Category:Nightless (Open Setup)

Nightless Mafia is similar to (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 a lynch, 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 100 total players.

Balancing Vanilla Mafia

The number of Townies needed to balance a given number of Mafia, M, grows quadratically with M (specifically, to balance a setup with M Mafia, about 4.1M² + 2.3M Townies are needed). This means that, from a purely EV standpoint, it is impractical to have any Vanilla setup with more than 3 Mafia.

The counts closest to a 50% EV balance are:

1:4 (46.67%), 2:19 (50.71%), 3:40 (49.97%)

Note that, while in most cases it is expected that Town will outperform their EV for a given setup, for Vanilla Mafia the Town has typically underperformed.