[SETUP] Pollock's Flag

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[SETUP] Pollock's Flag

Post Post #0 (ISO) » Thu Sep 20, 2018 7:02 pm

Post by implosion »

I just got a really dumb idea!

10 Vanilla Townies

Mafia White Flag
Mafia Grey Flag
Mafia Black Flag

Normal day/night cycle.

If the first mafia member to be lynched is the white flag, then town wins immediately (like the godfather in a vengeful game, but not just on day one).
If the first mafia member to be lynched is the grey flag, then the town wins if they lynch a second mafia member (the game becomes white flag).
If the first mafia member to be lynched is the black flag, then the town wins if they lynch all three mafia (the game becomes mountainous).
The mafia win if they reach parity with the town.

EV-wise, we can assume all three mafia are equally likely to be lynched first given that there is a mafia lynch at all. Ergo, the EV is the average of three EVs:

-White flag lynched first: town's odds of losing are their odds of not mislynching every single day, which is (1 - (10/13)(8/11)(6/9)(4/7)) = 78.7%
-Grey flag lynched first: white flag, known 47.8%
-Black flag lynched first: 10:3 mountainous, known 20.8%
Overall EV is the average, a lovely 49.1%. Actually remarkably close both to 50% and to a normal white flag game. Pardon the somewhat overloaded terminology/the fact that "white flag", "grey flag" and "black flag" are all already names for other setups :p

In practice, this is likely to be incredibly skewed and vary a lot from game to game; the mafia black flag may have incentive to play as a jester early on, but that could backfire horribly if the grey flag is lynched. Different mafia members would have different incentives to avoid being lynched and different incentives to bus in different ways, and since mafia members would flip with the color of their flag interactions would be very interesting.

Also pardon me if someone has come up with this before, as it wouldn't surprise me too much.
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Post Post #1 (ISO) » Fri Sep 21, 2018 9:44 am

Post by Invisibility »

sounds interesting
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Post Post #2 (ISO) » Fri Sep 21, 2018 10:20 am

Post by Irrelephant11 »

I don't know if this gets taken into account in EV, but I'd suggest it's less likely the white flag goon gets lynched than either of the other two (given mafia won't hammer him, but they might hammer another scum slot)

Regardless it sounds fun, and I like how it makes each of the three mafia roles feel like PRs even though they aren't really
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Post Post #3 (ISO) » Fri Sep 21, 2018 11:11 am

Post by Invisibility »

gf reading would be pretty cool though
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Post Post #4 (ISO) » Fri Sep 21, 2018 11:12 am

Post by Invisibility »

like who was what flag
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Post Post #5 (ISO) » Fri Sep 21, 2018 2:05 pm

Post by Awoo »

Your calculations look weird.

I don't know about them can someone (mith) confirm that's how it actually works? Like if you lynch the black flag day 1, it isn't 10-3 mountainous, it's 9-2 mountainous. ???
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Post Post #6 (ISO) » Fri Sep 21, 2018 2:12 pm

Post by Invisibility »

oh yeah thats a thing
also lynches dont determine the thing if they're just D1 its an all the time thing
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Post Post #7 (ISO) » Fri Sep 21, 2018 2:35 pm

Post by BNL »

This looks really weird. It’s too bad if town lynches Black then White right?
Also unless you lynch Grey, Black then town has to lynch White to win anyway.

Overall I think not much can be earned from flips, as lynching White first will end the game anyway, unless people go into preflp territory.

Also another question is, is it ever profitable for Black to scumclaim? Even doing so will put the game at worst 2:9, which is not well off as if Black wasn’t obvious they will need to hunt and lynch 2 scum anyway.

I have another idea which I will present in a different thread.
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Post Post #8 (ISO) » Fri Sep 21, 2018 6:14 pm

Post by implosion »

Also another question is, is it ever profitable for Black to scumclaim? Even doing so will put the game at worst 2:9, which is not well off as if Black wasn’t obvious they will need to hunt and lynch 2 scum anyway.
Yes, it is beneficial for scum if Black is lynched on day one. 9-2 mountainous has a 35% EV. But that doesn't mean they can scumclaim, because if they do then the town won't lynch them, because it's beneficial for scum if they do. So the Black flag player actually turns into a sort of jester, but they might not want to completely commit to the jester act in case the Grey flag is lynched. It's odd.
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Post Post #9 (ISO) » Fri Sep 21, 2018 6:48 pm

Post by BNL »

Oh wait yeah, claiming Black Flag is dumb because town will hunt in the remaining players for the other flags and if they lynch White flag they win, if they lynch Grey flag they also win because the Black Flag scumclaimed.

The issue is, what if a player scumclaims, but their flag is unknown? If it's White or (I believe) Grey flag they should lynch him, but if it's Black flag they shouldn't lynch him. This game sounds like it'll be really unfun.
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Post Post #10 (ISO) » Fri Sep 21, 2018 6:49 pm

Post by RadiantCowbells »

the assumption can be made if someone scumclaims that they're black or at LEAST grey
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 #11 (ISO) » Sat Oct 20, 2018 5:06 pm

Post by callforjudgement »

In post 5, Awoo wrote:Your calculations look weird.

I don't know about them can someone (mith) confirm that's how it actually works? Like if you lynch the black flag day 1, it isn't 10-3 mountainous, it's 9-2 mountainous. ???
This is a technically correct way to do an EV calculation if town's best breaking strategy would be the same in all three setups (it is; town's best breaking strategy is "lynch players at random" as it's a symmetrical setup), but on the other hand there's a lot of reason to believe that EV calculations aren't a particularly good fit for setups of this nature. So the resulting expected value is more of a curiosity than anything else.

Re: the "Black Flag claim" strategy, I'm suspicious that a townie might try gambitting the claim themself. This would almost certainly be a terrible idea, but that doesn't seem to stop most gambits…

An early Black Flag lynch would likely lead to the game becoming unfun (but it might be fun in other cases, e.g. before a scum lynch or if the grey flag was lynched early). I suspect that optimal scum strategy is for the Black Flag to selfhammer if they get the opportunity (and for other scum to subtly encourage the possibility of this situation without outright pushing).
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Post Post #12 (ISO) » Wed Dec 19, 2018 11:28 am

Post by mith »

I'm late to the party, but the EV calculation is correct. (It's clever, and not the way I would have done it.)

You can do some cute generalizations on the idea - for example, a 4 Mafia setup where 2 of the Mafia are "you need to lynch one more if this one is first", 1 is "you need to lynch two more if this one is first" and 1 is "you need to lynch them all" is 47.84% at 4:15.

This also gave me the idea of a "Half Flag" setup, where after the first Mafia lynch the remaining Mafia have to pick one member to be the "Flag Bearer" (stealing terminology from the other thread). For a 3 Mafia start, this is effectively White Flag half the time and normal the other half; for 4 or more, it could be normal or White Flag or Double White Flag, or... One benefit over the other flag bearer setup is that Mafia get some time to see how the game is going before they choose an insta-loss role.

[edit]I'll just put it in its own thread: Half Mast Nightless[/edit]
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Post Post #13 (ISO) » Thu Dec 20, 2018 6:31 am

Post by callforjudgement »

I'm happy that the "scum lose if this scum player is lynched" role finally has a name (it's been used often enough, after all…), so I added it to the wiki: Flagbearer.
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