Mafia is a party game. Actually, it's not a game you play at a party. It's a game you play with a group of people, preferably sober. Although, maybe it would be better with drunk people. Anyway, it can be played with 8 people or more (see below for other posssibilities.) One of the people is God, who knows everything about the game, and is not actually a player. One of the people is the cop, who has a special role, and two (if there are 7 players) are Mafia. The rest are villagers. The game goes as follows (assuming there are 7 players plus a god):
The cop is optional, and there are other possible roles not documented here, but I find that the cop improves play (though only slightly) and all other roles that I've come across make the game less fun and less pure.
Mafia with more people is essentially the same. With 10-13 people you play with 3 mafia, with 14-17 4 mafia, with...well, you get the idea. It has been suggested by Brian Rosenthal that with more players, you could play with two (independently working) cops. The parameters may be tweaked to make the game even; it depends on how good the people you're with are at being mafia versus how well they are at being townspeople. (And yes, this is psychology code.)
You can reduce the number of necessary players by one simply by not appointing a God. The roles are of course randomly assigned; during the first night one player acts as narrator, which consists of, while everyone's heads are down (including theirs), telling the mafia to look at each other. Whichever player dies during the first day then becomes God for the remainder of the match.
The smallest number of players that Mafia can theoretically support is three, but in practice it's five since the first day is largely random. (One mafioso.) The game loses some of its appeal; with multiple mafia you can try to figure out which players are conspiring, and with only one it is less interesting. There is, however, a cute little variant called Indian Mafia, which works with exactly five players (three is possible but stark; seven or more is likely too cumbersome.) I have only ever gotten this to work with one group of people, the group that invented the game (myself, Boris Granovsky, Daniel Stronger, Kirsten Wickelgren, and Michael Lipatov), but it's a very neat game in its own right.
In Indian Mafia, each player gets one card dealt from a standard 52-card deck (though the size of the deck is meaningless as long as it's large), which they place on their forehead so that it faces all the other players. There are two teams: the red team, which consists of the players with red cards, and the black team, which is the other one. Because of the geometry (players, as in Mafia, should sit in a circle), you know what team everyone else is on but not what team you're on. There is some discussion, during which everyone tries to figure out what team they're on; the play is as in Mafia, except without the formal accusation and defense.
Instead, as it's a speed game, you point to someone and say something isomorphic to "Vote to kill [person's name]"; if you can get three people (including yourself?) to raise their hands, the person dies. The object is to kill someone who's on the other team from yours; when someone is killed, everyone on their team loses, and everyone on the other team wins. Of course, since you don't know what team you're on ... rounds are quick, 30 seconds or so, and I think we played around 50 rounds that day, which turned out to have great personal meaning to me. But I digress. It's a fun game, though I can see how it might fail drastically with the wrong mix of personalities.
If you wish for more information (or better information), you may mail something to Igor Teper, from Uzbekistan, who taught me this game.