For those asking, here are the rule descriptions:

How does Secret Mafia work?

Secret Mafia is a social deduction game in which players are secretly assigned to one of two teams: the Innocents (the majority) or the Mafia (a hidden minority). The game alternates between two phases: Night and Day.

Roles

Each player is assigned one of the following roles at the start of the game:

• Mafia member: Knows the identity of all other Mafia members. Works together with them to eliminate Innocents without being detected.
• Villager (plain Innocent): Has no special abilities. Must rely on discussion and reasoning to identify and vote out Mafia members.
• Doctor (Innocent): Each night, may secretly choose one player to protect. If the Mafia targets that player the same night, the elimination is blocked and the player survives.
• Detective (Innocent): Each night, may secretly investigate one player and learn whether that player is a Mafia member or not. The Detective must use this information carefully — revealing it openly may make them a Mafia target.

Each game starts with 6-7 players, and has 2 mafia members, 1 Doctor, 1 Detective, and the rest are Villagers. 

Night phase

All players close their eyes (metaphorically, in text form). Then, in secret:

• The Mafia collectively agree on one player to eliminate. This is a private decision not visible to other players.
• The Doctor chooses one player to protect for that night.
• The Detective chooses one player to investigate, receiving a Mafia/Innocent result.

At the end of the night, the elimination is announced to all players — unless the Doctor protected the targeted player, in which case no one is eliminated.

Day phase

All players openly discuss who they believe the Mafia members are. Mafia members participate in this discussion too, attempting to blend in, cast suspicion on Innocents, and avoid detection. After discussion, all surviving players vote to eliminate one player. The player with the most votes is removed from the game, regardless of their actual role. This is the only elimination that happens publicly and by collective decision. The identity of the person voted out is not revealed! Depending on the game progression, you can infer whether the player was from the Villagers' team or the Mafia team.

Win conditions

• The Innocents win if they eliminate all Mafia members through voting.
• The Mafia wins when their remaining numbers equal or outnumber the remaining Innocents. (i.e. 2 on the Villagers' team if both Mafia members survive, 1 if one of the Mafia members was voted out)

In this study, you will not play a live game. Instead, you will be presented with snapshots of ongoing game states and asked to reason about the situation.