Talk:Vengeful Mafia

Probability for a 7-player vengeful (assuming random decisions)

(G,M,T)

TOWNIE WIN: (1,2,4) = (4/7)*(1,2,3)^ + (2/7)*(1,1,4) + 1/7

(1,2,3)^ = (1/6)*(0,2,3) + (2/6)*(1,1,3)

(1,1,4) = (4/6)*(1,1,3) + (1/6)*(1,0,4) + 1/6

(1,1,3) = .4 (confirmed)

(0,2,3) = (0,1,3)*(2/5)

(1,0,4) = (1,0,3)*(4/5) + 1/5

(1,3) = (0,1,2)*(3/4) + 1/4

(1,0,3) = (1,0,2)*(3/4) + 1/4

(1,2) = 2/3

(1,0,2) = 2/3

---

(1,2,4) = (4/7)*(11/60) + (2/7)*(1/2) + 1/7 = 11/105 + 2/7 = 41/105

(1,2,3)^ = (1/6)*(3/10) + (2/6)*(2/5) = 11/60

(1,1,4) = (4/6)*(4/10) + (1/6)*(4/5) + 1/6 = 15/30

(1,1,3) = .4 (confirmed)

(0,2,3) = (3/4)*(2/5) = 3/10

(1,0,4) = (3/4)*(4/5) + 1/5 = 4/5

(0,1,3) = (2/3)*(3/4) + 1/4 = 3/4

(1,0,3) = (2/3)*(3/4) + 1/4 = 3/4

(0,1,2) = 2/3

(1,0,2) = 2/3

So townie win is 41/105, mafia win is 64/105. This turns out to be (39.05% - 60.95%), very similar to 40%-60% but slightly off. --Phenomist 14:57, 10 April 2011 (EDT)