pyxxy wrote: ↑Sat Jan 14, 2023 3:56 pm
Seanzie wrote: ↑Sat Jan 14, 2023 3:32 pm
DrWilgy wrote: ↑Sat Jan 14, 2023 3:31 pm
Seanzie wrote: ↑Sat Jan 14, 2023 3:02 pm
DrWilgy wrote: ↑Sat Jan 14, 2023 2:19 pm
Aye, I think it's weird that Sean knew to dig but didn't know that votes were locked.
Like, how much of a slip is it to try to swing for the early power roles?
Yeah, don't really have an explanation. I even remembered all the other things mentioned in the bolded "Important:" thing, but was not aware votes were locked. Clearly I am a great reader
Why would trying to get a power role be a slip?
It's the eagerness.
Scum starts with more data than town SoD1. Figured it may be better for wolves to leverage it while it's available.
Digging early maximizes the chance of getting a power role for either alignment, so the eagerness is NAI.
Why does it maximize the chance?
tldr: since I didn't dig the hole I knew was empty, the remaining 35 holes are a little more likely to be empty than the 35 I choose from.
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I didn't completely work out the math, so it is possible I am overlooking something, but my intuition strongly suggests that digging first maximizes the chance. To explain, consider a simpler situation with three holes, one PR and just two people, both of whom are VT, VT1 and VT2.
VT1 digs first, and won't select the hole they know is empty, so has a 1/2 chance of getting the PR.
Now let's look at VT2. WIth probability 1/2 VT1 hit VT2's empty spot, so VT2 randomly chooses from the other two spots and VT2 has probability 1/2 of getting the PR, so this situation contributes 1/4 probability of VT2 getting a PR. The second situation to consider is that with probability 1/2 VT1 misses VT2's empty spot. In this case, VT1 must have gotten the PR, so VT2 has 0 chance of getting the PR.
Thus, with 3 holes, 2 VTs and 1 PR, the one who digs first has probability 1/2, while the other has probability 1/4 of getting the PR. Twice as likely.
With more holes, the differences in probabilities are significantly less than this, and it is worth noting that digging first also maximizes the probability of getting lizardead. Also, I didn't think too hard about how the people with extra powers or the mafia knowledge affects things, but I think it is still likely that digging first maximizes the chances of getting a PR.
This is a little like a backwards version of the goat and car probability puzzle (being someone who studies probability theory, you'd think I'd know the name of this super famous puzzle off the top of my head...).
