Mafia Pointing Theory

By Axelrod

For anyone who has ever attempted to design a Mafia game, one of the most important questions, perhaps the single most important question, that they must ask themselves is this: Is this set-up balanced?

"Balanced" in this context meaning simply, “is this a set-up where both sides have a reasonable chance of winning?” Which is not the same thing as an “equal” chance. Given the host of intangibles present in any Mafia game, creating a set-up in which both sides might be said to have perfectly equal chances of winning is an impossibility. Ideally, one should simply try to create a set-up in which the chances for either side are close enough so that no one will look back at the end and have the extremely frustrating feeling that they never truly had a chance to begin with.

What follows are some of my ideas concerning balance in Mafia games, including the system that I currently use to evaluate games that I review. These are ideas that I developed over a long period of time, based on games played, read, and designed, but which I had never put down into numbers.

In particular, my goal was to see whether or not a “point” based system – one in which all the roles of the game are given a numerical value – could be made to work.*

Obviously no point based system is going to be perfect, but it seemed like a good place to start, and after using this system for more than a year-and-a-half and applying it to many, many different types of Mafia set-ups, I have developed great faith in it.

The Basic Role Values:

Vanilla Townie = 1

Cop = 4

Doc = 3

Vigilante = 3

Roleblocker = 2

Mafia Goon = 4.5 (I have tried this several different ways. Valuing a mafia at 5 seems too high, but valuing one at 4 seems slightly low. I therefore, brilliantly, put it right in the middle. How scientific of me)

Where did I get these numbers from? I started by plugging them into some very basic Mafia set-ups (using 25% Mafia as baseline):

12 players: 9 town, 3 mafia

Town = 1

Mafia = 4.5

In this set-up, the town has 9 points (nine vanilla townies worth 1 point each.) The mafia has 13.5 points (three mafia worth 4.5 each.) Because the mafia “score” is higher, the mafia should win a majority of the games using this set-up if it's correct, and I do believe it is correct. To “balance,” change 2 of the basic townies to a Cop and Doc. Now the points are: Town 14, Mafia 13.5, which is at least close to being even.

The margin of error I decided on is +/- 1 mafia member (or 4.5 points). In other words, if the points add up so that the two sides are within 4.5 of each other, it shouldn’t play as too unbalanced. The vanilla set-up above is actually within this margin of error, and I believe you could play the vanilla set-up and no one would jump up and down at the end about how unfair it was. Similarly, adding a Vigilante role to the town in addition to the Cop and Doc. doesn’t unbalance the game, it just shifts the odds around a little.

The point isn’t to be exact, but to get things in the ballpark.

20 players: 15 town, 5 mafia

Town = 1

Mafia = 4.5

Here the town has 15 points, while the mafia has 22.5. Again, if you played this exact set-up, I believe the mafia would win a significant majority of the time. If we add a Cop and a Doc. role then the town has 20 points to the mafia’s 22.5. This is much closer, though I think such a set-up still favors the mafia a bit. So again, it seems right.

It is my belief that, for a 20 player game with no abilities (i.e. Mountainous Mafia), the closest balance you can achieve is to have 16 town players (16 points) and 4 mafia players (18 points).

24 players: 18 town, 6 mafia

Town = 1

Mafia = 4.5

Here the town has 18 points, while the mafia has 27. This would appear to swing very strongly in favor of the mafia, and, again, I believe that actual games played would bear out that assumption. You can cut an entire mafia here (I think 5 mafia is probably correct in a 24 player game). At a minimum, you could add a Cop and a Doc, making the town score 23 and Mafia score 27. This is still favoring mafia, which I think is true, but it is definitely closer. Again, whether one agrees on the exact number values doesn’t matter.

The Serial Killer

A Serial Killer (SK) in the mix throws the numbers off. A SK will typically give an edge to the mafia simply by virtue of the fact that he will usually be hitting a townie at least 2/3 more often. How much of an edge the presence of a SK gives is an open question (possibly deserving of it’s own article), but my working premise is that a SK should be valued as an extra mafia - using my numbers = 4.5 points. These would be points added to the total mafia score for purposes of determining game balance.

*Note: I make no effort to balance the SK role itself. His chances of winning are never good, and it would be a great mistake, in my opinion, for a game moderator to try and design a game where the serial killer’s chances were equal to the town and mafia’s.

Returning to a typical 20 player set-up, with a SK in the mix there are two primary ways to distribute the roles. One could have 15 town, 4 mafia, and 1 SK, or 14 town, 5 mafia and 1 SK.

In the former scenario, before counting the SK, the town has 15 points, and the mafia has 18. In the second scenario, the town has 14 points and the mafia score is 22.5.

Counting the SK as an “extra” mafia, then in Scenario #1, the mafia score would go up to 22.5. In the second scenario, the mafia score would go all the way up to 27.

So to “balance” these scenarios for the town, they need more. A Cop/Doc/Vig. gives the town in the first scenario 22 points vs. the mafia 22.5. That’s close. In scenario #2, the Cop/Doc/Vig. gives the town 21 points to the mafia’s 27. This is still not “balanced.” Here you would want to give even more power to the town (or simply cut a mafia and go with scenario #1).

All this is with a completely vanilla mafia. If you want to give the mafia any abilities, which most moderators do, then that would increase the value of the mafia roles (over and above the 4.5 they are worth to begin with).

Rough estimates on other Role values:

Back-Up Cop/Doc: 2.5/2

Watcher: 2

Tracker: 2

1-Shot Vigilante: 2

Masons (with confirmation that co-masons are town):

-2 man group: 2 points each, total 4.

-3 man group: 2.5 points each, total 7.5

-4 man group: 3 points each, total 12

(this assumes a large 20+ person game. A Mason group in a mini-game is even more powerful because they make up a larger percentage of the total town. I don't think confirmed Masons should ever represent more than .20% of the total town bodies.)

In addition, it is possible to have roles with negative values which take points away from their respective sides (or are simply worth less than 1). For example, I typically value a “Miller” role on the side of the town as .5 points. He still has some value to the town – he can vote, and provide analysis - but his drawback makes him worth less than even a vanilla townie.

A role that the mafia does not have to eliminate to win (such as a Survivor role) would be zero points, generally speaking.

There are other considerations as well, such as Day Start vs. Night vs. Kill vs. No-kill 1st Night. These I have not examined quite as closely, but I have a few additional premises:

-A day start generally favors the town = +1 to total town score

-Cop Head Start (Night start with use of all abilities but no kills allowed = +2 to town (and this could potentially be even more if the town had multiple investigate roles or more useful actions to take during the night.)

The number and variety of roles that creative moderators can design are literally limitless, but what I have found is that the foregoing system provides a very solid foundation for balancing all type of mafia games, and that it is not difficult to estimate a value for a new role simply by comparing it to the values of roles already known.

I hope this system is of some use to new (and even experienced) mafia moderators. It is still very much a work in progress, and I welcome any comments or feedback players may have.

*I do not claim any of these ideas as blindingly original thoughts. You can find some very similar suggestions in several Discussion Threads in the forums at Mafiascum, and I am indebted to several individuals over there for inspiring me to try and create a more comprehensive system. The ultimate methodology described herein, however, is almost entirely my own.