On the seventh day, we SPAMMED

Not the kind with cardstock and pawns. Mostly play by post Mafia so far.

Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Sun May 17, 2015 4:22 pm

Tamien, can you say explicitly that to your knowledge you're not possessed? EDIT: Never mind, you did already. Reading comprehension fail.

In the abstract, there are 4 possible people who could be possessed: me, Shoal, michaelblume, Tamien. The following strategy is guaranteed to win us the game for 3 of those 4 people being possessed:

1. We kill one of our own today. As a Schelling point I suggest Tamien because she has devil powers and needs to die at some point anyway. :p
2. I nightkill Shoal tonight.
3. Finally, I vote to lynch michaelblume tomorrow.

This avoids a tie tomorrow between two of us, one potentially possessed, which risks losing the game.

Obviously if I'm the demon this is not something you want to do. I repeat again that as far as I'm aware I'm not. If you *do* think I'm the demon you should obviously both vote for me to die today, which gives Azef=Tamien the kill-assigning power tonight. But as far as I can tell, regardless of who's possessed there is absolutely no reason to kill michael until tomorrow (the only exception would be if he actually turns up and votes then, but I think we can rule that out at this point).
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Re: On the seventh day, we SPAMMED

Postby Shoal » Mon May 18, 2015 4:57 am

huh, all this time I thought I was the backup leader. That's weird.

Your strategy of course only works if you're not possessed.

in alphabetical order:
If Jalapeno is the demon
If Jalapeno is the demon:
lynch: Tamien, nightkill Shoal, lynch michael: DEMON WIN
lynch Shoal, nightkill Tamien, lynch michael: DEMON WIN
lynch Michael, nightkill Shoal, lynch jalapeno/tamien: 50:50 DEMON/MAFIA WIN
lynch Michael, nightkill Tamien, lynch jalapeno/shoal: 50:50 DEMON/MAFIA WIN
lynch Tamien, nightkill Michael, lynch jalaepno/shoal: 50:50 DEMON/MAFIA WIN <-- this won't happen, he has a better victory path
lynch Shoal, nightkill Michael, lynch jalapeno/tamien: 50:50 DEMON/MAFIA WIN <-- this won't happen, he has a better victory path
lynch Jalapeno, MAFIA WIN


if michael is the demon: no matter what we do MAFIA win (because he isn't voting).

If shoal is the demon
if shoal is the demon:
lynch Tamien, nightkill michael, lynch jalapeno/shoal 50:50 DEMON/MAFIA win
lynch michael, nightkill Tamien, lynch jalapeno/shoal 50:50 DEMON/MAFIA win
lynch jalapeno, nightkill michael, lynch tamien/shoal 50:50 DEMON/MAFIA win
lynch Tamien, nightkill Shoal, MAFIA WIN
lynch michael, nightkill Shoal, MAFIA WIN
lynch jalapeno, nightkill Shoal, MAFIA WIN
lynch Shoal: MAFIA WIN


if tamien is the demon
if tamien is the demon:
lynch jalapeno, nightkill shoal, lynch michael: DEMON WIN
lynch shoal, nightkill michael, lynch jalapeno/tamien 50:50 DEMON/MAFIA win
lynch michael, nightkill shoal, lynch tamien/jalapeno 50:50 DEMON/MAFIA win
lynch jalapeno, nightkill michael, lynch tamien/shoal 50:50 DEMON/MAFIA win <-- this won't happen, she has a better victory path
lynch shoal, nightkill Tamien, MAFIA WIN
lynch michael, nightkill tamien, MAFIA WIN
lynch tamien: MAFIA WIN


So if Jalapeno is the demon, the plan he suggested is his best course of action for his own demonic win condition.
If michael is the demon then we win unless he starts playing again.
If I am the demon, then I want anybody but me to be lynched, and anybody but me to be nightkilled.
If Tamien is the demon, then Tamien wants jalapeno to be lynched today but will settle for anybody but her, then she wants anybody but her to be nightkilled, which she can control if jalapeno is lynched.

There are 3 surefire paths to demon victory depending on who is guilty.

they are:
lynch shoal, nightkill tamien <--if shoal is lynched today, this will happen for sure if jalapeno is the demon
lynch tamien, nightkill shoal <-- if tamien is lynched today, this will happen for sure if jalapeno is the demon
lynch jalapeno, nightkill shoal <-- if jalapeno is lynched today, this will happen for sure if tamien is the demon

every other path forces the demon's best path to come down to THE COIN. If whoever is holding the gun is reasonably sure that somebody else is the demon then we can just shoot them and win. If moderately sure then we can use this decision tree to try to minimise one person's win chances in particular

The assumptions I am making here is that the mafia leader is not going to give the kill to anybody but themselves regardless of their alignment. If they're not possessed then it would be stupid to hand the gun to the potential demon. If they are possessed, it would be stupid to let someone potentially kill them, and that the game will be called after we catch the demon even if michael is still alive, the way last game was called when pistachi0n and I could no longer win.


Anyway I need to get food, jalapeno please poke holes in my logic if I'm missing something obvious. The approach I'm taking is we need to try to minimise the demon's win strategies. as far as I can tell we have 3 more chances to get this right (lynch, nightkill, lynch) and the only way we can change who has the nightkill is to lynch jalapeno but we have to decide if that's what we want or not. I think that since jalapeno is going to be doing the nightkill, the day lynch should minimise jalapeno's winning chances in case he's the demon, unless we're really sure about someone in particular. as such it might make more sense to lynch michael today.
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Re: On the seventh day, we SPAMMED

Postby Tamien » Mon May 18, 2015 8:50 am

Shoal, this all looks reasonable to me.
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Re: On the seventh day, we SPAMMED

Postby Shoal » Mon May 18, 2015 2:38 pm

great.

let’s have one of these on each page

Image
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Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Mon May 18, 2015 2:42 pm

So I made my own version of Shoal's tables:

possible outcomes, v1
Code: Select all
jalapeno_dude demon
lynch michael
   nightkill Shoal -> coinflip
   nightkill Tamien -> coinflip
lynch Shoal
   nightkill michael -> coinflip
   nightkill Tamien -> demon win
lynch Tamien
   nightkill michael -> coinflip
   nightkill Shoal -> demon win
lynch jalapeno_dude -> mafia win

michael demon -> mafia win

Shoal demon
lynch michael
   nightkill Shoal -> mafia win
   nightkill Tamien -> coinflip
lynch Shoal -> mafia win
lynch Tamien
   nightkill michael -> coinflip
   nightkill Shoal -> mafia win
lynch jalapeno_dude
   nightkill michael -> coinflip
   nightkill Shoal -> mafia win

Tamien demon
lynch michael
   nightkill Shoal -> coinflip
   nightkill Tamien -> mafia win
lynch Shoal
   nightkill michael -> coinflip
   nightkill Tamien -> mafia win
lynch Tamien -> mafia win
lynch jalapeno_dude
   nightkill michael -> coinflip
   nightkill Shoal -> demon win


Staring at this table for a while, there are a few possibilities we can eliminate. If one of us is lynched and doesn't turn out to be the demon, it always makes sense to nightkill the other remaining mafia member--or, equivalently, it never makes sense to nightkill michaelblume. This results in the kill assigner always winning, regardless of whether they're Mafia or Demon.

After removing those possibilities:
possible outcomes, v2
Code: Select all
jalapeno_dude demon
lynch michael
   nightkill Shoal -> coinflip
   nightkill Tamien -> coinflip
lynch Shoal
   nightkill Tamien -> demon win
lynch Tamien
   nightkill Shoal -> demon win
lynch jalapeno_dude -> mafia win

michael demon -> mafia win

Shoal demon
lynch michael
   nightkill Shoal -> mafia win
   nightkill Tamien -> coinflip
lynch Shoal -> mafia win
lynch Tamien
   nightkill Shoal -> mafia win
lynch jalapeno_dude
   nightkill Shoal -> mafia win

Tamien demon
lynch michael
   nightkill Shoal -> coinflip
   nightkill Tamien -> mafia win
lynch Shoal
   nightkill Tamien -> mafia win
lynch Tamien -> mafia win
lynch jalapeno_dude
   nightkill Shoal -> demon win


So the win probabilities depending on who we lynch are, in fact, all equal:

lynch michael: 2 mafia win, 2 coinflip -> 75% win
lynch Shoal: 3 mafia win, 1 demon -> 75% win (lose when jalapeno_dude is demon)
lynch Tamien: 3 mafia win, 1 demon -> 75% win (lose when jalapeno_dude is demon)
lynch jalapeno_dude: 3 mafia win, 1 demon -> 75% win (lose when Tamien is demon)

It's true that lynching michaelblume prevents the demon, whoever they are, from winning immediately, but it means that if I pick wrong at night there's a COINflip to decide the game.

However, these are the probabilities if you have no knowledge other than that one of us is possessed. I have more information that that, because I don't know myself to be possessed. If that meant I was in fact certain not be possessed, I could eliminate the "jalapeno_dude demon" part of the table. That gives the following win probabilities:

jalapeno_dude not demon
lynch michael: 2 mafia win, 1 coinflip -> 83.3% win
lynch Shoal: 3 mafia win -> 100% win
lynch Tamien: 3 mafia win -> 100% win
lynch jalapeno_dude: 2 mafia win, 1 demon win -> 66% win (lose when Tamien is demon)

This means I would prefer to lynch one of you, which would guarantee a win, and strongly prefer not to get myself lynched, which would drop our win chance to 2/3. This is the strategy I came up with before. Of course it also guarantees a win for me if I'm possessed, which I'm not.

Of course, I don't really know I'm not the demon--it could be that I'm possessed and don't know it. Regardless, because it doesn't matter who we lynch in the zero-knowledge case I should prefer to vote for Shoal or Tamien if knowing that I haven't been told I'm possessed makes me even a little bit less likely to be possessed, which I think it does.

I can do the same thing for you guys, too. Shoal, if you know you're not possessed, your probabilities are:
lynch michael: 1.5 mafia win, 1.5 coinflip -> 75% win
lynch Shoal: 2 mafia win, 1 demon -> 66% win (lose when jalapeno_dude is demon)
lynch Tamien: 2 mafia win, 1 demon -> 66% win (lose when jalapeno_dude is demon)
lynch jalapeno_dude: 2 mafia win, 1 demon -> 66% win (lose when Tamien is demon)

You want to keep all of the mafia going alive into tonight so the demon can't win outright if they're the kill assigner.

Tamien, if you know you're not possessed, your probabilities are:
lynch michael: 1.5 mafia win, 1.5 coinflip -> 75% win
lynch Shoal: 2 mafia win, 1 demon -> 66% win
lynch Tamien: 2 mafia win, 1 demon -> 66% win
lynch jalapeno_dude: 3 mafia win -> 100% win

You want to kill me because then you're guaranteed to win regardless of whether or not you're possessed.

Interestingly, all three of us should be indifferent about which of Tamien or Shoal should be lynched if they had to choose between those two options only.

So, if we were all unpossessed and acting independently to maximize our win conditions, the votes should be:
me: Tamien or Shoal
Shoal: michaelblume
Tamien: jalapeno_dude

That's in fact the same voting preference each of us would have if we *were* knowingly possessed!

If this were the preliminary voting I'd have no reason to change my vote (I'd calculate a (1+5/6+2/3)/3 = 83.3% chance of winning, the same as if I switched to voting for michaelblume and better than voting for myself). Shoal would calculate a (3/4+2/3+2/3)/3=69.4% chance of winning, better than voting for anyone other than michaelblume. Tamien would calculate a (1+2/3+3/4)=80.6% chance of winning, better than voting for michaelblume or Shoal/Tamien. So, I think this is stable. Whether I'm voting for Shoal or Tamien doesn't matter because as noted above neither of you should care if you or Tamien is lynched (2/3 chance either way). (If one of you *is* knowingly possessed then of course you'll care, though.)

I conclude that the votes above make the most sense for everyone regardless of whether they're mafia or not, and voting any way other than that would make your win condition decrease, again regardless of whether you're mafia or not. So we might as well just submit our votes right now and let THE COIN decide.
Last edited by jalapeno_dude on Mon May 18, 2015 2:52 pm, edited 2 times in total.
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Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Mon May 18, 2015 2:45 pm

Let me note that this is *not* what I expected to find when I started doing the math. (I *especially* didn't expect to find that everyone should vote the same today regardless of whether or not they're possessed!) But, thinking about it after the fact, I think I have some intuition for why it makes sense. Everyone wants to put the game into the situation where they have as much control as possible regardless of win condition. For Tamien, that's killing me and getting the nightkill. For me, that's killing people with votes. For Shoal, it's minimizing the power of the other voters.
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Re: On the seventh day, we SPAMMED

Postby Tamien » Mon May 18, 2015 3:23 pm

I am amused that your math justifies my mistrust of you :P

In fact, your math does a pretty good job of describing my opinions. I do in fact think it's safest if we lynch you, but would accept michaelblume, and I am indeed indifferent between my death and Shoal's while disprefering both options. I am not sure to what extent my thinking you're acting suspiciously is due to you being higher threat if I misjudge your possession status than Shoal would be. I find it kindof annoying that I get control of nightkills if you die, which makes it looks like a power grab if I go against you, when I really don't want the responsibility. But I suppose if I were in Shoal's position, then I would probably feel differently about everyone's threat levels precisely because I would be last in the line of succession.

I feel like the compromise solution is to find the one that gives each of us the highest chance of winning independently, but I have no idea how to math that, and probably shouldn't trust other people's math. Based on yours, it looks like us lynching michaelblume is the "compromise" option. I would be willing to go with this compromise.
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Re: On the seventh day, we SPAMMED

Postby Shoal » Mon May 18, 2015 4:17 pm

that's interesting. I wasn't expecting that either but it makes sense the way you described it: we each want to be in control or at least to minimise the other people's control. i think your math is right, though I want to look at it again when I'm fresher. I am indeed indifferent to whether it's tamien or me so long as we get the mafia win but I do prefer michael to be the lynch of the day. Maybe there's a nash equilibrium to be found, some kind of compromise strategy anyway.

I think I would prefer not having the fate of the game decided on a three way coin flip but I'll need to examine that in the morning to see whether it's just a counterintuitive result or if there's something more there. But a 75% win chance is heartening.
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Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Mon May 18, 2015 5:18 pm

Shoal wrote:Maybe there's a nash equilibrium to be found, some kind of compromise strategy anyway.
Right, this is what I was attempting to argue with the stuff about no one wanting to switch votes from the situation I presented. Of course then Tamien promptly went and offered to switch her vote to one that should be less advantageous from her point of view. :p (That actually makes me a little bit more suspicious of her...)
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Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Mon May 18, 2015 5:20 pm

Also, having the fate of the game decided on an epic COINflip seems entirely in keeping with the way it's gone so far... :p
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