[QUOTE=SuperJack;936794]Still waiting for solution.[/QUOTE]
What in the world is this necro...?
Anyway, OP seems young and much less-informed about game theory than they are now - there is no pure game theory solution to guarantee a win.
But this problem is still interesting, even if it doesn't have a clear-cut solution.
As others have noted your biggest threat is the SK.
So at night you tell both killing roles to not attack anyone. The SK has nothing to gain by listening to you, which is why you make a comment at night such as "And Mr. Executioner, let's continue with our plan, we vote up whichever person ignored our plan"
The GF has nothing to gain by attacking, so they very likely won't attack in this instance. And the only way the SK loses is by getting voted up the following day, the presence of two other neutral roles ensures that this is always a risk since the SK can't kill both. So the goal of the Judge should be to maximize the perceived probability that the SK will be voted up if they defect from the Judge's orders. Implying that the executioner is already on-board with the plan is a good method to maximize the doubt in the SK's mind.
And then if you survive the night, who cares what you do, court one, win with the other.
(Oh and you definitely don't reveal who you are if roles haven't been publicly outed - just increases the risk of dying to an SK that is willing to gamble with the executioner)
What in the world is this necro...?
Anyway, OP seems young and much less-informed about game theory than they are now - there is no pure game theory solution to guarantee a win.
But this problem is still interesting, even if it doesn't have a clear-cut solution.
As others have noted your biggest threat is the SK.
So at night you tell both killing roles to not attack anyone. The SK has nothing to gain by listening to you, which is why you make a comment at night such as "And Mr. Executioner, let's continue with our plan, we vote up whichever person ignored our plan"
The GF has nothing to gain by attacking, so they very likely won't attack in this instance. And the only way the SK loses is by getting voted up the following day, the presence of two other neutral roles ensures that this is always a risk since the SK can't kill both. So the goal of the Judge should be to maximize the perceived probability that the SK will be voted up if they defect from the Judge's orders. Implying that the executioner is already on-board with the plan is a good method to maximize the doubt in the SK's mind.
And then if you survive the night, who cares what you do, court one, win with the other.
(Oh and you definitely don't reveal who you are if roles haven't been publicly outed - just increases the risk of dying to an SK that is willing to gamble with the executioner)