Calculating Probabilities in Mafia Party Game

In summary, the conversation discussed the game "Mafia," specifically looking at probabilities for winning based on certain assumptions. The calculations showed that the probability of good players winning is non-monotonic, meaning that it is not always higher as the number of players increases. The conversation also included a JavaScript code to demonstrate this phenomenon.
  • #1
Gerenuk
1,034
5
Does anyone know the game
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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  • #2
I don't understand what happens if it arrives at 1 of each on a day slot (either would have to be very dumb indeed to vote to chop himself), but assuming they draw lots the lack of monotonicity is real.

E.g. it may be surprising that starting with a day slot the goodies do better to have one goody v one baddy than two goodies v one baddy but if you think about it it's right.

I append a javascript. (To run paste into a .htm file and drop it into a browser. Set the range values to lowest and highest numbers of players for the two sides.) The first number shown is the goodies and the 'n' or 'd' represents night or day start.

<script>

range=[1,9]

function p(g,b,n){
if(g<0||b<0||(b==0&&g==0))return NaN
if(b==0)return 1
if(b>g)return 0
if(n)return p(g-1,b)
else return (g*p(g-1,b,1)+b*p(g,b-1,1))/(b+g)
}

for(k=0;k<2;k++)
for(i=range[0];i<=range[1];i++)
for(j=i;j<=range[1];j++)
document.writeln('('+j+','+i+','+(k?'n':'d')+') '+p(j,i,k).toFixed(3)+'<br>')

</script>
 
Last edited:

1. What is the probability of being assigned a specific role in the Mafia Party Game?

The probability of being assigned a specific role in the Mafia Party Game depends on the number of players and the specific rules of the game. Generally, the more players there are, the lower the probability of being assigned a specific role. For example, if there are 10 players and 2 Mafia roles, the probability of being assigned a Mafia role is 2/10 or 20%.

2. How do I calculate the probability of winning as a Mafia member?

The probability of winning as a Mafia member also depends on the specific rules of the game and the actions of other players. However, in general, the probability can be calculated by considering the number of Mafia members in relation to the total number of players, as well as the likelihood of successfully deceiving and eliminating other players.

3. Is there a way to increase my chances of winning as a Town member in the Mafia Party Game?

Yes, there are strategies that can increase your chances of winning as a Town member in the Mafia Party Game. Some tips include paying attention to voting patterns, keeping track of information and clues, and working together with other Town members to identify and eliminate Mafia members.

4. How do I calculate the probability of successfully performing a night action as a Mafia member?

The probability of successfully performing a night action as a Mafia member depends on the specific rules and actions of other players. For example, if there are multiple Mafia members and they all choose to target the same player, the probability of successfully eliminating that player is higher compared to if they target different players.

5. Can the probability of winning in the Mafia Party Game be influenced by luck?

Yes, the probability of winning in the Mafia Party Game can be influenced by luck, as with any game involving chance. However, players can still strategize and make logical decisions based on the information available to increase their chances of winning, reducing the impact of luck on the outcome of the game.

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