Stuff you need
There are multiple ways of handling this game's randomness and hidden information. The rest of these rules assume you use cards, which means you need some cards (the number of players plus one innocent cards (red playing cards) and the number of players minus one conspirator cards(black playing cards)), writing utensils, small slips of paper and eyelids. If you're having a human doing the moderation, you need some sort of randomizer (or not) and a secret way to convey information. If you're having a computer do the moderation, everyone needs a private way to communicate with the computer.
Decide on a time limit for the main phase of the game. (It doesn't have to be a specific time, if you want to make things less certain. It could be, for instance, "whenever enough people show up to play something else")
Sort the cards into two piles, one for red cards and one for black cards. Move one random innocent card into the conspirator card pile. This means there should be two piles containing one card for every player, one containing all reds and one containing mostly black and one red. Choose a pile at random (This should involve lots of passing and switching the piles so nobody knows which is which) and deal one card out to each player.
A player who receives a black card is a conspirator. After the cards are dealt out, everyone closes their eyes and the conspirators open theirs to identify the other members of the conspiracy. The goal of the conspiracy is to convince the innocent that there is no conspiracy. A player who receives a red card is an innocent, who will try to uncover the existence of the conspiracy.
(If you're not playing with cards, what this does is to ensure an equal chance of there being or not being a conspiracy composed of all players except one. The conspirators know who's innocent, and people not in the conspiracy, innocents, know nothing.) Once setup is complete, the main phase begins and lasts for the predetermined time limit.
The main phase is one of discussion, detection and deception, in which the innocents try to figure things out and the conspirators try to cover their existence. Anyone can say anything, true or false. Private communication is permitted and encouraged. However, you may not reveal your card or otherwise prove you are or are not a member of the conspiracy. When the time limit has expired, move to the decisive phase.
All players write down on a slip of paper or otherwise communicate to the moderator whether or not they believe there is a conspiracy, usually in the form of a yes or no answer to the question "Is there a conspiracy?" (The decision of conspirators makes no difference, but it is important that they go through the motions of deciding so as to properly confuse the innocent. If you want to be cruel, draw a little smiley face.)
If there is a conspiracy, and the single innocent player believes there is no conspiracy, all conspirators win. If the single innocent player decides that there is a conspiracy, he wins.
If there is no conspiracy, all players who decide that there is no conspiracy win. The rest of the players spend their life making vocal websites and taking photos of trash can lids, gorillas, and weather balloons. (It is to be considered better for those who do win if fewer win. You can represent this when playing with score through having some amount of points split among the winners.)
The Pie Observation
To the best of his knowledge, this modification was originally discovered by the user Pie_is_good. The game of conspiracy as it is commonly played is, in fact, unbalanced - a rational innocent will always guess that there is no conspiracy. There is a full 1/2 chance that a person will be an innocent and the game will be not contain a conspiracy, but there is only a 1/6 chance that a person will be an innocent and the game will contain a conspiracy. This means that, given the knowledge that a person is an innocent, it is three times more likely that the person is an innocent under no conspiracy than an innocent under a conspiracy. The way to remedy this problem is to simply modify the weighting - if there is a 3/4 chance of a conspiracy and a 1/4 chance of no conspiracy, the odds of being an innocent under a conspiracy and the odds of being an innocent not under a conspiracy are both 1/4. As this game can easily be modified to be played with more than 3 people, the odds of a conspiracy in an N player game should always be (N)/(N+1), and the odds of no conspiracy should be (1)/(N+1).
To put it another way, during the setup of an N player game, the following options are available:
- Conspiracy against Player 1
- Conspiracy against Player 2
- Conspiracy against player N
- No Conspiracy
A game should assign an equal probability (1/[N+1]) to each of the above options.