Open 734: Paris Mafia (13-player variation) - Game Over

[Jingle]

Innocentvillager is being prodded.

This is my surprised face:

[Fink]

IV's lurking has gotten more and more extreme and deliberate feeling. Like I'm not really buying the "Jingle is Vig" thing as genuine. And that makes me think Mime, because that's not going to get him lynched but it feels like the sort of thing that

might

enrage people if you're a jester highly disengaged from the game and trying to come up with some half-baked idea to get lynched.

The end of yesterday has me thinking Jingle is not Mime. Overall I think there was a moment where Jingle was a potential lynch yesterday, if he didn't have GL so firmly locking him as town. If Jingle were Mime that would probably be his best chance all game and he played in a way that made it so I really should have been the lynch, when he could have subtly scummed it up a bit I think.

GL is my secondary pick for Mime, and I don't feel like going into it or talking about Mafia reads unless someone other than GL has something they want me to talk about. Partly still a sheep of Ari's read, partly thinking that all the reasons I scumread him could be manipulation that just hasn't worked on Eragon for whatever reason.

[Thor665]

Point. I'm not sure why, but I was thinking there was some utility in killing the watcher then the mime for a minute there. Still irrelevant to: Lynching thor means the mime has to use their power in the way both most likely to out them to town AND most likely to give town the advantage, while not lynching makes mafia the single faction most likely to win the game, despite there still being a large chance of a forced HEA.

You keep saying things, I'mma think you're not as good at math as you keep saying and are suggesting some rather oddball interpretations of optimal play for the various factions.

I'll agree that lynching me frees up the Mime to use their power.
I fail to see how that remotely helps town wincon compared to lynching me tomorrow whether I hit Mime or town.

[Jingle]

The optimal outcome for tonight for town is a 3v1v1 with a confirmed mime and a confirmed town.
The only way to reach this optimal outcome is to lynch Thor today.

Regardless of what we do, the most likely result of our actions is a draw. I want the chance for our best chance at actually winning.

[Thor665]

The optimal outcome for town is to end up in 3v2 with a dead Mime and a caught scum.
But, yeah, I'm sure you know math better than I.

[Thor665]

Oh, also, statistically my magical best outcome is vastly more likely to happen than your pipe dream outcome.

[Jingle]

The optimal outcome for town is to end up in 3v2 with a dead Mime and a caught scum.
But, yeah, I'm sure you know math better than I.

It's really not.

Because this is the same as a 2v1 LYLO with no conftown. Mathematically, this is equivalent to a 1v3 MYLO with a conftown.

3v1v1 with a caught mime on the other hand, has the same odds of lynching scum as said 1v3 MYLO with a conftown, and a possible mislynch outcome of a 2v1 LYLO WITH a conftown.

And, if the 3v1v1's chance at happening fails (the mime doesn't correctly guess the scum AND the scum choose not to holster their shot) then there is still the chance at a 2v1 LYLO. Which is what your "optimal result for town" is.

[Thor665]

I'll agree there is a "chance".
You're ignoring the actual likelihood of those assorted chances though.
I'm right.

[Jingle]

Okay, I'm going to remove the possibilities of really stupid scumplay for a moment here, and only cater to optimal targeting, because hoping scum is dumb enough to suboptimally target based on what I say at this point isn't worth potentially letting this opportunity slip.

Lynch Thor:

1/12 chance for Autowin because scum no shooting is incredibly dumb.
1/4 chance for 3v1v1 with no outed mime. 1/4 chance of a town win, 1/4 chance of a mimewin. Scumwin functionally impossible, because scum no shooting is actually incredibly dumb so mime KNOWS who scum is and thus can force the HEA.
2/3 chance for 2v1v1. Half of that turns into 2v1 LYLO (33% town, 66% scum) and half of that turns into HEA.

So in summary:

Town Win: 1/12+1/16+1/6 = 31.25%
Mafia Win: 2/9 = 22.2%
Mime Win: 1/16 = 6.25%
Happily Ever After: The remainder.

If we No Lynch (Logic from earlier post stands):

Town Win: 19.4%
Mafia Win: 30.6%
Mime Win: 0%
Happily Ever After: 50%

This, all in absence of reads.

If, on the other hand, both Eragon and mime can correctly figure out that I'm not scum (which, holy shit), then these numbers increase for both town and mime while decreasing for mafia in specifically the case that we lynch thor. It becomes a 50/50 between 3v1v1 (Autoloss for mafia) and 2v1v1. 1/3 of 3v1v1 scenarios become confirmed mime territory, but mime still needs to shoot for them because (and this is hilarious) MIME CAN ONLY WIN IN A 3v1v1 SCENARIO.

2v1v1 is, funnily enough, also autoloss for mafia if they shoot Eragon in this case, because the mime knows who the ramining mafia is. (Not me, not whoever they blocked the previous night.)

This obviously means mafia is going to shoot for mime, not for Eragon. Eragon still has the same pool of three people to watch in, meaning Eragon could feasibly catch the mime or the mafia (or create a 50/50 between the two.)

Therefore, not only is Lynching Thor optimal for town if we can't all decide I'm super obvtown here, but it's optimal for town if we can't.

[Jingle]

You're ignoring the actual likelihood of those assorted chances though.

Yes. I was. Aren't you glad I stopped long enough to actually work the math into percentages because you pissed me off by implying I'm bad at math?

[Jingle]

Please forgive the typos in 1158.

[Kmd4390]

Vote Count

Thor665 - 2 - fink, jingle
No Lynch - 1 - Eragon

Not Voting - Thor665, innocentvillager, Guiltylion

With 6 alive, it takes 4 to lynch

Deadline is Friday October 12 at 4:30pm EST

[Thor665]

The odds for my 3v2 situation happening are actually about 16%
Your theory best happening is about 8%

it's not a matter of chance to win at the state - it's chance that the state happens.

[Thor665]

So, for the slow - my plan results in a town victory twice as often as Jingle's plan.

[Thor665]

Feels like I should shoot whoever of Fink/Jingle isn't my partner though, because that does look like votes for Mime wincon increase.

[Jingle]

So, for the slow - my plan results in a town victory twice as often as Jingle's plan.

10% less as often actually.

Your plan happens in 33% of cases where we no lynch (You have a 1/3 to shoot the mime correctly, because one of the mime suspects is your partner and thus not mime). Town wins 33% of those cases. 11.1%. 11.1% of a town victory specifically through your best case scenario of a 3v2.

The 8% is specifically the odds that the 3v1v1 autowin happens. Not the odds that town wins, but the odds that town wins through that specific chance to win in my plan.

I could do this for all of the outcomes, but it makes the post really big. The combined percentages I listed are in fact the combined likelihoods of all possible outcomes leading a win by each faction and a draw, as weighted by the likelihoods of those outcomes actually happening.

If we lynch you, we have a ~31% chance of winning. If we don't, we have a ~20% chance. Not through specifically the best case scenario, but all resultant scenarios.

Keep flailing though.

[Thor665]

Explain where you get the 25% win chance for town with no outed Mime in 3v1v1 and I'll accept that you know what you're talking about.

[Jingle]

3v1v1 with no subjective values taken into account assuming optimal play.

5 players alive, one of which is confirmed to be town.
It is impossible to lynch the confirmed town, because to do so requires a town player to vote them violating the parameters of optimal play.

Remaining: 4 possible lynch choices, two of which are mathematically identical.

Lynch Mafia: 25% Town win.
Lynch Mime: 25% Mime win.
Lynch Town (x2): 50% Night phase: 2v1v1. Assumed HEA.

Admittedly I did some hand waving of the math for the 2v1v1, but I did so because any situation where the mime is not aware of the identity of the mafia in a 3v1v1 is predicated on the Mafia no killing, which is suboptimal play, and noted the fact that I was ignoring reads and the possibility of suboptimal play in my determination of probabilities. I can work out those numbers as well, if required, to show WHY mafia no killing is virtually game throwing, but I feel like the premise is fairly solid without a mathematical explanation.

Of course, subjective values like reads accuracy change those percentages when taken into account, but we can't use them in these determinations because they cannot be proven or disproven until the game is over, so we use random chance to model the lynches. If we ignore the information from the rest of the game the mime is actually slightly more likely to be lynched than any other player and the mafia is the least likely to be lynched (except the conftown), but the exact percentages of those likelihoods aren't something we can pin down with any degree of accuracy without running the trial experimentally repeatedly.

[Jingle]

It's also worth noting that some of those percentages are rounded, because anything after the third significant digit really isn't relevant to the conversation. Mafia win was 22.2 repeating, if I recall correctly, but there's functionally no difference there and it's just not worth the trouble.

[Thor665]

Lynch Mafia: 25%

Town

Mime win.
Lynch Mime: 25% Mime win.
Lynch Town (x2): 50% Night phase: 2v1v1. Assumed HEA.

FTFY
Your math is ridiculously full of errors.
I stand by my original statement.

[Jingle]

You realize that if we lynch both mafia the mime is endgamed, right?

[Jingle]

Okay, I can't remember and it isn't made explicit in this game's OP, so I'll ask here.

@mod: Do Mimes endgame town if both mafia and the vig die? If not, what is the resolution?

Town would win in that case.

[Eragon]

yes,

the problem is having the mime willing to lynch someone at this stage

[Jingle]

But we don't need the mime to lynch in 3v1v1. We need the mime to lynch in 3v2v1. Which they will do, because it is conveniently the only way to reach 3v1v1 which is the only way the mime even has that 6% chance at a win.

In 3v1v1, a town consensus is enough.

[Eragon]

but we arent lynching for thor today, other wise im dead tonight and there will be no consensus easy tommorow or shot of mafia hitting mime/wolfy town tonight