KovacsC wrote:
Explain away...
I will but not really got time right now - have a read of the wiki page
http://en.wikipedia.org/wiki/Mafia_%28party_game%29I like the maths behind odds
Quote:
Mathematical study
Mafia is a complicated game to model, so most analysis of optimal play has assumed both: (a) that there are only townsfolk and mafiosi, and (b) that the townsfolk never have a probability of identifying the Mafia that is better than chance. Early treatment of the game concentrated on simulation,[78] while more recent studies have tried to derive closed-form equilibrium solutions for perfect play.
In 2006, the computer scientists Braverman, Etesami and Mossel proved that without detectives and with perfect players the randomized strategy is optimal for both citizens and mafia. They showed that when there are a large number of players and the win probability for either side is 50%, the innocent's lack of information means that the Mafia numbers need only double when the total number of players quadruple for the win chances to remain even.[66] With simulation, they confirmed that 50 mafiosi would have almost a 50% chance to win among 10,000 players, and that when m mafiosi remain among P total players:
The Mafia's chance of victory, W(m, P) \approx \frac{m}{\sqrt{P}} —When: \frac{m}{\sqrt{P}} \le 40%
As the Mafia's concentration increases beyond 40% of the square root of total players, the chance of a Mafia win grows less linearly with concentration, but converges to near certainty by the time P < 3m2.[79]
If any detectives are added to the game, Braverman et al. proved that the number of mafiosi must remain at a fixed proportion of the total number of players for their chance of winning to remain constant.[80]
In 2008, Erlin Yao of the Chinese Academy of Sciences derived specific analytical bounds for the mafia's win probability when there are no detectives, W(P, m) when m mafioso remain among P total players:[81]
\sqrt\frac{2(m-1)}{P} \le W(m, P) < \frac{m}{\sqrt{P}}
For example, four mafioso have a 50% to 100% chance of beating twelve innocents in this model.
I would also suggest these pages on the Mafiascum wiki
http://mafiascum.net/wiki/index.php?tit ... ting_StageQuote:
When one is voted for they are closer to be Lynched. Being lynched is something to avoid, so a player who has a greater chance of being lynched will talk more to defend himself. The more someone talks, the more they reveal. If a Mafia member or other Scum reveals too much, he gives himself away. So voting for someone one thinks is a member of the mafia can lead to discovering who really is a member of the mafia.
However often one has no real information to go on at the beginning of a game. In this case, one cannot actually do better than acting at random -- and someone has to do something, or nothing will happen. It is assumed here that voting is the only action one can take at this stage of the game with any real effect.
And
http://mafiascum.net/wiki/index.php?tit ... ood_Townie