[SETUP] Lynchpin

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callforjudgement
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Post Post #0  (ISO)  » Wed Feb 07, 2018 7:48 pm

Lynchpin
  • Day Start, normal day/night cycle, lynch mechanics, etc.
  • Mafia have a regular night kill (although it's compulsive and cannot target the lynchpin).
  • Pregame, the Mafia nominate one townie as the "lynchpin", a special role within the game.
  • The identity of the lynchpin is known only to the Mafia (and moderator); in particular, the lynchpin isn't told that they're the lynchpin (they got a Vanilla Town PM earlier, and aren't told that anything has changed).
  • Apart from that, the setup is purely vanilla other than win conditions:
    • Mafia win when their numbers equal the town's.
    • Town win if they eliminate all the Mafia.
    • Additionally, if the lynchpin is ever lynched, town win immediately. (In other words, the Mafia effectively collectively act as an Unlyncher on a specific townie of their choice.)


Numbers will depend on game size, but history shows that games with instant-win conditions shouldn't be too large. As such, a good place to start might be 6:3 (with a resulting EV of 51.4%); that gives town a mislynch (thus a guarantee of at least two chances to hit the lynchpin, and of course they could just lynch scum instead, although an instant-win is likely easier). Note that associative tells are likely to make the lynchpin look scummy and/or the scum guarding them look scummy, and it's in scum's interests to give themselves up to save the lynchpin, so I'd imagine that there'll be a lot of bussing, distancing, and the like involved. It may well be, though, that scum have a large advantage compared to EV in this sort of setup, so perhaps 8:3 (with an EV of 61.6%) would work better. (As usual, the larger the setup is, the less useful an extra mislynch is, because the more likely it is that you'll just end up lynching a random VT.)

Oddly, if run with an even number of players and a compulsive lynch, the EVs appear to be identical to those of a nightless game with the same player count and faction sizes. I assume there's a mathematical reason for this, but it's an interesting coincidence that make the EVs easy to look up. (The correspondence doesn't hold if the total number of players is odd, with the EVs generally much higher; the main reason for this is that there are two different ways for town to win a 2:1 lylo.)

I'm curious as to what the best lynchpin selection strategy for scum is. Strong players are unlikely to get lynched, but putting a strong player into a position where they can't be nightkilled and they can't be "mis"lynched without scum automatically losing seems counterproductive. On the other hand, making the lynchpin a weak player is more likely to have them unintentionally do something scummy and end up getting lynched for it, and/or having them become a compromise lynch.
scum · scam · seam · team · term · tern · torn · town

Mathdino
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Post Post #1  (ISO)  » Fri Feb 09, 2018 6:51 pm

This is good. Really good.

It seems as if the best possible lynchpin would be someone who bleeds newbtown but isn't good enough for a nightkill. But then you run into WIFOM, etc etc. I think if this were run in succession it, like PYP X/Y, would start swinging around based on setup meta.

My gut says starting with 8:3 would be ideal. Scum control over the lynches is obviously a massive turning point. In 6:3, unless literally the entire town piles onto the lynchpin, the lynchpin will never EVER get lynched, making the mechanic worthless.

Assuming the lynchpin is never really in danger of being lynched due to scum interference (a bad assumption but a hypothetical that needs to be considered)... it seems super scumsided, with town unable to really combat the scum in non-mountainous ways outside of lynching people they think are the lynchpin. I wonder if another mechanic can be introduced to give town more agency/morale.

Other than that, it seems runnable.

Beefster
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Post Post #2  (ISO)  » Mon Feb 12, 2018 12:41 am

Maybe a 5:2 would be better?
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Post Post #3  (ISO)  » Mon Feb 12, 2018 7:27 am

The best strategy would be to just scumhunt as normal.

If it ever reaches 3:2 LyLo, town has 60% chance to not lose that day. If it ever reaches 2:1 LyLo, town has 66% chance to win.
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Post Post #4  (ISO)  » Mon Feb 12, 2018 7:28 am

Sorta townsided. Would remove lynchpin when 2:1 LyLo.
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Mathdino
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Post Post #5  (ISO)  » Mon Feb 12, 2018 12:42 pm

In post 4, Creature wrote:Sorta townsided. Would remove lynchpin when 2:1 LyLo.

I can agree with this. Scum kinda runs out of options in 2:1 unless the town crossvotes.

A few scenarios can happen:
Alfred votes Bob
Claire doesn't hammer
Town realises it's either Claire-scum with Bob-lynchpin, Bob-scum, or Alfred-scum with Claire-lynchpin.
From Bob's perspective, he MUST then vote Claire. At this point, if Bob-scum and Claire is lynchpin, Bob always loses. So then it's Bob-scum with Alfred-lynchpin.
At this point there should be enough game material to figure out which scenario doesn't work.

Townsided but really only for LyLo.

Something_Smart
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Post Post #6  (ISO)  » Mon Feb 12, 2018 1:45 pm

Interesting idea; basically a reversal of the Chosen mechanic that doesn't pigeonhole scum quite so much.

I want to call 6:3 really scumsided. Maybe the EV is close to 50% but with that high a scum ratio, they can pretty much control the game.

Winning via lynchpin is basically never going to be feasible as it either requires all 5 townies to be wrong on the one person scum doesn't want them to be wrong on day 1, or it requires the lynchpin to self-vote.

And Mathdino's argument for 2:1 is not totally valid because scum can WIFOM vote the lynchpin if they want. (I realize this contradicts the previous statement, but the previous statement is assuming simple strategies whereas this is a potential advanced meta strategy that goes above and beyond the previous analysis.)

I'm feeling like this might be better as 6:2. From what cfj said, the EV is apparently balanced, and it doesn't have the problem of scum controlling everything nor the problem of 2:1 LYLOs being weird and wifom-y. Of course, it does have the drawback of being perpetually even which is annoying as hell. So maybe 5:2 would be better then. Definitely think 8:3 is a step in the wrong direction as the lynchpin matters less and less the more townies are added.

callforjudgement
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Post Post #7  (ISO)  » Mon Feb 12, 2018 10:59 pm

Well, the lynchpin can't matter any less in 8:3 than in 6:3, because an 8:3 becomes a 6:3 after a mislynch and the lynchpin is still there.

I'm kind-of assuming that scum will play this setup a bit like a White Flag, and try to avoid the 2:1 endgame because it's so nasty for them. Playing on evens normally sucks, but I can see the merit of wanting the "final lylo" to be 3:1, so perhaps evens is a better choice here? (In that case, you'd need to make both kills and lynches compulsive.)

I'm also assuming that the lynchpin mechanic mostly shows up in making scumhunting more accurate. The mechanic has too much of an influence on the game for scum to ignore, so they pretty much have to try to manipulate the lynches. That should be something that shows up and that the other players can detect. (I can sort-of see the lynchpin winning via self-vote, too; it may well be possible to realise that scum are trying to keep you alive. Possibly the most common way I catch scum is that they have a read on me which doesn't seem like it can possibly be justified from their point of view, whether that's a town read or a scum read.)
scum · scam · seam · team · term · tern · torn · town

mith
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Post Post #8  (ISO)  » Wed Feb 14, 2018 11:38 am

You can prove the EV for compulsive even setups by induction, but I haven't seen an obvious way to make that correspond to what happens in Nightless.

Interesting setup though. (And I think it would be kinda fascinating to just run a bunch of 2:1 nano game WIFOM-fests and see what strategies emerge.)

callforjudgement
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Post Post #9  (ISO)  » Wed Feb 14, 2018 11:48 am

Huh, this actually does work with 1 scum, and that's something that I hadn't considered at all. (Normally 1 scum setups don't work because you don't get associatives, but in this setup there are town/scum associatives.)

I think it'd work better at 3:1, though, otherwise town has too much of an incentive to just guess immediately. I'm going to try that in the Micro Queue right now.
scum · scam · seam · team · term · tern · torn · town

mith
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Post Post #10  (ISO)  » Wed Feb 14, 2018 12:38 pm

For odd T+M, Nightless (T+3):M seems to be a pretty good EV approximation even for low counts, and it looks like it converges on this for high counts.

The biggest differences are at the boundaries of T:1 (exact EV for Lynchpin T:1 is Nightless (2T+1):1) and (T+1):M; it's quite good in the middle, and (3M-3):M converges on 50% (corresponding to Nightless 3M:M), so 3:2, 6:3, 9:4, etc. should all be good counts.

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Post Post #11  (ISO)  » Wed Feb 14, 2018 5:25 pm

oh hi mith
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mith
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Post Post #12  (ISO)  » Wed Feb 14, 2018 7:06 pm

>_>


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