Because this comes from a game, I wonder if we have all the information required. It would be odd for a game not to have a correct answer.
Moreover Evan seems to have dropped mysteriously out of consideration. I'd really like to have the complete and exact instructions. There may be a clue that is missing from the problem's paraphrase.
Hey
This scenario comes from a game called Among Us that I watched some people play. In the game there are 10 players, 8 of which are Crewmates ( good guys) and 2 Impostors ( bad guys). The game takes place in a spaceship with different rooms and areas and the Crewmates have to complete a certain number of tasks around the spaceship to win. The Impostors have to kill the Crewmates so that they may win. During the rounds, only Impostors can kill and can only kill Crewmates. Impostors know who the other Impostor is but Crewmates do not. If a player (either Crew or Impostor) finds a dead body around the spaceship, they can report it and the game stops and everyone goes into a meeting where they try to figure out who might have killed the player. At these meetings, a vote takes place to see who gets eliminated. Anybody can be eliminated, but only one person per meeting. If the majority votes for one player, that player is eliminated. If there are ties or no majority for a player, no one gets eliminated and the next round starts. Again, Crewmates win if they manage to complete all given tasks or if they manage to sus out and vote out both Impostors. Impostors win if they manage to kill or vote out enough Crewmates until there are an equal amount of Impostors as Crewmates.
Ok so I was watching a game where there were 7 people were left, 5 Crew and 2 Impostors. In the round, 2 people get killed, a body gets found and all remaining players go into a meeting. Now here is where the problem from my initial post comes from:
From player Al's point of view, Al knows he is Crew, and Al had spent all of that round with Evan, so he is absolutely sure Evan did not kill anyone that round. He also know that both kills are done by different people because the game has a setting where after an Impostor kills, there is a "cooldown" period where he cannot kill again for 25 seconds, and that round lasted less that 25 seconds. So it could not be the case that one Impostor kills, cools down and kills again, so the 2 kills must have been done by 2 different people. Since Al knows he is Crew, and now knows Evan is also Crew, this leaves the 2 killers to be between the rest of the people (Bob, Carl and Dan). By a few details of this particular game, Al and Evan deduce that one of the kills must have been done in an area where Carl and Dan were ( This is why in my initial post, I said that it is known that between Carl and Dan, one is definitely the killer).
As was shown in previous posts in this thread, this was not useful information. I created the first post in this thread because I wanted to see, given this scenario, if there was a strategy for Al where he could sus out the impostors with higher probability, but now I don't think so.
In the vast majority of Among Us games, concepts like equal probabilities, randomness and independence do not apply, because players decide who to vote for in meetings based on influence from other players and previous rounds and personal suspicions, but in this one particular game, the player Al really did not lean one way or another among the 3 suspects, and so assigned equal probabilities to all three suspects.
This is a long post, I don't know it makes things clearer for you, but I hope it helps.
Thanks to everyone else who engaged.
