming. I can see the angle where Scum wouldn't want to give away anything by forcing one of their own to claim, but it seems initially to me that Scum isn't putting themselves out there too much doing this. But I guess coming down to play, if Doc claims in their first post, that is going to force Scum to act very quickly. I will say that in my games that I mod, I usually allow Scum to discuss things during the proverbial N0 while They wait for everyone to confirm their role so the game can actually start. Along with Scum acting quickly, they also have the option to out-wait the other Scum team to force the other Scum team to claim first so they don't have to. But I would say there

should

be at least 3 Doc claims. Ofc when I talk about time, this is completely separate from EV analysis.

[LicketyQuickety]

I think you’re still not following, but I want to think about this some more anyway. I’m coming around to the one claim each strategy.

TBH, I am bad at following. Never been one to sheep. I should probably address that at some point...

[LicketyQuickety]

I'm confused, admittedly.

You detail why it's bad for any given Scum to do any particular action, but then at the end of the post you say it may be better for them to have a single Scum claim Doc from each Scum team...

I have no idea how you arrived at this...

[LicketyQuickety]

I'm detailing why it's bad for scum to do those actions

if

the outcomes are such that it is a Prisoner's Dilemma.

As of post 17, I am not convinced that the particular case we were discussing (whether scum should fake claim) actually has a Prisoner's Dilemma payoff.

Imma stop trying to explain this now.

Ugh, you didn't explain how you arrived at the conclusion that it's not a prisoners dilemma..

[LicketyQuickety]

That's because I haven't arrived at that conclusion yet. I'm not convinced that it *is* a Prisoner's Dilemma, but I'm not sure it isn't either. I need to crunch numbers.

Thanks for giving my idea some attention. Doesn't happen often. I hope you will give those numbers when you arrive at them.

[LicketyQuickety]

Will do, but no promises that it will be anything useful. As I said, EV for Multiball (and finding the correct strategies along the way) is already tricky, and the Doctors (in particular) may make it intractable even for a 2:2:5. Even just having them as powerless Named Townies introduces a slew of potentially nasty game theoretic equilibria to sort out. They may all turn out to be not at all nasty, but determining that will take some effort.

That said, I think it's a worthwhile extension of Multiball - basically making it "Neighborhood" Multiball, where the distributions of each group of claims is known. Say 2:2:5 splits into 1:1:3 and 1:1:2. And then you have to figure out which group town should lynch from (it's not obvious to me yet that it's the 1:1:2 group, even though that has a higher chance of success), and which group the scum groups try to nightkill into. The Doctors and Strongmen add something extra, but first you have to figure out the "Vanilla" part of the problem.

If I wanted to attempt to tackle this problem of proofing an EV for the vanilla equivalent, what would I have to know beforehand?

[LicketyQuickety]

I should really just write a guide to calculating EV and finding optimal strategies. There's a lot of good stuff to be said there.

As for your specific question, the main thing is that it is a lot of tedious work (if the setup is at all complicated), mostly in establishing what the best strategy is in LyLo or near-LyLo situations. Towns (and sometimes Mafia) often have non-obvious ways to increase their EV, and significant changes in small setup EVs carry over to the larger setups.

Other than that, it's all logic and math. If you want to generalize to an arbitrary size, the idea is to set up a recursive relationship to smaller setups (simple example: 2:5 Vanilla can either reduce to 2:3 or 1:4 after a lynch and nightkill, depending on whether you lynch Mafia or Town; to calculate the EV of 2:5, you need to know the EV of 2:3 and 1:4, along with the probabilities of reach both states, and similarly you need the EV of 1:2 to calculate those). In some setups, you can find a pattern and go back and prove the pattern holds via induction (see the Vanilla Variants thread for examples - that complicated mess in the most recent post is just the result of me putting things into a spreadsheet until I found the pattern). Some setups don't have nice non-recursive EV formulas (Vanilla doesn't), but some do (Nightless is (T-M)/(T+M)), and once you know what the answer is it's pretty easy to prove it.

The other thing to remember is that small changes can lead to huge complications. You want to approach EV in an incremental way, understanding the simplest setups first before you add even a minor role ability.

Thanks for explaining that.

I know you said that regarding the particular setup that we are dealing with in this thread that there may not really be "useful" information for me. However, and I hope I am not stepping out of bounds here, but I think if you DID provide a method to calculate the EV of any particular (vanilla?) setup, that this would become part of the knowledge base that would be incorporated for people to consider which would have a kind of follow through for the question "what is a proper setup?" I think it could have an effect on play as well, however small that may be.

[LicketyQuickety]

Was going to add this to the above post, but got quote sniped:

Investigative roles are a nightmare even at small counts, because of the addition of claiming strategies and fake claiming and so on. Killing roles are slightly better (counter claims aren't as effective if the real role can just kill the claimer). You can simplify these roles by making them non-counterable, though - that is, a Cop that can choose to claim at any time, and is then confirmed to be the Cop by the Mod.

And yes, having a baseline for EV is useful, that's why I started the Vanilla Variants thread and try to expand on it whenever I get in the mood.

I see. I am going to try and take another look at the EV threads to try and figure out what is going on there.