Trapping Mafia

This forum is for discussion of individual Open Setups, including theoretical balance.
Bicephalous Bob
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Post Post #0  (ISO)  » Fri Oct 13, 2017 8:44 am

Trapping Mafia

2 Goons
5 Townies

Once during the game, a townie may set a trap. If a goon attempts to kill a townie who set a trap, the goon is eliminated instead.
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randomidget
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Post Post #1  (ISO)  » Mon Oct 16, 2017 4:00 pm

so bsaically 2 v 5 PGOs?
seems like it could be decent, although a scum lynch day 1 kinda fucks scum a bit
vonflare (21:40)
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Post Post #2  (ISO)  » Mon Oct 16, 2017 7:09 pm

does a scum lynch day 1 in any micro not fuck scum?
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acidphoenix
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Post Post #3  (ISO)  » Mon Oct 16, 2017 8:14 pm

do you actually acknowledge the mechanics or just pretend it's nightless

Bicephalous Bob
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Post Post #4  (ISO)  » Wed Oct 18, 2017 3:58 am

In post 1, randomidget wrote:so bsaically 2 v 5 PGOs?
seems like it could be decent, although a scum lynch day 1 kinda fucks scum a bit

Not exactly, PGOs still die if they're shot while armed.

In post 3, acidphoenix wrote:do you actually acknowledge the mechanics or just pretend it's nightless

Oh man, can't believe I forgot to consider this. First solution that comes to mind is to only allow one no-kill and one no-lynch, but it's not really satisfactory.
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acidphoenix
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Post Post #5  (ISO)  » Wed Oct 18, 2017 9:43 pm

going to be honest as is I see very little incentive for scum to not go "nope not dealing with this shit" and shoot rarely if ever


no lynching isn't correct the mechanics benefit town so don't need to worry there though

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Post Post #6  (ISO)  » Thu Oct 19, 2017 4:16 am

I haven't run any numbers, but if a goon is lynched d1 and the remaining goon no-kills n1, it might be optimal to nl to force a shot and get back to odd numbers. Two nl's are probably never necessary, though.
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callforjudgement
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Post Post #7  (ISO)  » Thu Oct 19, 2017 10:21 pm

5:2 Nightless is close enough to balanced, so if the scum repeatedly no-kill the setup's in the right place.

I think the town have too much of a concentration of backfiring-kill power, though. A 5:2 most commonly only has two nightkills (it can have one or three, but two is the most common number). In a must-kill/must-lynch game, that means that half the town can arm N1 and the other half N2, to give a 3 in 4 chance of a backfiring kill on scum. That seems too high to me. Allowing one no-kill and one no-lynch spreads this out among 3 nights instead, meaning that if the town spreads their arming evenly over three night (the optimal, as scum will no-kill on the night when the most townies arm), that gives scum an 8 in 27 chance of avoiding a backfire all three times (i.e. a 19 in 27 or about 70% chance that at least one backfire happens). If a backfire happens, this setup balances similarly to a 6:1 with extra associative information, which is clearly too townsided.

I like the idea and think that this could probably be fixed just by changing the numbers. For a must-lynch/must-kill setup, I'd guess somewhere like 8:3 might work (I haven't done a formal EV calculation of this, but 6:3 feels scumsided and 10:3 feels townsided, so aim in the middle). Having three scum would be more tolerant of a D1 scum lynch, too. (Note that if the town decide to all arm on the same night, this basically makes the setup into Lynch Or No Lynch except that town get an additional lynch the night that they force a scum "sacrifice"; if 9:3 is balanced there, 8:3 is probably slightly townsided here, but Lynch Or No Lynch has never been run so maybe it's scumsided.)
scum · scam · seam · team · term · tern · torn · town

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Post Post #8  (ISO)  » Mon Oct 23, 2017 4:33 am

I calculated the binomial probs for the single no-kill setup, but I got different results. Am I correct in thinking you used n=3, p=1/3? It's n=2, since scum cannot die in the night they no-kill.

In post 7, callforjudgement wrote:this setup balances similarly to a 6:1

I'd say 5:1.

So town EV is 11 + .44 * (EV 5:1) + .44 * (EV 5:2) = .11 + .44 * 47% + .44 * 23% = 41%.
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