[SETUP] Amber Flag

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[SETUP] Amber Flag

Post Post #0 (ISO) » Sat Jul 06, 2019 2:20 am

Post by callforjudgement »

Amber Flag
  • 12 Vanilla Townies
  • 3 Mafia Goons
  • Mafia win if at least two of them are alive on N6. Town win if two scum die by N6.
  • The Mafia nightkill is
    not
    compulsive.


This setup was originally a thought experiment into the value of the scum nightkill. The maximum EV strategy is of course to never nightkill at all, but I have a feeling that the maximum winrate strategy may be different. I'm mostly interested in what the best scum strategy is here, because it's likely to give a lot of information as to how games with unusual kill patterns should be balanced.

The setup also looks surprisingly playable for a thought experiment, so I might as well post it as a [SETUP] (especially because the [EV] is trivial to calculate and possibly not that interesting).
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Post Post #1 (ISO) » Sat Jul 06, 2019 4:51 pm

Post by popsofctown »

If emotionless robots play the setup, they never NK.

If the setup is 11 Vanilla townies, 1 IC, 3 Goons and you have emotionless robots play the setup and you tell the scum robots to NK the IC, they'll say, "man, that doesn't actually make a difference, but sure, whatever, doesn't hurt."

In real forum mafia games, a couple players in the game are gonna go close enough to IC that you want to remove them from the game to keep them from solving. I think the number of players that become that strongly townread is far less than the number scum kill in 7:2 mountainous with quasicompulsive kills, but consistently higher than 0.
NKing a player for having a correct solve rather than for being townread is gutsy, because in this setup the townies know you didn't HAVE to nightkill anyone at all. NKA is weaker when the mafia have to kill somebody. For instance, if 3 softly townread players each have 3 scumreads, and Alice is NK'd, it is unclear that Alice had a 3/3 solve, perhaps Alice, Bob, and Carol all had 1/3 solves and Alice was shot because someone had to be. If Alice is shot in this setup, it suggests that her solve was 2/3 or maybe even 3/3 because the mafia sacrificed the possibility that Alice becomes a mislynch option to kill her. But it is still WIFOM: perhaps Alice is 0/3 and the mafia would like the town to believe she's 3/3

This is a great thought experiment.
"Let us say that you are right and there are two worlds. How much, then, is this 'other world' worth to you? What do you have there that you do not have here? Money? Power? Something worth causing the prince so much pain for?'"
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Post Post #2 (ISO) » Wed Jul 10, 2019 7:44 am

Post by popsofctown »

No one else? :(
"Let us say that you are right and there are two worlds. How much, then, is this 'other world' worth to you? What do you have there that you do not have here? Money? Power? Something worth causing the prince so much pain for?'"
"Well, I..."
"What? Nothing? You would make the prince suffer over... nothing?"
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Post Post #3 (ISO) » Wed Jul 10, 2019 8:00 am

Post by Irrelephant11 »

I read this and think it's interesting! It's a little big for "flag mountainous" which might make it hard to have fun, but I might still sign up
Hey all! Excited and nervous to play my first game with you!
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Post Post #4 (ISO) » Wed Jul 10, 2019 8:02 am

Post by popsofctown »

I think cfj isn't interested in actually running it :X
"Let us say that you are right and there are two worlds. How much, then, is this 'other world' worth to you? What do you have there that you do not have here? Money? Power? Something worth causing the prince so much pain for?'"
"Well, I..."
"What? Nothing? You would make the prince suffer over... nothing?"
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Post Post #5 (ISO) » Wed Jul 10, 2019 8:38 am

Post by Irrelephant11 »

true I guess

Reminds me of Creature's "gambling mountainous" (which is going into signups) wherein if >half the playerlist agrees someone is town, that player either becomes an IC or wins the game for scum. It doesn't change EV because it's just "do we all think this player is definitely town? If so we're never lynching them" which is already an aspect of mountainous games, just mechanized.
Similarly, the nightkill this game is "does the entire scumteam agree we're never mislynching this player? If so let's nightkill them" which is, again, simply making something mechanically true which was already true
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Post Post #6 (ISO) » Wed Jul 10, 2019 10:56 am

Post by callforjudgement »

I'd run it if there were interest (I agree it's a bit large, but it might make sense in something like Team Mafia which ran a pretty similar setup last time). The thought experiment was the main reason to post it, though, as getting enough interest seems difficult.

I like Irrelephant's comparison. (Perhaps you could even add the gambling mechanic to Amber Flag: you can vote to flip someone, but that also makes them lynchproof, although prevents them posting if they're scum. The white-flag ending means that an agreement to never lynch someone wouldn't necessarily lose the game if they were scum.) That said, Gambling Mountainous has a fairly well-known winrate without the special mechanic (i.e. almost unwinnable for town), but Amber Flag's scum win rate in the absence of kills is much less clear. (I'm guessing it's pretty townsided if scum never kills, but who knows? It's basically 15p Black Flag Nightless where the "losing numbers" are 7:1, which I'm guessing is rather more scumsided than the 10p version. That said, the 10p version has IIRC never been lost by town, so…)
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Post Post #7 (ISO) » Wed Jul 10, 2019 11:48 am

Post by RadiantCowbells »

In post 1, popsofctown wrote:But it is still WIFOM: perhaps Alice is 0/3 and the mafia would like the town to believe she's 3/3
in practice, scum essentially never make wifom kills. they shoot people who are obvtown or who have threatening reads.
2019 stats: Town WR 76.7%, overall WR 81.667%, 1 scum defeat involving a major mod error in lylo vs 8 scum wins.
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Post Post #8 (ISO) » Wed Jul 10, 2019 11:48 am

Post by RadiantCowbells »

In post 1, popsofctown wrote:But it is still WIFOM: perhaps Alice is 0/3 and the mafia would like the town to believe she's 3/3
in practice, scum essentially never make wifom kills. they shoot people who are obvtown or who have threatening reads.
2019 stats: Town WR 76.7%, overall WR 81.667%, 1 scum defeat involving a major mod error in lylo vs 8 scum wins.
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Post Post #9 (ISO) » Wed Jul 10, 2019 12:32 pm

Post by callforjudgement »

Making WIFOM kills would only be correct if town actually attempted to analyse nightkills, and even then it
still
wouldn't be correct most of the time unless town were fatally over-reliant on nightkill analysis
and
didn't give enouugh consideration to the WIFOM possibility.

In general, the WIFOM approach (i.e. doing something intentionally suboptimal because people believe you'd never do it as scum) is something that mathematically comes up as part of "unbreakable strategies" for scum, but the mathematical strategies typically suggest doing it only a small proportion of the time if town are playing perfectly. You do it more if town are giving a lot of weight to your actions but not considering WIFOM, and less if town aren't giving much weight to your actions or are considering WIFOM too much. "Town aren't giving much weight to your actions" is basically the meta we have at the moment.
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Post Post #10 (ISO) » Wed Jul 10, 2019 2:58 pm

Post by NotAJumbleOfNumbers »

Why is it called Amber Flag?
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Post Post #11 (ISO) » Wed Jul 10, 2019 5:40 pm

Post by callforjudgement »

In post 10, NotAJumbleOfNumbers wrote:Why is it called Amber Flag?
It reminded me of the other Flag setups (White Flag and Black Flag are the extreme versions of the setup, and Red Flag is related in that scum have a choice about what to do overnight). Amber seemed like a good colour for the flag to be.
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Post Post #12 (ISO) » Wed Jul 10, 2019 10:58 pm

Post by Gamma Emerald »

Wait how does a no kill help scum?
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Post Post #13 (ISO) » Thu Jul 11, 2019 2:21 am

Post by singletonking »

In post 12, Gamma Emerald wrote:Wait how does a no kill help scum?
By increasing the number of potential mislynch targets. Because their goal is to survive to N6, rather than to outnumber the town, they don't give town an extra mislynch by no-killing.

In practice, scum may want to kill anyway to get rid of town's best players.
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Post Post #14 (ISO) » Thu Jul 11, 2019 6:14 am

Post by popsofctown »

In post 8, RadiantCowbells wrote:
In post 1, popsofctown wrote:But it is still WIFOM: perhaps Alice is 0/3 and the mafia would like the town to believe she's 3/3
in practice, scum essentially never make wifom kills. they shoot people who are obvtown or who have threatening reads.
I agree but I liked including it in my analysis.
"Let us say that you are right and there are two worlds. How much, then, is this 'other world' worth to you? What do you have there that you do not have here? Money? Power? Something worth causing the prince so much pain for?'"
"Well, I..."
"What? Nothing? You would make the prince suffer over... nothing?"
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Post Post #15 (ISO) » Fri Jul 26, 2019 11:51 am

Post by mith »

I like this one. That is not at all surprising, though. :)
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Post Post #16 (ISO) » Wed Sep 11, 2019 7:13 am

Post by northsidegal »

what actually is the ev for this? i assume it's different for different strategies
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Post Post #17 (ISO) » Wed Sep 11, 2019 11:02 am

Post by callforjudgement »

If scum never nightkill, then town get 6 tries to find 2 out of 3 scum in 15 players; it doesn't matter what order they lynch in because they get no additional information from nightkills (there aren't any), and under EV assumptions, no additional information from flips either (because EV assumptions include "no associative tells"). So we can simply count the possibilities:
  • Number of possible arrangements of scum on the playerlist: (3 choose 15) = (15×14×13)÷(3×2×1) = 455
  • Number of arrangements in which exactly 3 scum are in the first 6 lynches: (3 choose 6) = (6×5×4)÷(3×2×1) = 20
  • Number of arrangements in which exactly 2 scum are in the first 6 lynches, thus 1 scum in the other 9 players: (2 choose 6) × (1 choose 9) = (6×5)÷(2×1)×(9)÷(1) = 135
  • Total number of arrangements in which town win: 155 out of 455
  • Total town EV: 155 ÷ 455 or approximately 34.066%.
If scum always nightkill a townie, the EV is equivalent to that of 12:3 White Flag. Mathdino did the calculations for that a while back, producing an EV of 53.6%.

Other nightkill strategies for town will have EVs that are somewhere in between.
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Post Post #18 (ISO) » Thu Sep 12, 2019 8:23 pm

Post by Gamma Emerald »

Given that with optimal play this would be really scumsided
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Post Post #19 (ISO) » Fri Sep 13, 2019 1:06 pm

Post by callforjudgement »

I don't think 34% is a scumsided EV for a Nightless (which is what you get if scum never kill).

The usually mentioned numbers for a Mini Nightless are 9:4, which has an EV of 1 - (8/13) = 5/13 or around 38.5%. So 34% isn't far from there.

That said, my guess is that scum's best strategy is to kill any players who are really strong as town, then stop killing, which is likely to really hurt town's chances without increasing the EV too much.
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Post Post #20 (ISO) » Fri Sep 13, 2019 3:04 pm

Post by Spangled »

In post 19, callforjudgement wrote:I don't think 34% is a scumsided EV for a Nightless (which is what you get if scum never kill).

The usually mentioned numbers for a Mini Nightless are 9:4, which has an EV of 1 - (8/13) = 5/13 or around 38.5%. So 34% isn't far from there.

That said, my guess is that scum's best strategy is to kill any players who are really strong as town, then stop killing, which is likely to really hurt town's chances without increasing the EV too much.
Yeah, scum are definitely going to kill UTR town leaders or people who are obvtown that they don’t think they can sway paranoia against.
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