The Deeptechs of Mafia are what fascinate me the most. To it belongs the concept of "Mountainous Mafia".
Mafia is a deductive game and to the concept of deduction belongs the concept of "chances" and "averaging". This enables mafia/werewolf to be actually a
mathematic game.
In the very late 90s with the rise of mafia in forums, the concept of "Vanilla Mafia", shortly after "Mountainous Mafia" got brought to life. The concept of playing with no powerroles and only sociopsychological skills. The balance got playtested and measured by the fact that a group of people need an average of 3 or 4 attempts in order to figure out who the wolves are. This maths were thought to believed correct, but they were if it were a real group of people comming eye to eye. Players figured out early on, that the 3-attempts rule does not apply to mafia. Based on Adam Ries, if you take away a natural number from a scale, you receive actually a second scale, the substraction. The concept has been applied to mafia since you lack the physical measurement in order to add this to your deduction to make a 3-attempt rule sufficient. As of that the "Rule of 5" got implemented into mafia and since then became the most standard measurement in mafia.
The rule of 5 says that not more than 5 attempts will be given to bring the game into a solveable state and that the most efficient way of playing is in fact the way of using the said window to the fullest and play accordingly to it.
The mountainous mafia game originally had 12 players. 2 Goons and 10 Vanilla Townies. In order to reach parity town has lose 4 attempts into lynching. And they have the reservation of having one correct attempt or the optionality to no lynch, in order to reach the fifth attempt. - The winrate of mafia in this game type over time has been analysed to be across 50-60% depending on the culture, experience levels, which back in the days was considered "mathematically correct" based on another concept, "the longest straw".
These maths since then have been deemed as "circular" for balancement. Which tries to achieve a circular distribution of game setups in order to reach a 50% win chance for both factions. Much to it, a player named Werebear figured out that, this very concept is not properly stimulating the high draft of town in the playerbase. Only with the know-how you were to reach equal standings between town and mafia, and as that; a type of inflation came to be (META), that made the mountainous setup way too easy to play. As that MafiaScum, the oldest remnant of the 90s era decided to implement the 13-players-cap-rule in order to help town in mountainous games. The 2 mafia versus 11 town mountainous setup has been created and since 2002, has been the standard adopted by forums worldwide. Almost as if it came naturally to be, following the Golden Ratio of chances (70% winrate for uninformed majority).
With just this one numerological change, town is now capable to reach the fifth attempt with no single no lynch.
11
FA1: 9
FA2: 7
FA3: 5
FA4: 3
FA stands for Failed Attempt, aka a mislynch and successful Faction Kill.
With 4 failed attempts town reaches 3 players, receiving the free fifth attempt to solve the game.
Andrew Plotkins dubbed this concept to be "even" and as that "Evenly Balanced Games" came to existence.
Those games are mathematically "polygonal" and if you have an even cornered polygon and draw lines connecting opposing corners, all lines will cross the center and always reach the fifth attempt.
The maths suddenly make a huge disproportional change when the number of goons would become 3. 3 Goons would naturally demand 12 vanilla town as opposition, in order to reach the fifth attempt:
12
FA1: 10
FA2: 8
FA3: 6
FA4: 4
4 Vanilla Townies face 3 Goons in the fifth attempt.
Based on this we can deduct the formula to be:
T=W+8+1
T= Number of Vanilla Town
W = Number of Wolves
8 = Fixed Mountainous Attempt Factor
+1 = Fifth Attempt Factor
Up today, this formula is still used, also outside of mountainous games, by replacing the factors and changing numbers accordingly.
T=W+AF+FAF
In the situation where a Vigilante is present in the game, the shots of the vigilante and additional amount of vanillas to compensate for the fixed attempt factor, you can determine them by the Fixed Attempt Factor. A Vigilante should never have more shots than wolves available, and for each killed wolf the Fixed Attempt Factor would count -2.
VS=W*0.75
where as the new AF formula would become:
AF=8-(VS*0.75)
T=W+AF+FAF+VS
So, for example when having 4 wolves and a vig with 3 shots you would:
T=4+(8-(3*0.75))+1+3
T=4+(8-2.25)+4
T=8+5.75=13.75 -> 14 additional townies
As that the setup would result as in follows:
4 goons
14 vanilla
1 3-shot Vigilante
15
FA1: 12
FA2: 9
FA3: 6
FA4: 4
This setup is circular and demands townies to vote no lynch in order to reach the fifth attempt. Hence with vig shots you might
consider to increase the Fifth Attempt Factor to 2.
This is a natural occurence as another killer is present in the game and this could theoretically be done in every game, where you could implement a "Fixed Fifth Attempt Factor" equaling the amount of nightkillers in the game.
This is just a small slice of the big whole huge assfuck that is waiting for ya'll mafia crackheads to deepdive into.
Also this gives town the golden winrate of 70%, which is the totally optimal winrate for town to have. The winrate is measured on reaching the fifth attempt. You can go back to barely 50% winrate if you remove the fifth attempt, but from a sociopsychological standpoint this would be a bit of disadvantage. The finetuning will come from expertise and cheesyness from players and how carefully you distribute roles.
Every role can have it's own formula that is insertable into the whole formula for additional townies. Formula only applies to additional vanilla townies.
If you want me to write an essay on the concept of "Jobs" and "Skill Measurements" in mafia, I would be ready to do so.