[EV] Roleblocker Madness

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[EV] Roleblocker Madness

Post Post #0 (ISO) » Sat Jul 07, 2018 9:44 am

Post by Ircher »

5 Town, 2 Scum; everyone is a roleblocker, and scum can kill and block at the same time.

Mutual and circular roleblocks cause all roleblocks in the chain to fail.

Anyone have an idea for the EV of this, and more importantly, is there some breaking strategy for this setup?
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Post Post #1 (ISO) » Sun Jul 08, 2018 4:19 am

Post by Awoo »

I don't know if there's a breaking setup at all with these numbers and 2 alive.
If people claim their blocks ahead of time, and mafia don't like where things are going, they choose one person to be the designated killer for the night, then set things up in a chain so the killer can make a kill.

Here's my attempt at a strategy

If town is lynched day 1 : 4 - 2 night -> I think there's literally nothing you can do that mafia can't counter so just block randomly and if it nokilled people all point at each other to indicate who they blocked as soon as the day starts? oh no.. not this... again... nope I quit

If mafia is lynched day 1: 5 - 1 night ->

ABCDEF

A -> C
B -> C
E -> D
F -> D

C and D block no one / each other

If there's no kill then maybe mafia is in CD or maybe the mafia no-killed. No lynch, switch the people to AB or EF or any arbitrary pairing of your choice, and execute the same strategy until mafia kill someone.

If there is a kill, C and D are inno childs because there is no way they could have killed. Meaning if mafia does kill, they need to kill one of C/D.
Then you're in 4 - 1 day with 1 inno child.

Lynch mafia -> win

Lynch town -> 3 - 1 night with 1 inno child. ABCI - I is inno child

A -> C
B -> C
I -> C

If there's a kill C is town, I or C dies, in the night giving you 2-1 with 1 inno child. No kill, no lynch and repeat.

Overall pretty a bit swingy, mafia get sacked if they get lynched d1.
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Post Post #2 (ISO) » Thu Dec 20, 2018 7:50 am

Post by mith »

This probably plays out mostly like Nightless if Mafia isn't forced to kill. If there is only one Mafia, it is probably better to take your chances with Nightless than give town info (until it gets to 1:2 night, maybe; not killing gives EV 2/3, attempting to kill gives an immediate win half the time so if Mafia can win better than 1/3 where the kill fails they are better off here - there might be some crazy Nash equilibrium here between killing and not killing). At 2:4, Mafia would rather town lynch down to 2:3 and have pretty good chances at killing there to win.

If Mafia are required to shoot, and town proposes a blocking strategy ahead of time, Mafia can almost certainly arrange their own blocks to make sure the killer is blocked (for example, in the ABD -> C, CEF -> D case, if AE are scum, A blocks E who shoots or vice versa. If AC are scum, C shoots. Etc.) So if town want to gain any information, it would have to be through random or mostly random blocks.
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Post Post #3 (ISO) » Thu Dec 20, 2018 7:27 pm

Post by BBmolla »

Yeah this kind of faces the problems the original mayo clinic had.
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Post Post #4 (ISO) » Fri Dec 21, 2018 5:05 am

Post by callforjudgement »

This is going to depend on the details of action resolution; "mutual and circular roleblocks fail" is ambiguous. For example, can scum ensure that their kill goes through simply by blocking each other?
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Post Post #5 (ISO) » Fri Dec 21, 2018 5:40 am

Post by mith »

Yeah, that's also true. My assumption would be that roleblockers not in loops would be resolved first, which is a bit of a headache to mod but better than the alternative.

For example:

M1 blocks T1, M1 kills T2, M2 blocks T2, T1 blocks M2, T2 blocks M1, T3 blocks M2
In this case, there is a loop of M1 -> T1 -> M2 -> T2 -> M1; however, T3 breaks the loop by blocking M2, which means T2 is not blocked and blocks M1 (and T1 is not blocked and blocks M2 again), and the kill fails.
If the loop is M1 -> T1 -> M2 -> T2 -> T4 -> M1, T3 prevents M2 blocking T2, so T2 blocks T4, M1 blocks T1. M2 is still blocked, but the kill goes through because M1 isn't.
If the loop is M1 <-> M2, then if T1 blocks M1, M2 is unblocked and can kill, but if T1 blocks M2, M2 can't kill (assuming other blocks don't affect this, obv).
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Post Post #6 (ISO) » Fri Dec 21, 2018 5:51 am

Post by mith »

In post 2, mith wrote:If Mafia are required to shoot, and town proposes a blocking strategy ahead of time, Mafia can almost certainly arrange their own blocks to make sure the killer is blocked (for example, in the ABD -> C, CEF -> D case, if AE are scum, A blocks E who shoots or vice versa. If AC are scum, C shoots. Etc.) So if town want to gain any information, it would have to be through random or mostly random blocks.
It's worth noting that this is only true if both scum are alive. If A, say, is the only scum, then the kill will go through, confirming C and D. If the kill fails, C or D is scum and town wins. (I don't see a way yet to force a win from this position, but the strategy Awoo posted gets very close.)
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