RE: I made a Mafia game, but it's way too complex...
03-15-2017, 08:38 PM
(This post was last modified: 03-15-2017, 08:39 PM by Kíeros.)
Let's look at the continuous mafia equation:
d/dt p̃m(t)=-m/(N-2t)p̃m(t)+(m+1)/(N-2t)p̃m+1(t)
Solving this equation, we get
p̃m(t)=MCm(1-√(1-2t/N))M-m√(1-2t/N)m,
which we can convert to 〈m̃〉(t)=M√(1-2t/N), which is always decreasing over time, so a low-quality mafia game is more likely to survive the later in time.
So go on ahead, there should be no problems whatsoever.
d/dt p̃m(t)=-m/(N-2t)p̃m(t)+(m+1)/(N-2t)p̃m+1(t)
Solving this equation, we get
p̃m(t)=MCm(1-√(1-2t/N))M-m√(1-2t/N)m,
which we can convert to 〈m̃〉(t)=M√(1-2t/N), which is always decreasing over time, so a low-quality mafia game is more likely to survive the later in time.
So go on ahead, there should be no problems whatsoever.