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Category:Nightless (Open Setup)

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Nightless Mafia

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.

Nightless EV Table
T \ M 1 2 3 4 5 6 7 8 9 10
2 33.33% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
3 50.00% 20.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
4 60.00% 33.33% 14.29% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
5 66.67% 42.86% 25.00% 11.11% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%
6 71.43% 50.00% 33.33% 20.00% 9.09% 0.00% 0.00% 0.00% 0.00% 0.00%
7 75.00% 55.56% 40.00% 27.27% 16.67% 7.69% 0.00% 0.00% 0.00% 0.00%
8 77.78% 60.00% 45.45% 33.33% 23.08% 14.29% 6.67% 0.00% 0.00% 0.00%
9 80.00% 63.64% 50.00% 38.46% 28.57% 20.00% 12.50% 5.88% 0.00% 0.00%
10 81.82% 66.67% 53.85% 42.86% 33.33% 25.00% 17.65% 11.11% 5.26% 0.00%
11 83.33% 69.23% 57.14% 46.67% 37.50% 29.41% 22.22% 15.79% 10.00% 4.76%
12 84.62% 71.43% 60.00% 50.00% 41.18% 33.33% 26.32% 20.00% 14.29% 9.09%
13 85.71% 73.33% 62.50% 52.94% 44.44% 36.84% 30.00% 23.81% 18.18% 13.04%
14 86.67% 75.00% 64.71% 55.56% 47.37% 40.00% 33.33% 27.27% 21.74% 16.67%
15 87.50% 76.47% 66.67% 57.89% 50.00% 42.86% 36.36% 30.43% 25.00% 20.00%
16 88.24% 77.78% 68.42% 60.00% 52.38% 45.45% 39.13% 33.33% 28.00% 23.08%
17 88.89% 78.95% 70.00% 61.90% 54.55% 47.83% 41.67% 36.00% 30.77% 25.93%
18 89.47% 80.00% 71.43% 63.64% 56.52% 50.00% 44.00% 38.46% 33.33% 28.57%
19 90.00% 80.95% 72.73% 65.22% 58.33% 52.00% 46.15% 40.74% 35.71% 31.03%
20 90.48% 81.82% 73.91% 66.67% 60.00% 53.85% 48.15% 42.86% 37.93% 33.33%
21 90.91% 82.61% 75.00% 68.00% 61.54% 55.56% 50.00% 44.83% 40.00% 35.48%
22 91.30% 83.33% 76.00% 69.23% 62.96% 57.14% 51.72% 46.67% 41.94% 37.50%
23 91.67% 84.00% 76.92% 70.37% 64.29% 58.62% 53.33% 48.39% 43.75% 39.39%
24 92.00% 84.62% 77.78% 71.43% 65.52% 60.00% 54.84% 50.00% 45.45% 41.18%
25 92.31% 85.19% 78.57% 72.41% 66.67% 61.29% 56.25% 51.52% 47.06% 42.86%
26 92.59% 85.71% 79.31% 73.33% 67.74% 62.50% 57.58% 52.94% 48.57% 44.44%
27 92.86% 86.21% 80.00% 74.19% 68.75% 63.64% 58.82% 54.29% 50.00% 45.95%
28 93.10% 86.67% 80.65% 75.00% 69.70% 64.71% 60.00% 55.56% 51.35% 47.37%
29 93.33% 87.10% 81.25% 75.76% 70.59% 65.71% 61.11% 56.76% 52.63% 48.72%
30 93.55% 87.50% 81.82% 76.47% 71.43% 66.67% 62.16% 57.89% 53.85% 50.00%
31 93.75% 87.88% 82.35% 77.14% 72.22% 67.57% 63.16% 58.97% 55.00%
32 93.94% 88.24% 82.86% 77.78% 72.97% 68.42% 64.10% 60.00%
33 94.12% 88.57% 83.33% 78.38% 73.68% 69.23% 65.00%
34 94.29% 88.89% 83.78% 78.95% 74.36% 70.00%
35 94.44% 89.19% 84.21% 79.49% 75.00%
36 94.59% 89.47% 84.62% 80.00%
37 94.74% 89.74% 85.00%
38 94.87% 90.00%
39 95.00%

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.

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