Category:Nightless (Open Setup)

Nightless Mafia is similar to Vanilla Mafia (also known as Mountainous), with only Mafia Goons and Vanilla Town, with the difference being that the game does change to a night phase after an elimination, and thus the Mafia does not get a Night kill.

Nightless setups have been run with different player counts, with each count having a different Balance.

EV Calculations

The EV of a Day Start setup with M Goons and T Townies can be calculated as follows:

• EV[M,T] = (T-M)/(T+M)

Proof by induction:

EV[M,M] = 0/2M = 0 EV[0,T] = T/T = 1 For 0<M<T:

• EV[M,T] = M/(T+M) * EV[M-1,T] + T/(T+M) * EV[M,T-1]
• = M/(T+M) * (T-M+1)/(T+M-1) + T/(T+M) * (T-M-1)/(T+M-1)
• = (MT-MM+M + TT-TM-T)/((T+M)(T+M-1))
• = (TT-T-MM+M)/((T+M)(T+M-1))
• = ((T+M)(T-M)-(T-M))/((T+M)(T+M-1))
• = ((T+M-1)(T-M))/((T+M)(T+M-1))
• = (T-M)/(T+M)

• For T = 3M, EV = 1/2.

EV for Select Setups

The EV calculated in this table is the expected win percentage for Town. To calculate for Mafia, subtract each from 100%.

EV has been calculated up to M = 1000 (and T > 4000000); this table gives values up to 10 Mafia and 40 total players.

Balancing Nightless Mafia

The number of Townies needed to balance a given number of Mafia, M, is linearly related with M.

For Nightless Mafia the Town has typically overperformed the EV - it is suspected that this comes from the Mafia's inability to get rid of Townies that they don't want around, as they can do in non-nightless games using the nightkill.