Does anyone know the game(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Mafia_(party_game)

?

I was trying to calculate probabilities with the assumptions that all players are dumb and slay a random person at day. Basically every night one of the good people dies and then a random one of the rest dies. So I wrote down (g=good, b=bad)

P(g,b)=(g-1)/(g+b-1)*P(g-2,b)+b/(g+b-1)*P(g-1,b-1)

P(g<=b)=0

P(b=0)=1

for the probability that the good people win.

Now I was surprised about the non-monotonicity. In my calculations it seems for example

P(g=4,b=1)>P(g=5,b=1)

Have I missed something out? Why does it depend on odd/even so much?

By this calculations werewolves should sometime be decreased if the number of players is increased?

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# Probabilities at Mafia

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