Resistance Avalon - any strategy better than staying silent?

Question

I am looking for any game theoretical insights for the most basic form of The Resistance: Avalon. Specifically I am looking at a 5 player game, with just two added roles: Merlin and the Assassin. I am looking at strategies that can be executed without using psychology, tells, hidden messages (including but not limited to cryptography and signing) etc.

Without the additional roles - ie the vanilla version of the original Resistance game - it is quite easy to calculate the winning chances for the rebels if both sides play optimally - for it is 30% (assuming the traitors can avoid double-failing missions with two spies). The good team basically has three chances to identify the spies (or the good team). And they have nothing better than chance to rely on, so they will choose each of the 10 possible teams with equal probability, for a total of 3/10 winning chance.

When adding Merlin, things seem to be worse for the good guys! If he takes no action to help the good team, he just reduces their winning chances to 20% (since he has a 1/3 chance of being killed). If he does help the good team, he increases their winning chances - but he also increases his chances of being killed. Any action he takes, or statement he makes, which sways the other players to choose the right team, will also be visible by the bad guys. Assuming no hidden communication, they will see each of the statements made, and know who encouraged the winning team, or discouraged the losing ones.

So is there any strategy for the good team which does better than 20% in this setup? The strategy must be known to all players ahead of time. Just to make it absolutely clear: I am not asking for ways to "hint" to your team-mates which team to pick, without the bad guys noticing or understanding what is going on.

Answer 1

Let me start with the giant caveat that if you're trying to analyze any Mafia-genre game (which both Resistance and Avalon are) without including psychology, you have missed the point of the game. These are at least as much psychology games as they are logical deduction games. With that aside, let's move on to a purely theoretical analysis. In the following, "team good" is a stand-in for the Rebels or team Arthur, and "team evil" is a stand-in for the spies or team Mordred (due to there being multiple versions of the game referenced in the question).

A big thing you've missed in your analysis is the nominations and voting. Both nominations and voting are sources of data even in the vanilla game. For example: you're running mission 4 and team good have already scored 2 points. Team evil cannot afford to lose another mission to team good, and so will vote "no" on any proposed team that doesn't contain an evil player (or that doesn't contain two evil players if you are at a player count where mission 4 requires two fail cards to fail). By noticing who is voting as a block, and also by examining who was nominated by people that you deduce are evil, you can often get a lot of information that gives team good a substantially better than a 30% chance of winning, even for lack of psychological evaluation.

Given that, there are several things Merlin can do to be effective without necessarily revealing themself:

1. Nominate an all-good team in one of the early rounds. This is most powerful when nominating the first mission of the game. If you can have that initial team be successful (ex. yourself and one other good person in a 5 or 6 player game), you can immediately score one point for team good and establish two or three semi-trusted people for future missions without it being obvious that you are Merlin (from the perspective of team evil, there is a 50% chance you picked your mission-mate by luck in a 5 player game).
2. Be able to cut through debate to nominate an all-good team in a late round when there is not enough information to tell which of two players is good and which is evil. So long as there is sufficient ambiguity, this could be also attributable to luck.
3. Be able to recognize which nomination or voting pattern is incriminating and point it out to the other good players.

Essentially, Merlin gets to do one fairly subtle intervention in order to be minimally suspicious. However, one well-played intervention changes the odds of success for team good enough to at least counterbalances the risk of Merlin being assassinated. The psychological aspect of the game also act as important cover for Merlin; as Merlin, you know who is lying, and can point out specific behaviors as "proof" that those people shouldn't be trusted as evidence for why you are making decisions that are good (so long as you aren't too clairvoyant, and spread suspicion on good players as well). Anecdotally, I've seen team good win in a majority of my games of Avalon, even taking into account assassinating Merlin, though I usually am playing with 6+ players.