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 Shoal » Tue May 19, 2015 3:22 am

Image

it's been a while since i watched the open yale Game Theory lectures and so the terminology isn't fresh in my head but I think you'll understand if I describe what I'm thinking?

On the topic of recursion, one of the games that was discussed was the case of two passengers who both lost their luggage at the same time with the same luggage contents, say they both had an identical vase or something. The airline asks them each to write down separately the value of the vase not exceeding $100. The lowest number will be assumed to be the true value of the vase, and the person who wrote it will be given an extra $2 for their honesty and the person who didn't will be penalised $2 for their dishonesty.

If they both write $100 they both get $100. But if one of them writes $99 and the other writes $100 then the first one will get $101 and the second will get $98, which seems better, but the second one, knowing the other guy will write $99 then has an incentive to write $98, and by recursion it goes all the way down to a nash equilibrium of them both writing $1. Which is terrible. Obviously $100 is better than $1 and they should prefer to write $100 because who cares about the extra $1. I would rather receive money in the range $98-$101 depending on what the other guy does than to receive $1 because logic. $1 is the right answer but it's the dumb answer.

We're not exactly in that situation because we can consult with each other beforehand. My girlfriend and I have agreed to co-operate if we're ever in a prisoner's dilemma which breaks it.

So maybe the nash equilibrium if we all choose our best strategy is coinflip. But maybe there's a broader a solution that, while still not our preferred strategy, if adopted is overall more preferable to each of us than the coinflip solution? If everybody's second best option leads to a higher winchance for the group.

I mean, from where I sit I would rather convince you both to vote michael than coinflip but will accept coinflip if it comes down to it.
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Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Tue May 19, 2015 3:25 pm

Shoal wrote:So maybe the nash equilibrium if we all choose our best strategy is coinflip. But maybe there's a broader a solution that, while still not our preferred strategy, if adopted is overall more preferable to each of us than the coinflip solution? If everybody's second best option leads to a higher winchance for the group.

I mean, from where I sit I would rather convince you both to vote michael than coinflip but will accept coinflip if it comes down to it.


So I think this depends on what you mean by "the group".

-If you mean an observer who wants the mafia to win, e.g. Tulip and pistachi0n, it doesn't matter who we lynch--each option leads to a 75% chance of winning.

-If you mean simply averaging all three of our calculated sets of probabilities, we get
lynch michaelblume: 7/9=77.8% chance of winning
lynch Shoal: 77.8% chance of winning
lynch Tamien: 77.8% chance of winning
lynch jalapeno_dude: 77.8% chance of winning
Again it doesn't matter who we lynch. (Why is this chance of winning higher than the 75% chance above? That was derived assuming that each of us had a 1/4 chance of being a demon. But by averaging these probabilities together we're implicitly assuming that there's now only a (1/3+1/3+0)/3=2/9 probability that each of us is a demon, which is less than 1/4.)

But the problem is that each of us both has additional knowledge beyond what an outside observer would have and places less value on everyone else's claim to not being possessed. Given that, each of us thinks (perfectly rationally) that we know better than the other members what's best for the group. It would be both dumb and, more importantly, anti-Mafia of me to vote for myself, or for michaelblume for that matter, because from my perspective it would make it less likely for the Mafia to win the game! Similarly it would be anti-Mafia from her perspective for Tamien to vote for anyone other than me, and it would be anti-Mafia for Shoal from their perspective to vote for anyone other than michaelblume.

Given all of that, I would strongly prefer that Shoal or Tamien be lynched today. I will grudgingly accept the 3-way COINflip presented because it is still better than any other option besides them being lynched. And the same should go for both of you. If you are contemplating any other option than this (i.e. voting for your preferred candidate) then the burden is on you to explain how you are not being anti-Mafia! E.g. Shoal should not be willing to join Tamien in voting for me because that makes it less likely, from their perspective, that the mafia will win. Tamien should not be willing to join Shoal in voting for michaelblume for the same reason. And neither of you should be willing to join me in voting for each other.

There are only two rational reasons to change your vote, as far as I can see:
1. You're not, in fact, mafia-aligned. (Though I still think Tamien would want to kill me and Shoal would want to kill michaelblume if they were the demon, but maybe "live as long as possible" takes priority over "kill everyone else" or something like that.)
2. You dispute the probabilities I assigned above, either because I made a math error (which you should point out) or because you've convinced yourself that one of us is definitely not Mafia-aligned or that all of us are definitely Mafia and can't be possessed (I think this last is impossible because there's a possibility that you might not even know that you're possessed). I personally have not convinced myself of that, and similarly I have tried to be very clear why I believe my proposed vote is the best thing to do given that I want the mafia to win.

(I am aware that I am probably coming off as a little bullying here, and I'm sorry for that, but my overriding motivation right now is not to stupidly throw the game to the demon at the last minute.)
Last edited by jalapeno_dude on Tue May 19, 2015 3:35 pm, edited 1 time in total.
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Re: On the seventh day, we SPAMMED

Postby Shoal » Tue May 19, 2015 3:34 pm

I plan to vote for michael. I'll vote now if you want. I would of course be happiest if the two of you would join me in that, which from my own perspective leads to the surest mafia victory.

What I was asking mainly was "is there something the three of us could agree on that is better for the mafia than the coinflip given if we concede our first choices".maybe the answer is no.
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Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Tue May 19, 2015 3:36 pm

Shoal wrote:What I was asking mainly was "is there something the three of us could agree on that is better for the mafia than the coinflip given if we concede our first choices".maybe the answer is no.

Yeah, I think that the answer is no. This was the point of this:

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.)
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Re: On the seventh day, we SPAMMED

Postby Shoal » Tue May 19, 2015 3:43 pm

Yeah, makes sense. I spent the day trying to think of some other way but I don't think there is. I strongly prefer to lynch michael. You pretty strongly prefer to lynch me or Tamien. Tamien seems to strongly prefer to lynch you but is willing to compromise on michael. I, of course, prefer Tamien to compromise on michael too, and you of course do not.

This is kind of like 3 person instant LYLO (instant because we can't take anyone's previous 6 days of behaviour into account) but I don't know anything about how to play in that situation, I mean mass claim is a given but we've all claimed unpossessed so that's a dead end.

It's all like SK (serial killer) hunting because that's what it is, but my only experience with an SK, the tracker had a guilty on the SK and he conceeded and I was town then anyway. Some general tells that "a player in public who is speculating on the SK instead of speculating on the mafia is either the SK or mafia" but that's in public and it doesn't apply here because we're mafia, not town, and we're in the end game.

I'm definitely asking BSS about it in the postgame though. Did you find anything about the demons will reading over the thread?
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Re: On the seventh day, we SPAMMED

Postby Tamien » Tue May 19, 2015 3:44 pm

jalapeno_dude wrote: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...)


I'm not sure how I offered to switch my vote when a) I haven't voted at all and b) my first post suggested that we lynch michaelblume.

Your latest post talks about how we should all vote for separate people as though this will maximize our chances of winning, and I'm not really convinced. With the knowledge I have, plus the suspicions I've gained, I would rather lynch you, but I obviously won't convince you to vote for yourself, and I don't think I can convince Shoal to vote for you. I do think that we can come to an accord on lynching michaelblume, and that this gives us acceptable odds of winning (not as high as I'd like, but I'll take what I can get).

Maybe a 3-way COINflip is better, since we know that at most 1/3 of us are possessed, and a 1/3 chance of demon win is better than a 1/2 chance. Ugh. I am trying to think about this clearly but I keep reading your math with this warning light going off in my head of "do not trust him, he is trying to obfuscate things, there is something important he is leaving out, demon demon demon demon" and like. Maybe I *should* just vote for you. But apparently you *want* me to vote for you and my not trusting you makes me feel like I should therefore not do what you want and cooperate with Shoal. Or maybe I'm just concerned that you're trying to engineer a tie and then throw it at the last moment (except that if I vote for you, and Shoal votes michaelblume, that only lets you break the tie in one of the directions you're arguing against, so that doesn't make sense...)

(Shoal, if you are the demon, you are doing a very good job of avoiding suspicion. At this point I am increasingly convinced that jalapeno_dude is possessed, even though I don't actually feel like I have any good evidence for it, nor can I say what would convince me he's not. I really *should* be equally suspicious of both of you. And yet I find myself trusting you and not jalapeno_dude, and I can only assume this is because I know that jalapeno_dude being possessed is a greater threat, because I really have no other explanation.)

Rrrgh I miss the days of friendly mafia trust and teamwork.
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Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Tue May 19, 2015 4:13 pm

Sorry, by "offered to switch" I mean you said you were willing to vote for michaelblume after saying you preferred to vote for me.

Note for after the game ends: I need to work on seeming less suspicious when innocent.
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Re: On the seventh day, we SPAMMED

Postby jalapeno_dude » Tue May 19, 2015 4:22 pm

Tamien wrote:But apparently you *want* me to vote for you and my not trusting you makes me feel like I should therefore not do what you want and cooperate with Shoal.
I don't want you to vote for me. But given that Shoal is voting for michaelblume, you can only help me by voting for you or shoal, which I don't think you'll do. Given that, I saw no harm it pointing out what the math from your perspective seems to indicate. The fact that you're not doing that is alarming to me, and I am now probably going to nightkill you if it comes up, when before I was planning on killing Shoal. I hope very much that this does not lose us the game.

Rrrgh I miss the days of friendly mafia trust and teamwork.
I do too.
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Re: On the seventh day, we SPAMMED

Postby Shoal » Tue May 19, 2015 4:29 pm

I miss it too. I've really enjoyed being scum with you guys.

Being town in LYLO is really stressful the few times I've been in it. It was pretty exhilarating as scum with modrony in day 6 even though she caught onto us. but this feels more like town LYLO again with all the stress of having to figure things out. we've been coasting on the townie's suspicion lists all game.

I think jalapeno is accusing you of not voting the way his math says you should want to but we each approach things differently. He does math and I...usually look for associations between people but that doesn't apply here, so in absence of that I also used math to try to work out what the demon might want in case we could prevent i from happening. I use reaction tests some in LYLO but the ones I have up my sleeve don't apply in this situation because they're for catching teams not individuals, like the "if 4 out of 5 want to vote for a player or 6 out of 7 then that means the player is town" tell. But it explicitly doesn't work in 3 player lylo because (in absence of the kill order mechanic) each of us should be theoretically indifferent between the other two being killed, none of us has a scumbuddy we're trying to save like when you were trying to save me yesterday or when we were trying to save tamien or back on day 1 when we were all trying to save aestrix.
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Re: On the seventh day, we SPAMMED

Postby Tamien » Tue May 19, 2015 5:27 pm

jalapeno_dude, nightkilling me is a bad idea if you are mafia. I don't understand why my actions are alarming to you and am frustrated that I have apparently made myself suspect by trying to find compromise solutions?? If you really think Shoal is likely to be possessed, please make a case and I will consider voting Shoal (it will be a high bar since doing that is handing you the game if you're possessed). I honestly don't understand why voting michaelblume is a bad plan ASSUMING that I think it's much more likely you're the demon than Shoal is. I have a hard time keeping track of enough of the math at a time to really compare that many options against each other, so maybe I'm just missing some straightforward math here. Or maybe I just have a bias towards wagoning over COINflips, even when the wagon will most likely lead to a COINflip with worse odds? I am trying to figure out if it really makes sense from my perspective to vote for you and let the COIN fall where it will rather than cooperate with Shoal/cross my fingers that michaelblume is the demon and we're all bickering over nothing.

There are 4 players remaining, one of which is possessed. If we simply wait until the demon has to jump hosts again, they'll die, kill one person in the process, and possess a third. Which would leave one person vs the demon on the last day, which would just lead to another COINflip, and it's not even guaranteed to be a mafia/demon flip if somehow michaelblume makes it through all that. So... not killing anyone is definitely a much worse option than killing someone.

If we lynch no one, then jalapeno_dude will nightkill one person of his choice, probably me. This leads to the same situation tomorrow, but with worse odds (1:1 mafia:demon instead of 2:1).

If we lynch someone today, then there's a 1/4 chance that that person is the demon and we win. If we lynch jalapeno_dude and he is not the demon, then I get the nightkill, and have a 1/2 chance of hitting the right person during the night. If I get it wrong, the game ends with a 50-50 COINflip the next day. If we lynch me, Shoal, or michaelblume, then the same scenario plays out except jalapeno_dude has to make the decision.

If we all vote for our preferred targets (me: jalapeno_dude; jalapeno_dude: me, apparently; Shoal: michaelblume) then there's a 3-way COINflip and the only person not at risk of death is Shoal. Okay, so clearly given my suspicion rankings, I actually really *should* have let you continue trusting me more than Shoal and voted for you. Heck :P

Good job convincing me to vote for you, I guess?
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