10 Vanilla Town
Before the game, each player is randomly assigned a lottery position. (These are public.) Each position has a certain chance of being drawn as Mafia:
A: 135/1001
B: 132/1001
C: 128/1001
D: 123/1001
E: 116/1001
F: 103/1001
G: 77/1001
H: 51/1001
I: 38/1001
J: 31/1001
K: 26/1001
L: 22/1001
M: 19/1001
Virtual ping pong balls* are then used to select the Mafia (with repeats being redrawn).
I haven't done much math** on the specific numbers - they aren't arbitrary, but the spread may well be too big. The EV should be *roughly* how likely it is all three Mafia are in A-F, I think, which is (again roughly) 33%. There are other considerations though, like one of the unlikely players not being nightkilled. Anyway, the basic idea is that town has a lot of probabilistic information day 1, but nothing that solves the game for them.
*This is based on the NBA draft lottery, which uses 14 ping pong balls and assigns each team some number of combinations of 4 of those balls - 1001 = 14 choose 4. It doesn't have to actually be drawn this way, and the denominator could be any sufficiently large number.
**The spread of probabilities is based on a logistic function. Gold star to anyone who can figure out exactly what I did...
**The spread of probabilities is based on a logistic function. Gold star to anyone who can figure out exactly what I did...