Stoofer's 3rd Law

[Mr Stoofer]

Stoofer's 3rd Law has now been added to the MafiaWiki. I may need to refine the wording, but essentially it is this:

When designing game of Mafia, as the number and complexity of Pro-Town power roles is increased, the balance moves in favour of the Scum.

The full Wiki entry is under construction but currently reads as follows (it's actually easier to read in the original):

In March 2007, in light of some recent experiences, Mr Stoofer tentatively formulated his 3rd Law. It is still under review, but it currently takes the following form:

When designing game of Mafia, as the number and complexity of Pro-Town power roles is increased, the balance moves in favour of the Scum.

The point is that (contrary to what one might think), it is is actually less helpful to the Town to have lots and lots of elaborate power roles. There is obviously a turning point somehere. Having a Cop is more helpful to the Town than just having plain Townies. But the point quickly comes where adding more power roles just makes life more difficult for the Town.

Reasons for this effect include the following:

1. The power roles interact with each other in ways which are unpredictable (to the Town). For example:
. . . 1. A Roleblocker blocks a pro-town player.
. . . 2. A Tracker sees a pro-town player target someone who is also killed that night -- leading them to suspect the pro-town player
. . . 3. A Vigilante kills a pro-town player.
. . . 4. A Doc stops a Vig killing a Scum.
. . . 5. And so on.
2. This leads to confusion, which can only hurt the town. In such a situation it will be much easier for the Scum - i.e. the informed minority to work out what is going on than the Town.
3. For one thing, only the Scum will be able to separate the genuine claims from the fake claims. Thus:
. . . 1. Truthful claims by Pro-Town players may appear to be false - e.g. where a doc claims to have protected the victim of a nightkill, but failed to protect him due to being roleblocked or having his choice switched.
. . . 2. It becomes easier for Scum to get away with fake claims (they can explain away inconsistencies by reference to some unidentified complexity such as roleblocking).
. . . 3. It becomes impossible or difficult for anyone to confirm themselves. This is the worst of all possible outcomes: when a player claims a power role, and the Town doesn't believe him but the Scum knows he is telling the truth.
4. Even without any interactions, someone claiming a complex role is less likely to be believed -- leading to power roles being lynched after they claim. For example, MeaningofLife42 was lynched in Mini 383: Ben & Jerry's because his role claimed seemed so elaborate as to be made up. It wasn't - it was in fact a potentially very useful Pro-Town role.
5. Once it becomes apparent that the set-up is complex, it can lead to all sorts of paranoia by the Town. An example is Mini 167: Les Miserables, where Changling Bob was a confirmed Mason, but was still lynched because MeMe thought he might be a scum-mason-recruiter!
6. Having a complex set-up also leads to claims by Pro-Town players being disbelieved on the grounds that the game would be overbalanced if they were telling the truth. The Town suffered in Mini 167 from this too: see for example this post by MeMe, which contributed to the Mason's lynching.
7. Conversely, where there is a complex set-up it gives the Scum much more leeway in coming up with fake claims. Once it has been established that there are complex/improbable roles in the game, the Scum can make up complex/improbable fake claims, safe in the knowledge that they will not be counterclaimed and the improbability of their claim will not be used against them. Although the game ended in a Town win, DP12: JeepFest Mafia contains a good example of this: MeMe (Scum) survived for a long time, and came close to winning the game, with an elaborate and improbable fake claim. Mini 167 contains an example of this too: gootentag claimed not to be able to vote at all. Despite the improbability of this role in a 9 payer game, he survived until endgame and won the game for the scum (where he hammahed to win the game for the Scum).

PS:

Vote: spectrumvoid

.

[Zindaras]

I've actually noticed this before. There is obviously another Stoofer's constant here. I think a good game that would've proved this would have been Mini 372, by Kain. We never got to the part where we did a mass claim, but my role was disbelieved because of balance and such.

[IH]

I'M A BELIEVAH!

[GreenLiquid]

Also, giving the town a lot of powers usually has to be evened out by giving the scum abilities, which makes the game harder to balance.

[JDodge]

Wouldn't it be true that it is not just pro-town power roles, but power roles in general that do this, including third parties such as lynchers and SKs?

[Primate]

Complexity, yes. I don't think a setup with a large

number

of power roles gives the scum sufficient advantage though, especially if any of those abilities are remotely testable. You end with a situation where it's 'confirm your abilty or die'.

[Yosarian2]

When designing game of Mafia, as the number and complexity of Pro-Town power roles is increased, the balance moves in favour of the Scum.

I strongly disagree. Misetings games always have lots of incredibly complicated and bastard-modded pro-town roles, and those games are almost always games with a very strong advantage to the town.

As the number and complexity of pro-town roles increase:

1. It gets harder for scum to claim safely.

2. It gets easier for the town to figure stuff out.

3. It becomes more and more likely that there's some complicated way to use the intereactions between the pro-town roles to break the game, or at least to help the town in a way the mod had not thought of when he designed the game.

4. You tend to end up with more and more confirmed or confirmable good guys, which usually dooms the scum in the endgame.

That's not to say that games complicated roles can't be balanced, but usually the more complex the game is, the harder you have to work to give the scum anything like a fighting chance.

[Yosarian2]

PS: for example, all those examples you use ("doc stops a vig from killing a scum, tracker sees a pro-town role target someone the night they die, roleblocker stops a pro-town role from doing something") usually do end up forcing a couple of claims which can hurt the town (although not so much when the town has so much power), but in the process they usually figure it out and you end up with a couple of mostly-confirmed townies; and usually there ends up being more power claimed then the scum can kill each night, which can lead to claimed trackers and roleblockers and cops revealing their result every day even without a doc keeping them safe, which gives the town even more information.

[HackerHuck]

I've actually noticed this before. There is obviously another Stoofer's constant here. I think a good game that would've proved this would have been Mini 372, by Kain. We never got to the part where we did a mass claim, but my role was disbelieved because of balance and such.

I'd disagree on that one. Part of it was the bizarre role, but the way you acted to fit in with that role seemed very scummy.

I also disagree with the 'confirm your ability or die' benefitting the town. If the scum have a roleblocker, that in essence gives them the ability to sabotage any proving of pro-town abilities.

[bigAl]

It seems to me that when designing a game, you have to balance the number/powers of mafia with the amount of power roles in the game.

For example, in a twenty player game, if the town is all vanilla, it might be balanced with only 3-4 scum. If playing in a twenty player game with many different power roles, then two scum groups of three people each might be balanced. No matter how many power roles, ideally the mod should be able to balance the game in such a way so that it doesn't matter how many power roles there are and still retain a resonable chance for everyone to win.

Though I don't really know anything about balancing a game.

Of course, the more different fractions there are in a game, the lower the probability that your fraction will win. Since there is often more different fractions if there are more power roles, then yes, I guess that's true.

[jeep]

I don't think that this necessarily is true. You do have to remember that not all abilities are benficial abilities. Generally a role-blocker is neutral to negative for the town. A cop is helpful. Imagine this set-up:
18 sane cops; 4 mafia

You can't say that the number of cops will DECREASE the town's ability to win, can you?

When designing a game, you must be careful to understand the impact of any special role you include. Including more does not always balance towards scum.

-JEEP

[Yosarian2]

Generally a role-blocker is neutral to negative for the town

I strongly disagree with this.

Let me put it this way. Say a roleblocker uses his ability at random night zero. Let's also say that this is a 12 person mini game with more town power then average, with a cop, a doc, a vig, a roleblocker, with 3 person mafia, and a SK.

The vig probably shouldn't do anything night zero anyway, so if you block him, no big deal.

So there's a 1/12 chance you prevent the cop from one investigation, which stops the town from getting an investigation off, but also means that the cop can confirm your claim later if needed. Small - for the town.

There's a 1/12 chance of blocking the doc, but he's only got a 2/12 chance of stopping a kill night zero, so the odds of stopping a doc from saving someone is only 2/144. Not worth worrying about.

There's a 2/12 chance that you'll stop either a scum kill or a SK kill, and either way you both prevent a kill (more likely then not a kill on a good guy), and once you figure out that there's usually two kills, you also might have a pretty good idea you might have blocked a scum night 1. Huge + for the town.

So even on night zero, with no information, a random roleblock is more likely then not the right decision for the town.

Later in the game, when you start to have an idea of who might be scum and who might be pro-town power roles, it usually gets better, although there are situations where you might not want to use the ability (say, it's a situation where if you accidently block the doc you could cost the town the game).

And in the endgame, it can be incredibly powerful, turning a lost game into a won game (say, game goes into night with 1 scum, 1 townie, and 1 roleblocker).

A roleblocker is a pretty solid pro-town role; not as strong as a cop or a doc, but probably better then a vig.

[Trojan Horse]

This law definitely has exceptions (like the 18 cops vs. 4 mafia scenario mentioned above), but I do agree with the general idea. Let me give you my scenario, which I think is what Mr. Stoofer is getting at:

A game I modded in scumchat (with a Gilligan's Island theme): 2 scum, 1 forced roleblocker (had to use his ability every night), 1 tracker, 1 doctor, 1 one-shot nightkill immune, 1 vanilla townie. Turned out having extra power roles hurt the town's chances.

Day 1: Townie lynched.

Night 1: Scum tries to kill tracker, but doc saves tracker. Tracker tracks a scum.... the one that did not make the kill (too bad). Roleblocker blocks the one-round NK-immune (which, in my book, canceled the immunity for the night).

Day 2: A big argument ensues between the roleblocker and the NK-immune. Both make their claims. Each is sure that they personally stopped the kill, and each is sure that the other is scum (both wrong on both counts). After a while, the roleblocker is lynched.

Night 2: Easy time for scum! Obviously a doctor stopped the night 1 kill; who's the doctor? Not the guy that claimed NK-immune, and not the guy that scum tried to kill night 1. So there's only one person that could be the doctor. Doctor dies, game over.

Too many power roles. Too many ways to prevent a kill. Town loses.

[Mr. Flay]

I don't think this one is any more true than Stoofer's 1st Law, but it's something to keep in mind.

[Mr Stoofer]

Perhaps I should clarify. My point is that as you start adding in

more

and

complex

pro-town roles,

at some point

they start to become less helpful to the Town.

So arguments like this don't really undermined Stoofer's 3rd Law:

I don't think that this necessarily is true. You do have to remember that not all abilities are benficial abilities. Generally a role-blocker is neutral to negative for the town. A cop is helpful. Imagine this set-up:
18 sane cops; 4 mafia

This is obviously very pro-town powered, which is partly a result of being

very simple

.

In any event, consider how this would work in practice. As all the cops came out, the Town would very quickly assume that they were involved in some sort of dethy game. The scum would start claiming cop results which would be hard to untangle from the real results, and there would be general confusion. I am sure in a 22 player game such as this the scum would eventually all be caught, but I would bet every penny I had that at an early stage in this game you would get an example of this:

6. Having a complex set-up also leads to claims by Pro-Town players being disbelieved on the grounds that the game would be overbalanced if they were telling the truth.

"We can't

all

be sane cops!!!".

And you might even get some of this:

5. Once it becomes apparent that the set-up is complex, it can lead to all sorts of paranoia by the Town.

In other words, I bet the game wouldn't be such a cakewalk as one might initially think.


***

Of course Stoofer's 3rd Law does not apply to Open Set-ups.

[jeep]

Generally a role-blocker is neutral to negative for the town

I strongly disagree with this.

Let me put it this way. Say a roleblocker uses his ability at random night zero. Let's also say that this is a 12 person mini game with more town power then average, with a cop, a doc, a vig, a roleblocker, with 3 person mafia, and a SK.

OK... you assume that the roleblocker can even stop the mafia. In games I've run in the past, that was a reasonable assumption, since I made the mafia tell me who was doing the kill. 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

[jeep]

Perhaps I should clarify. My point is that as you start adding in

more

and

complex

pro-town roles,

at some point

they start to become less helpful to the Town.

Okay, so without more information on what you mean by "more and complex" then I don't think it's a very useful law.

-JEEP

[Mr Stoofer]

My point is simply: there comes a point when adding more different power roles make life harder. Where that point is, depends on the setup.

I know it's not really a law. It's more of a "thing for game designers to bear in mind". But I needed a third law and this is it. Stoofer's 1st Law isn't a law either.

[Mr Stoofer]

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!

[spectrumvoid]

vote: Stoofer

Oh no, not another one!

[Zindaras]

I'd disagree on that one. Part of it was the bizarre role, but the way you acted to fit in with that role seemed very scummy.

I also disagree with the 'confirm your ability or die' benefitting the town. If the scum have a roleblocker, that in essence gives them the ability to sabotage any proving of pro-town abilities.

Oh, I know I acted really weird in that game. But the role was part of it.

This is not one of those things you can prove with numbers and math, because it's more psychological in nature. The town tends to try and outguess the mod in cases like that.

[Primate]

I've actually noticed this before. There is obviously another Stoofer's constant here. I think a good game that would've proved this would have been Mini 372, by Kain. We never got to the part where we did a mass claim, but my role was disbelieved because of balance and such.

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.

[Fiasco]

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

[Kelly Chen]

I agree with Yosarian's thoughts.

But I think it's quite possible that you could design a power-heavy game that is so confusing that the power doesn't help the town's accuracy to be better than under a mountainous setup.

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.

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.)

[Fiasco]

There's an important difference between setups that hurt the town because they hurt the town, and setups that hurt the town because the town handles them badly. If it's the latter, you'd expect that effect to go away as towns became more skilled.