Stoofer's 3rd Law

[Zindaras]

it kinda disproves the complexity aspect a little though. If someone had just claimed 'billy bunroe, doc', with no additional details, they would have been lynched straightaway, after the wifom discussions. A similar thing happened in higher mathmatics mafia, where the roles were all so complicated that the scum had to go with simple claims.

If my memory serves me well, there were also pretty normal roles in that game. Vanilla townies and such. I d'no. I guess the knife cuts both ways.

I rate roleblockers as more powerful than doctors. They're like a hybrid cop-doc. Doctors are only stronger when they know who they need to be protecting.

Whoa girl.

The only reason Cops can dominate games are due to Docs. A lot of games degrade into a "Catch the Doc before the Cop gets enough investigations to confirm enough alignments."-game for the scum. Roleblockers can't possibly do that. Also, comparing roleblockers to Cops doesn't go very far. A roleblocker cannot ever state with 100% surity that someone is scum. A no-kill can occur due to many things.

A doc, in itself, is not a powerful role. However, it adds a lot of value to other roles, even if there is no actual doc. The Mafia will always be afraid that there could be one and avoid otherwise optimal hits.

[Mr. Flay]

I could probably accept it if the 3rd Law was reformulated in the negative, i.e.:

Increasing the number and complexity of Pro-Town power roles in a game does not always lead to a greater Pro-Town advantage.

But that's watered down enough to be nearly meaningless.

[Zindaras]

Well, if you can't think of a new Third Law, I suggest "Kittens are awesome."

[Thestatusquo]

I think it's fairly obvious that what stoofer's law should posit two prongs of analysis.

One, that as the number of action changing interactions(say that three times fast) between pro town power roles goes up, the set up favors scum.

For instance, in jeeps example, with 18 sane cops and 4 scum, there would be relatively few changing interactions, except for of course, the obvious mass confusion once someone was pushed to claim.

But in the several interactions that stoofer described above, there is much action changing interaction.

And Two, that as complexity goes up, once again, advantage scum.

[Mr Stoofer]

Good posting by Thestatusquo.

I think Mr. Flay's version is too watered down. Stoofer's 3rd Law is not a law (one counterexample does not disprove it) but I think that in pretty much

any

set-up, there comes a point where increased complexity hurts the town: i.e. Thestatusquo's second limb.

[Zindaras]

I could probably accept it if the 3rd Law was reformulated in the negative, i.e.:

Increasing the number of Pro-Town power roles in a game does not always lead to a greater Pro-Town advantage.

But that's watered down enough to be nearly meaningless.

I think that's a better version, and it's definitely not meaningless.

Actually, I think that I'm just saying what shea's saying, except a bit differently, so he's right.

[jeep]

In one game the cop was blocked and the doc prevented the kill.

So there were two pieces of bad information in the mix

. I understand your comments, but I don't agree with how serious the "misses" are or how valuable the "hits" are.

This is exactly my point!

Yeah. I just don't think your "law" is phrased accurately. I agree with some of the idea behind it.

As to roleblocker, I strongly feel that it's not a positive town role unless it's an open setup. The roleblocker can never know if they blocked anything from happening or if it was just a fluke that the SK targetted the godfather or...

-JEEP

[Mr Stoofer]

Perhaps a better way of expressing it would something like this:

• The greater the complexity of the set-up, the more difficult it is for the Town (the uninformed minority).
• Complexity of a set-up is a function of (amongst other things) the number and complexity of power roles.
• Therefore adding a Pro-Town power role, especially a complex one, may not benefit the Town, but may instead hurt the Town because it increases the complexity of the set-up.

This is of course too longwinded for a "Law" but it encapsulates my point. Maybe the last bullet point is the law and the first two bullet points are the reasons for it.

Although the last bullet point is rather similar to Mr. Flay's formulation...

[Norinel]

As to roleblocker, I strongly feel that it's not a positive town role unless it's an open setup. The roleblocker can never know if they blocked anything from happening or if it was just a fluke that the SK targetted the godfather or...

It doesn't necessarily catch scum, but the more complex the game gets, the more likely it is that the blocker can confirm his night action, or block actions that'd hurt the town.

I think in general we should distinguish between how night game actions affect the night game (Roleblockers, for instance), how night game actions directly impact the day game (Blocking/causing kills, for instance) and how night game actions inform the day game (Cops, for instance).

Perhaps a better way of expressing it would something like this:

• The greater the complexity of the set-up, the more difficult it is for the Town (the uninformed minority).

That certainly isn't always true, though, particularly for the step from vanilla to, say, cop+doc.

Here's how I'd restate/derive it:

Any particular setup has an optimal degree of how much the town should trust night game information vs. day game information. This degree tends to go down as the game becomes more complicated, but in general the town doesn't sufficiently compensate for it. Thus, the town

plays worse

when the setup is more complex.

Every example in this thread was either a case of night game actions balancing itself or the town overtrusting the night game (The night game information balancing itself, if you will). Because there are very few roles that thwart day game information (Death millers being the most prevalent example I can think of), overtrusting the day game is either impossible or can't lead the town much worse than a comparable vanilla game.

[Kelly Chen]

As to roleblocker, I strongly feel that it's not a positive town role unless it's an open setup. The roleblocker can never know if they blocked anything from happening or if it was just a fluke that the SK targetted the godfather or...

They don't need to know this to be useful. It's already useful to stop a kill. Same as with a doctor.

It's true that a doctor is less likely to accidentally make a move that hurts the town. But a roleblocker, like a vig, is trying to target scummy people. If we don't imagine they have an ability to pick out scummy people then a vig is not a very positive role either.

[Adele]

I certainly agree that:
-> All roles (pretty much) have some cost.
-> They should also have a benefit.
-> But the benefit suffers from diminishing returns under Stoofer's law at a greater rate than the costs do.
-> Thus as amount and complexity of roles increases (complexity within roles also, such as a commuter has a greater effect here than a bulletproof), the town's power increases more slowly and may eventually be harmed.

-->

Exception

: interaction of protective and investigative roles.

If towns are losing because their power roles don't sound plausible, then perhaps townies aren't lying enough.

DIE SUCK DIE

[Yosarian2]

Governor is the main role I think of as an example of a neutral-negative role in town hands. (Though I've seen a governor save someone who claimed in twilight. But that's a weird situation.)

I tend to consider any role that you can use or not use as you choose, and that does what you think it does, as at least slightly better then a vanillia townie; after all, if there never comes up a situation where the right move is to use the role, then you can never use it. And I can think of situations where it's a good idea to use the role; for example, if there's some wierd late-game situaiton where a no-lynch is the best move, the town can instead lynch and pardon in order to confirm the governor instead, as I've never seen that role as scum.

Granted you can use it stupidly and hurt the town, but if the town loses because pro-town players make bad decisions, I don't really think it's a balance issue.

Even a role like this, I would consider at least as good as a townie:

You are a day-vig townie killer. Once in the course of the game, you can choose to try and vig someone during the day; if they're a vanillia townie, they die, and if they're not, then nothing happens. You win with the town.

There are some situations where even that role would be useful (say, it's probably better to day-vig a townie and continue in day rather then lynch him, so if you're about to lynch someone might as well try and day-vig him first just in case you're wrong), and if the player uses a role like that in a dumb way, well, bad play deserves to lose.

[HackerHuck]

This all sounds much like the law of diminishing returns...

[Yosarian2]

But in practice, it generally turned out to be bad. In one game the cop was blocked and the doc prevented the kill. So there were two pieces of bad information in the mix. I understand your comments, but I don't agree with how serious the "misses" are or how valuable the "hits" are.

-JEEP

(shrug) Two pieces of imperfect information are, theoretically, better then no information, so long as everyone involved knows the information could be wrong. The roleblocker knows that the person he blocked is more likely then random to be scum, and the doc knows the person he protected is less likely then random to be scum. One of them might be wrong, or they might be lucky and both be right just through random chance. Anyway, supplement that imperfect information with day information, and it's got to increse the town's odds of winning over having no night information, in theory.

Anyway, the scum could create the same confusion by just not making the kill and letting the doc and/or roleblocker run around like chickens with their heads cut off. But it's usually not worth doing it. So even if the roleblocker and the doc have a risk of confusing each other if one of them stops a kill and the other dosn't know it, it's still usually better to risk that confusion rather then let the scum get off their kill, so I would say that if either one stops a kill it's inherently a good thing.

[Adele]

This all sounds much like the law of diminishing returns...

Yes, I know, I just said...

But the

benefit suffers from diminishing returns

under Stoofer's law at a greater rate than the costs do.

Like an hour and a half before your post.

[Blackberry]

Fiasco is my hero... <3

[Cogito Ergo Sum]

the town can instead lynch and pardon in order to confirm the governor instead, as I've never seen that role as scum.

See my upick game.

<_<
>_>

[Mr Stoofer]

I certainly agree that:
-> All roles (pretty much) have some cost.
-> They should also have a benefit.
-> But the benefit suffers from diminishing returns under Stoofer's law at a greater rate than the costs do.
-> Thus as amount and complexity of roles increases (complexity within roles also, such as a commuter has a greater effect here than a bulletproof), the town's power increases more slowly and may eventually be harmed.

I <3 Adele.

[Norinel]

(shrug) Two pieces of imperfect information are, theoretically, better then no information, so long as everyone involved knows the information could be wrong. The roleblocker knows that the person he blocked is more likely then random to be scum, and the doc knows the person he protected is less likely then random to be scum. One of them might be wrong, or they might be lucky and both be right just through random chance. Anyway, supplement that imperfect information with day information, and it's got to increse the town's odds of winning over having no night information, in theory.

That's precisely the point I was trying to make.

To make a more concrete example, suppose you're playing a relatively complicated theme game, and player A's claimed cop, and everyone's pretty sure that A is telling the truth and sane. (Of course, in a game there'd probabl be some uncertainty about that, but let's ignore it for the time being) One day, he comes out with a guilty result on player B.

A lot of players would probably lynch B without much further thought. But that's poor play, because it doesn't take into account that information from the night game is uncertain. There are actually something like four possibilities to deal with:

1) B is scum.
2) B is pro-town and a miller of some sort.
3) B is pro-town and there is a framer of some sort and the framer targetted B last night.
4) B is pro-town and there's some more complicated interaction going on that could throw off a cop result.

1 is certainly the simplest option to consider, but because the players already know the setup's more complicated, the night game aspects of 2, 3, and 4 become more likely. You can only fully trust night game information if it comes with an extreme explicit guarantee which almost never shows up outside of Open Games.

If you were going to do a Bayesian analysis or something on these possibilities, you'd be weighting a combination of night game events, guessing the setup, and day game behaviors, and the town's knowledge of the complexity of the setup should impact how heavily the day game's weighted. When it doesn't, that's poor play.

[Yosarian2]

Again, when there's a lot of very compliacted roles, there's usually a way to break the game. Look at Stark's math mafia, for example; although that was abandoned, the town had already figured out how to set it up so they couldn't lose.

The more town power roles there are, the more information the town can get from claims, and interactive claims, confirming each other and making it harder for the scum to fake a claim. For example:
Mith:"I tried to track Glork, but the mod said I targeted Yosarian and nothing happned."
Glork "Ah, I'm a re-director, and I re-directed Mith's ability to Yosarian, he's telling the truth."
Yosarian "I'm untargatable at night; I breadcrubed this back in post #15. " After this, all three of our role abilities, although not our alignmnets, are mostly confirmed.

If a scum has a provable night ability, they might be able to slip by, but if not, this can make it quite easy for the town to find the scum simply through process of elimination. The downside of this is that the large number of claims will help the scum find pro-town power roles, but when the town has so many roles with night powers, the scum simply can't kill them all. Also, very quickly the town can use these interactive roles to work with each other to give them more options at night; for example, in the example above, Glork can re-direct someone he thinks is scummy over to me, thus allowing him to act as a roleblocker instead if he wants.

Very often, there comes a critical point where lots of complicated pro-town roles add up to some logical ways to "Solve" the game as a logic problem simply using night abilities, and the interactions of them.

[Yosarian2]

Yosarian's General Rule Of Thumb Which Isn't A Law: The more and the more complex pro-town power roles the mod puts into the game, the faster the theoretical power of the town grows, often in ways the mod dosn't expect.

[Mr Stoofer]

I can agree with that, and can think of examples, but in my experience it is more common this "theoretical" translates into Town confusion.

[Glork]

I can agree with that, and can think of examples, but in my experience it is more common this "theoretical" translates into Town confusion.

I think the practical interpretation of 'theoretical of the power' differs on a case-by-case basis and is dependent largely upon the ability of the players in the town.

Elaboration to come, possibly not until next week though.

[Yosarian2]

I can agree with that, and can think of examples, but in my experience it is more common this "theoretical" translates into Town confusion.

That might be true on mafiascum, but if so, it's only because most people here are not used to extremly compex roles and set-ups and so tend to disbelieve "flying pumpkin" type claims as a rule of thumb. On sites where complex games are the norm, and the town is psycologically prepared for them, they tend to result in very strong towns.

[Mr Stoofer]

Now that's something that I had not considered...

If the Town accepts that it is never going to figure out the setup, that information such as cop results must be treated with the utmost care even when shown to be reliable in the past, then the Town can simply play the game as though it is vanilla or almost so. A cop being role-blocked doesn't matter if you are not going to place a huge amount of weight on a cop's results -- even if his last 5 investigations have all proved to be correct.

Disclaimer: Stoofer's Laws only apply to Mafiascum.