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[QUOTE=yzb25;914747]It is kind of what I said, at least conceptually. The thing is, this paper actually assumes the town still has a chance of winning when there's 50% mafia and 50% town. It simply assumes there is a 50/50 chance of a mafia getting lynched at that phase. If there is only 1 town and 1 mafia, the paper assumes the winner is determined by a coinflip rather than simply handing mafia the tie-winner.

That's why the probability of a mafia win goes up for odd numbers rather than even numbers. In this paper, the even numbers allow for 3 mafia 3 town, which is better odds than 3 mafia 4 town. If we assume mafia automatically wins ties, then even numbers become worse again like you'd expect.

p;edit this paper is really goofy. When there is a single mafia and 100s of town, the probability that the single mafia wins a game with 2n players becomes asymptotically close to an equation of n with pi in it. 2n = root(2/n*pi) (roughly). For example - for 2000 players, the probability of mafia victory is extremely close to root(2/(1000*pi))[/QUOTE] [MENTION=8570]yzb25[/MENTION]
Is it possible for you to confirm or deny that the calculator linked [URL="https://forum.mafiascum.net/viewtopic.php?f=5&t=16958"]here[/URL] is based on the same folly math? [I]( [MENTION=5896]Cryptonic[/MENTION] had that calculator linked somewhere in the SC2Mafia forums too, but that link is dead)[/I]

That calc spikes at even numbers hard. 4vs21 is much higher chance for town than 4vs28, like wtf?

Originally Posted by yzb25

It is kind of what I said, at least conceptually. The thing is, this paper actually assumes the town still has a chance of winning when there's 50% mafia and 50% town. It simply assumes there is a 50/50 chance of a mafia getting lynched at that phase. If there is only 1 town and 1 mafia, the paper assumes the winner is determined by a coinflip rather than simply handing mafia the tie-winner.

That's why the probability of a mafia win goes up for odd numbers rather than even numbers. In this paper, the even numbers allow for 3 mafia 3 town, which is better odds than 3 mafia 4 town. If we assume mafia automatically wins ties, then even numbers become worse again like you'd expect.

p;edit this paper is really goofy. When there is a single mafia and 100s of town, the probability that the single mafia wins a game with 2n players becomes asymptotically close to an equation of n with pi in it. 2n = root(2/n*pi) (roughly). For example - for 2000 players, the probability of mafia victory is extremely close to root(2/(1000*pi))

@yzb25
Is it possible for you to confirm or deny that the calculator linked here is based on the same folly math? ( @Cryptonic had that calculator linked somewhere in the SC2Mafia forums too, but that link is dead)

That calc spikes at even numbers hard. 4vs21 is much higher chance for town than 4vs28, like wtf?

Let's imagine this to be a basic FM formula that determines the outcome of the game:

[CENTER]
[B][COLOR=white]([/COLOR][/B][COLOR=green] Tt [/COLOR][B][COLOR=white]+[/COLOR][/B][COLOR=green] Th [/COLOR][B][COLOR=white])[/COLOR][/B] [B][COLOR=white]-[/COLOR][/B] [B][COLOR=white]([/COLOR][/B][COLOR=red] St [/COLOR][B][COLOR=white]+[/COLOR][/B][COLOR=red] Sh [/COLOR][B][COLOR=white])[/COLOR][/B] [B][COLOR=white]=[/COLOR][/B][COLOR=blue] Outcome[/COLOR]
[/CENTER]
Where
[CENTER]
[COLOR=green]Tt[/COLOR] = Towns ability to Appear Town.
[COLOR=green]Th[/COLOR] = Towns ability to Scum Hunt.
[COLOR=red]St[/COLOR] = Scums ability to Appear Town.
[COLOR=red]Sh[/COLOR] = Scums ability to derail Scum Hunts.
[/CENTER]


The challenge is to make a different formula. A formula that is as complex as possible, with lots of variables presumably.

[hr][/hr]
And a probability-based question:
Is this statement true?
[I]"adding an odd player always increases the mafia winning-chance"[/I]
Like, in a normal FM setup, when you have 12 player slots - adding 1 citizen would always crease the mafia odds of winning?
It's random statement found [URL="https://www.researchgate.net/publication/46583340_A_mathematical_model_of_the_Mafia_game"]here[/URL]. I understand none of it, but I can read a text and found such a sentence in it.

Let's imagine this to be a basic FM formula that determines the outcome of the game:

( Tt + Th ) - ( St + Sh ) = Outcome

Where

Tt = Towns ability to Appear Town.
Th = Towns ability to Scum Hunt.
St = Scums ability to Appear Town.
Sh = Scums ability to derail Scum Hunts.

The challenge is to make a different formula. A formula that is as complex as possible, with lots of variables presumably.

---

And a probability-based question:
Is this statement true?
"adding an odd player always increases the mafia winning-chance"
Like, in a normal FM setup, when you have 12 player slots - adding 1 citizen would always crease the mafia odds of winning?
It's random statement found here. I understand none of it, but I can read a text and found such a sentence in it.