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So I was thinking about this in the shower, want to see what some people come up with.
Setup:
Standard game with Medic, Detective and Mafia.
The players left alive:
1 Medic
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:
1 Medic
Townies A and B
1 scum
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.
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I would hit the remaining townie. If he is protected I would roleclaim medic to the remaining townie and convince him that I'm the true medic. I obvious caught the last guy. Then I would spam GG mafia throughout the thread to sound convincing. I would be like taunt taunt taunt!!! It would be fun...
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i would go with a nokill night given that if you fuck up your night kill, you're going to lose for sure -- and you might have good chances of getting B lynched next day if you don't.
otoh, when the day comes and everyone sees there was a nokill.. hmm tough, but i think if you can argue it well, this is probably best
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@JeeJee: If everyone sees there's a no kill the Medic just knows the Mafia didn't take a shot. If you as scum don't say this first you are in a bit of a spot. And since you'd be roleclaiming Medic at this point you just kinda screwed yourself over imo.
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It all depends on who the last remaining people are...
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at first it seemed like a bit of a wine in front of me situation, but then thinking about the messages the players get when they are protected, it would be better to hit the medic, so that they don't both get a message saying "you were saved," and "you saved someone," or whatever, because then you still have a chance the next day weather you win or not.
The problem with Chezinu's thing, the medic could just message the townie that he has protected him at the right time (like right before the day post), and bam the townie sides with the medic. The medic is basically gambling anyway; if he protects the mafia the town auto loses, so role claiming to the one the medic thinks is a townie before the day post wouldn't be risking anything more.
Edit: @ Ace, yeah your answer is good. lol
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+ Show Spoiler +Medic's options:
Prot self: 100% chance of success
Prot fellow townie: 50% chance of success (might prot mafia instead)
Let's say that the probability the medic will prot self is P(s). The probability the medic will attempt to prot his teammate is 1-P(s).
If the mafia hits the medic, his hit will succeed with a probability of 1-P(s); if he hits the other townie, the hit will succeed with a probability of 1-0.5*(1-P(s)) which is equivalent to 0.5+0.5P(s).
If this scenario was a game you could repeat many times, the mafia will choose the path of least resistance, i.e. hit the target against which he'd have the highest chance of success. If the medic is very likely to prot himself, his teammate will die; if the medic is very likely to prot his teammate, he'll die himself. There is an equilibrium at the point in which the mafia's chances of success are equal regardless of who he hits:
1-P(s) = 0.5 + 0.5P(s)
P(s) = 0.33
And the mafia's chance of success is 67% regardless of who he hits. Likewise, the medic will cover the target that will most likely negate the mafia's hit.
P(m) is the chance the mafia will hit the medic, and 1-P(m) is the chance he'll hit the green townie. The medic's payoff for protecting himself is P(m), and his payoff for protecting the townie is 0.5*(1-P(m)) = 0.5 - 0.5P(m). To keep the medic guessing, the mafia will equate the payoff for the medic's actions:
P(m) = 0.5 - 0.5*P(m)
P(m) = 0.33
The mafia will hit the medic 33% of the time, and the medic will prot himself 33% of the time. Mafia's chance of success is 67%.
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@Chezinu: Explain that, I don't get it.
@Iaaan: Agreed with everything except part of the second paragraph. Why would the Townie auto side with the Medic? The Medic isn't confirmed so why should the Townie believe him? Even so, let's say the medic does do that.
Mafia goon hits the medic. If the medic prots the townie, game over.
If the Medic prots himself, he's fucked now because he just lied to the Townie. So the townie says how did you take a hit when you said you were going to protect me? Mafia goon sees this and says because he isn't the doctor, I protected you. The goon now has leeway over Townie B to get the Medic lynched because he just got caught in a lie he didn't have to make.
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On February 18 2010 12:28 Zato-1 wrote:+ Show Spoiler +Medic's options:
Prot self: 100% chance of success
Prot fellow townie: 50% chance of success (might prot mafia instead)
Let's say that the probability the medic will prot self is P(s). The probability the medic will attempt to prot his teammate is 1-P(s).
If the mafia hits the medic, his hit will succeed with a probability of 1-P(s); if he hits the other townie, the hit will succeed with a probability of 1-0.5*(1-P(s)) which is equivalent to 0.5+0.5P(s).
If this scenario was a game you could repeat many times, the mafia will choose the path of least resistance, i.e. hit the target against which he'd have the highest chance of success. If the medic is very likely to prot himself, his teammate will die; if the medic is very likely to prot his teammate, he'll die himself. There is an equilibrium at the point in which the mafia's chances of success are equal regardless of who he hits:
1-P(s) = 0.5 + 0.5P(s)
P(s) = 0.33
And the mafia's chance of success is 67% regardless of who he hits. Likewise, the medic will cover the target that will most likely negate the mafia's hit.
P(m) is the chance the mafia will hit the medic, and 1-P(m) is the chance he'll hit the green townie. The medic's payoff for protecting himself is P(m), and his payoff for protecting the townie is 0.5*(1-P(m)) = 0.5 - 0.5P(m). To keep the medic guessing, the mafia will equate the payoff for the medic's actions:
P(m) = 0.5 - 0.5*P(m)
P(m) = 0.33
The mafia will hit the medic 33% of the time, and the medic will prot himself 33% of the time. Mafia's chance of success is 67%.
+ Show Spoiler +
I've got an issue with using probability in Mafia games - this is a weighted scenario. Probability of success isn't really useful for the Mafia goon because imo the goon isn't playing to win - he's playing so he doesn't outright lose. So the likelihood of calculating his hits are different.
But ok I'm going to try and follow.
The Medic starts out with a 50% chance of successfully protecting his teammate is throwing me off. Imo shouldn't it just be 33% since it's an equal likelihood that *anyone* can be hit? Remember you have no idea which one is the goon. If you did then yes, you are certainly down to just a 50% chance between 2 players getting hit. However since any of the 2 remaining players can be Mafia that means all 3 of you can be hit. So isn't it a 1/3rd shot?
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ok, what if you dont know which is the medic and they know who you are, is it still 50/50 on whether or not you win? or don't lose... w/e... what are the odds here?
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If you as the scum don't know who is the medic and honestly have no shot at guessing then you shoot "the medic" anyway or really, seriously think about not shooting at all. Remember this is a weighted situation where you've already gotten your partner killed - you look pro-town. I'm actually kind of leading towards not shooting as the best option if I think I can convince "the medic" to lynch Townie B.
The good news is that the night goes by with a no kill, everyone realizes this unless the medic lies about being hit. In this case I act surprised, but also supportive of the claim. I obviously say Townie B must be Mafia because he didn't counter-claim (what a legit townie would do) and go from there. As long as I make no indication of knowing the Medic is obviously lying by flat out ignoring it I think I have a shot.
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could you act as if you were the medic (during the no hit) and convince townie b that the other person is the mafia with the statement like "i know ONE of you is mafia, because i protected myself and got hit..." then the medic may be forced to roleclaim medic second, and the townie will think that the real medic was the one who did a hit during the no hit and you protected yourself....
right?
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Yea that's highly possible. The only reason I wouldn't try to fake claim medic is that not only is Townie B in a better position to get lynched, but what if Townie B says ok - prove it. What were your night actions? The real medic has an easier time because even if I can make up night actions, can I make up motives with those actions that make sense? So while it's possible it's also more work (assuming the Townie is even somewhat smart).
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what if the voting is a 3 way tie?
no lynch?
everyone dies?
first to vote wins?
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If there's a no lynch situation we move on to night again. I get another shot.
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if you went into the day and one of them voted for the other, would you vote with them or for them?
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I'd still side with the Medic. Since I'm acting pro-town even if I see them fighting I have to stay consistent in my argument. If I flip and turn on the Medic just like that, it looks kinda scummy doesn't it? That could backfire and end up with both of them calling me out.
Of course, if there isn't a voting deadline and it's Majority Lynch AND their both dumb enough to vote early then I'd immediately place a vote and get one of them offed ^_^
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but would you go with the first voter or the second
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On February 18 2010 12:47 Ace wrote:Show nested quote +On February 18 2010 12:28 Zato-1 wrote:+ Show Spoiler +Medic's options:
Prot self: 100% chance of success
Prot fellow townie: 50% chance of success (might prot mafia instead)
Let's say that the probability the medic will prot self is P(s). The probability the medic will attempt to prot his teammate is 1-P(s).
If the mafia hits the medic, his hit will succeed with a probability of 1-P(s); if he hits the other townie, the hit will succeed with a probability of 1-0.5*(1-P(s)) which is equivalent to 0.5+0.5P(s).
If this scenario was a game you could repeat many times, the mafia will choose the path of least resistance, i.e. hit the target against which he'd have the highest chance of success. If the medic is very likely to prot himself, his teammate will die; if the medic is very likely to prot his teammate, he'll die himself. There is an equilibrium at the point in which the mafia's chances of success are equal regardless of who he hits:
1-P(s) = 0.5 + 0.5P(s)
P(s) = 0.33
And the mafia's chance of success is 67% regardless of who he hits. Likewise, the medic will cover the target that will most likely negate the mafia's hit.
P(m) is the chance the mafia will hit the medic, and 1-P(m) is the chance he'll hit the green townie. The medic's payoff for protecting himself is P(m), and his payoff for protecting the townie is 0.5*(1-P(m)) = 0.5 - 0.5P(m). To keep the medic guessing, the mafia will equate the payoff for the medic's actions:
P(m) = 0.5 - 0.5*P(m)
P(m) = 0.33
The mafia will hit the medic 33% of the time, and the medic will prot himself 33% of the time. Mafia's chance of success is 67%. + Show Spoiler +
I've got an issue with using probability in Mafia games - this is a weighted scenario. Probability of success isn't really useful for the Mafia goon because imo the goon isn't playing to win - he's playing so he doesn't outright lose. So the likelihood of calculating his hits are different.
But ok I'm going to try and follow.
The Medic starts out with a 50% chance of successfully protecting his teammate is throwing me off. Imo shouldn't it just be 33% since it's an equal likelihood that *anyone* can be hit? Remember you have no idea which one is the goon. If you did then yes, you are certainly down to just a 50% chance between 2 players getting hit. However since any of the 2 remaining players can be Mafia that means all 3 of you can be hit. So isn't it a 1/3rd shot?
+ Show Spoiler +50% is the chance that he will successfully place his protection upon his fellow townie if he tries to do so, because he will either target the townie or the mafia. This is regardless of who the mafia hits- even if the mafia hits the medic, this doesn't guarantee the medic's success or failure in figuring out who his fellow townie is and protecting him properly.
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behavior and game feel would sway it from 50% imo
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EPT
