Standard game with Medic, Detective and Mafia.
The players left alive:
3 Town players (A,B,C)
2 Mafia goons
On an arbitrary Day, lets call it Day 4, one of the players is lynched. The Mafia Goon, aka scum had convincingly gotten his partner lynched because of circumstances. Either his partner slipped up or got caught in a lie, doesn't matter. The major proponents of this lynch were the Medic, himself and Townie A. Townies B and C eventually voted but they were a bit apprehensive.
At night time one of the Townies is killed by the remaining goon. Lets assume it is Townie C.
New state of the game:
Townies A and B
So now it comes down to this. Everyone is still unsure as to who is definitely Mafia. Amazingly Townie A gets lynched because he messed up somehow and all 3 of the remaining players caught on to it. Innocent mistake.
Now the important part!
You are the Mafia goon and it's night time - what do you do? It's between the Medic and Townie B. Medic can protect himself/herself. Everyone obviously doesn't trust each other but there are varying degrees of trust.
The Mafia goon knows who the Medic is for sure due to whatever happened during the game.
Towny B doesn't know who the Medic is, and the Medic doesn't know that the Mafia Goon has deduced his role but he is thinking about that possibility heavily.
I'll put the answer I came up with in a spoiler below. Don't read it if you don't want to be "swayed" by the logic I used ^_^
Also I don't think there's really a right answer to this, but I do think there is a great way of figuring out the best play.
+ Show Spoiler [Ace's Answer] +
Ok the way I approached this is that you play not to lose, instead of trying to outright win the game with a Night Kill.
The day before in the previous lynch you along with the Medic got a scum lynched, while Townie B wasn't really for it. This isn't a dead giveaway as the Medic isn't fully on my side but he obviously leaned toward me.
So imo, whatever happens during the Night, the next day if you come out neutral with the same 3 players I have a good shot of getting Townie B lynched based on those events. This is my worst case scenario and it's a pretty good one.
With that known let's look at what I do the previous night. No matter what I should take a shot. Not shooting is a bad idea in this scenario. So who do I hit? The Medic.
The Medic isn't sure about my role. But if I hit the Townie and the Medic happens to protect him I'm in a rough spot. The Medic is now 100% sure I'm a goon, and now instead of going into the day with Townie B in a bit of trouble I have to argue against the Medic. I've also got to now convince Townie B I'm the medic instead of the easier path of convincing the Medic Townie B is Mafia since he was already leaning towards me. Hitting Townie B at night gives out too much information if I fail.
However hitting the Medic is a huge advantage. Needless to say if the Medic protects me the game is over. But in this situation I shouldn't even care. Just hit the medic, if he protects himself it doesn't matter - he gets no new information. We go back into the day phase with the same setup, the medic knows one of us is Mafia and says he got hit last night. I don't even bother to argue and counter-claim him because I don't need to. Townie B is the one I want lynched. If Townie B doesn't instantly deduce I have to be Mafia via this role claim and argue this point he's instantly gone. If he does argue now we're right back to square one with the Medic leaning towards me.