What is Balanced?

[Axelrod]

I am trying to get a sense of exactly what kind of set-up is considered "balanced." Everyone talks about balance and how to achieve it, but I haven't seen a discussion about just what kind of set-up would be balanced. What I would like to do is start with a basic set-up that I "knew" was balanced and then just play around with the roles--a little here a little there--the idea being that if you start balanced, your final result will be close to balanced.

So what is a balanced "basic" set-up. For example, it seems to me that in a 20 person game, 5 mafia, one sk, 1 cop, 1 doc and maybe 1 vigilante would be balanced. Is that right or way off? Is this too hard for the town? Would a 3 person mason group balance it? Or taking away 1 mafia? Or does it, in fact, favor the mafia?

How do back-up cop/doc roles factor in? Or "negative" town roles like insane/paranoid cops?

I'm really only interested in getting a sense of what is fair with the basic roles in games of various starting sizes: 24 people; 20 people; 12 people.

Thanks for your input.

[Yggdrasil]

Well, here's somewhere to start when thinking about game balance: http://www.mafiascum.net/cgi-bin/wiki.p ... %2c_Part_1

This page gives the town's odds of winning assuming random lynches everyday. Of course, this model does not include the effects of special roles, nor does it consider the fact that it's usually easier to find the other scum once you've caught one.

[mathcam]

There's also a wide range of things people can mean when they talk about "balance." For example, it could mean

1) Fair in the sense that any of the teams in the game have (assuming random play) an equal chance of winning.
2) Fair in the sense that (assuming random play) pro-town and anti-town have an equal chance of winning.
3) The game is not "broken" in the sense that one team has a very high probability of winning, even if it's not the case that all teams have the same chance of winning.
4) A stronger version of "balanced" in which not only is the game balanced in one of the sense above, but also that single random events won't skew the game too much.

So the term is unfortunately vague. On the other hand, there are several heuristics to make sure that a game-in-design comes out well. The numbers that Yggdrasil posted are a great start, and then keeping track of an estimate of how much the roles you've put in slant the balance one way or another. As a double-check, it's always a good idea to run a simulation of the first couple of nights with random or reasonable night choices being made by all players.

Axelrod, is your name in reference to Robert Axelrod of Prisoner's dilemna fame?

Cam

[Phoebus]

Balance is a judgement call and eventually, intuition.
Sometimes symmetry is balance but that can get predictable.

I'll throw this one at jeep though. We were talking about this the other day and I haven't caught him since then.

You mentioned perfect balance. What is "perfect" balance?

[Axelrod]

What I mean by "balance" is that both sides have reasonable possibility of winning, while recognizing that nothing is perfect. Just because a game gets down to the final three with the last lynch deciding it all, doesn't mean the game was well balanced. Similarly, there could be games very well balanced that the town wins with half the population (or more) still alive, due to any number of factors.

I am most interested in people's opinions on the "basic" set up I outlined (i.e. in a 20 person game, 5 mafia, 1 SK, 1 Cop, 1 Doc, 1 Vig.). Whether that is inherrently balanced or unbalanced. And what would be the numbers with games of different sizes (24 people? 12 people?) Come on, everyone is so non-committal!

I saw those numbers Yggdrasil linked to, but they don't really help since they don't account for the special roles and I don't know how to factor them in. I could do "random" simulations, but I'm not sure what to look for. If the "town" wins consistantly with X number of players left alive then we conclude it's not balanced? What's the X? Also, this obviously can't account for the fact that the lynches (and nightkills) get less random as the game goes on.)

And mathcam: my name comes from a Magic the Gathering card "Axelrod Gunnarson" which I have an unhealthy relationship with (I came over here from MTGNews/Salvation, where I first caught the Mafia bug)

Thanks for your advice.

[Seol]

And mathcam: my name comes from a Magic the Gathering card "Axelrod Gunnarson" which I have an unhealthy relationship with (I came over here from MTGNews/Salvation, where I first caught the Mafia bug)

Much as I love Magic: the Gathering (I came here from Misetings), were I in your position here I'd have quickly googled up Robert Axelrod and then told mathcam he was right, and attempted to pass myself off as being the intellectual sophisticate he would at least momentarily believe me to be.

But that's just me. I crave respect and approval, especially when I fool people into offering it to me when unjustifiably.

:trey:

oh, wait, they don't have :trey: here...

EDIT: Eh? It's not even good. Why?

[Aelyn]

Yes, Seol...

They don't have a Trey smilie here...



Note for the Annorax'd: The Trey smilie is a custom MiseTings smilie. It implies shiftiness on the part of the Trey user.

[Seol]

Yea, I know you can Photobucket it. Too much effort.

Besides, isn't the whole point of inside jokes to, y'know, exclude people? Bah. You're no fun today.

[Aelyn]

I WILL USE THE TREY SMILIE EVERYWHERE!!!

Happy?

[Seol]

Yea, now you've edited your post, I'm happy.



See?

[Axelrod]

Much as I love Magic: the Gathering (I came here from Misetings), were I in your position here I'd have quickly googled up Robert Axelrod and then told mathcam he was right, and attempted to pass myself off as being the intellectual sophisticate he would at least momentarily believe me to be.

But that's just me. I crave respect and approval, especially when I fool people into offering it to me when unjustifiably.

:trey:

oh, wait, they don't have :trey: here...

EDIT: Eh? It's not even good. Why?

Intellectual sophistication is over-rated. I know where I come from.
And don't go bad-mouthing my card. I'll have to bust you up. (I know it's not good. But you never forget your first love, do you?)

I'm annoyed no one wants to answer my question.

[Seol]

And don't go bad-mouthing my card. I'll have to bust you up. (I know it's not good. But you never forget your first love, do you?)

Of course, and I apologise for criticising your taste. It certainly has an old-school charm to it, but speaking as a relative newcomer to the game of Magic, it's got that "eh?" feeling that a lot of the early legends had. Shows how far we've come... but, at the same time, how much we've lost.

On the setup you were talking about - 5 mafia, 1 SK, 1 Cop, 1 Doc, 1 Vig... 11 straight vanilla townies?

It certainly seems quite a "pure" setup but it does seem a bit swingy (by which I mean that early random events can have a big effect on one team's chances of winning - taking out the cop early on makes it difficult for the town), which I guess is why for the larger games having a larger number of pro-town roles (of varying power) seems to be the norm. But that's some baseless hypothesising in an attempt to stir up criticism and therefore discussion there, so take it with a pinch of salt.

[Dasquian]

I'd define "balance" as a setup where the outcome is determined more by how the players play the game than how the roles interact. If the mafia are pretty much set to win unless someone plays like a complete tool, I'd call that unbalanced. SK's are a bit different because a good SK run probably involves getting close to end-game rather than winning.

How to get to that point is just a matter of experience. Obvious catches are working out worst and best case scenarios for every role and team. If the mafia can win after one bad lynch, or there are only four roles that are unable to prove their own innocence when they claim, you've got issues. Likewise if a role can find two mafia in Night 1 by dumb luck, you might want to consider toning it down.

[mathcam]

I am most interested in people's opinions on the "basic" set up I outlined (i.e. in a 20 person game, 5 mafia, 1 SK, 1 Cop, 1 Doc, 1 Vig.). Whether that is inherrently balanced or unbalanced. And what would be the numbers with games of different sizes (24 people? 12 people?) Come on, everyone is so non-committal!

I'm so non-committal precisely because the questions you ask are so hard. For example, to simulate this game, you'd have to know optimal cop, doc, SK, mafia, vig,

and

townie strategy for

any

possible configuration that could arise in the game. That's no mean feat, and

then

you have to encode it all and run the software thousands of times. Maybe we can get JEEP to post in here with any results he's found.

And mathcam: my name comes from a Magic the Gathering card "Axelrod Gunnarson" which I have an unhealthy relationship with (I came over here from MTGNews/Salvation, where I first caught the Mafia bug)

Ah, I remember Axelrod Gunnarson! Yeah, he sucks.

Cam