What is Balanced?

[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

[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