Mafiascum.net

Will do, but no promises that it will be anything useful. As I said, EV for Multiball (and finding the correct strategies along the way) is already tricky, and the Doctors (in particular) may make it intractable even for a 2:2:5. Even just having them as powerless Named Townies introduces a slew of potentially nasty game theoretic equilibria to sort out. They may all turn out to be not at all nasty, but determining that will take some effort.

That said, I think it's a worthwhile extension of Multiball - basically making it "Neighborhood" Multiball, where the distributions of each group of claims is known. Say 2:2:5 splits into 1:1:3 and 1:1:2. And then you have to figure out which group town should lynch from (it's not obvious to me yet that it's the 1:1:2 group, even though that has a higher chance of success), and which group the scum groups try to nightkill into. The Doctors and Strongmen add something extra, but first you have to figure out the "Vanilla" part of the problem.

In post 25, mith wrote:Will do, but no promises that it will be anything useful. As I said, EV for Multiball (and finding the correct strategies along the way) is already tricky, and the Doctors (in particular) may make it intractable even for a 2:2:5. Even just having them as powerless Named Townies introduces a slew of potentially nasty game theoretic equilibria to sort out. They may all turn out to be not at all nasty, but determining that will take some effort.

That said, I think it's a worthwhile extension of Multiball - basically making it "Neighborhood" Multiball, where the distributions of each group of claims is known. Say 2:2:5 splits into 1:1:3 and 1:1:2. And then you have to figure out which group town should lynch from (it's not obvious to me yet that it's the 1:1:2 group, even though that has a higher chance of success), and which group the scum groups try to nightkill into. The Doctors and Strongmen add something extra, but first you have to figure out the "Vanilla" part of the problem.

If I wanted to attempt to tackle this problem of proofing an EV for the vanilla equivalent, what would I have to know beforehand?

I should really just write a guide to calculating EV and finding optimal strategies. There's a lot of good stuff to be said there.

As for your specific question, the main thing is that it is a lot of tedious work (if the setup is at all complicated), mostly in establishing what the best strategy is in LyLo or near-LyLo situations. Towns (and sometimes Mafia) often have non-obvious ways to increase their EV, and significant changes in small setup EVs carry over to the larger setups.

Other than that, it's all logic and math. If you want to generalize to an arbitrary size, the idea is to set up a recursive relationship to smaller setups (simple example: 2:5 Vanilla can either reduce to 2:3 or 1:4 after a lynch and nightkill, depending on whether you lynch Mafia or Town; to calculate the EV of 2:5, you need to know the EV of 2:3 and 1:4, along with the probabilities of reach both states, and similarly you need the EV of 1:2 to calculate those). In some setups, you can find a pattern and go back and prove the pattern holds via induction (see the Vanilla Variants thread for examples - that complicated mess in the most recent post is just the result of me putting things into a spreadsheet until I found the pattern). Some setups don't have nice non-recursive EV formulas (Vanilla doesn't), but some do (Nightless is (T-M)/(T+M)), and once you know what the answer is it's pretty easy to prove it.

The other thing to remember is that small changes can lead to huge complications. You want to approach EV in an incremental way, understanding the simplest setups first before you add even a minor role ability.

In post 27, mith wrote:I should really just write a guide to calculating EV and finding optimal strategies. There's a lot of good stuff to be said there.

As for your specific question, the main thing is that it is a lot of tedious work (if the setup is at all complicated), mostly in establishing what the best strategy is in LyLo or near-LyLo situations. Towns (and sometimes Mafia) often have non-obvious ways to increase their EV, and significant changes in small setup EVs carry over to the larger setups.

Other than that, it's all logic and math. If you want to generalize to an arbitrary size, the idea is to set up a recursive relationship to smaller setups (simple example: 2:5 Vanilla can either reduce to 2:3 or 1:4 after a lynch and nightkill, depending on whether you lynch Mafia or Town; to calculate the EV of 2:5, you need to know the EV of 2:3 and 1:4, along with the probabilities of reach both states, and similarly you need the EV of 1:2 to calculate those). In some setups, you can find a pattern and go back and prove the pattern holds via induction (see the Vanilla Variants thread for examples - that complicated mess in the most recent post is just the result of me putting things into a spreadsheet until I found the pattern). Some setups don't have nice non-recursive EV formulas (Vanilla doesn't), but some do (Nightless is (T-M)/(T+M)), and once you know what the answer is it's pretty easy to prove it.

The other thing to remember is that small changes can lead to huge complications. You want to approach EV in an incremental way, understanding the simplest setups first before you add even a minor role ability.

Thanks for explaining that.

I know you said that regarding the particular setup that we are dealing with in this thread that there may not really be "useful" information for me. However, and I hope I am not stepping out of bounds here, but I think if you DID provide a method to calculate the EV of any particular (vanilla?) setup, that this would become part of the knowledge base that would be incorporated for people to consider which would have a kind of follow through for the question "what is a proper setup?" I think it could have an effect on play as well, however small that may be.

Was going to add this to the above post, but got quote sniped:

Investigative roles are a nightmare even at small counts, because of the addition of claiming strategies and fake claiming and so on. Killing roles are slightly better (counter claims aren't as effective if the real role can just kill the claimer). You can simplify these roles by making them non-counterable, though - that is, a Cop that can choose to claim at any time, and is then confirmed to be the Cop by the Mod.

And yes, having a baseline for EV is useful, that's why I started the Vanilla Variants thread and try to expand on it whenever I get in the mood.

In post 29, mith wrote:Was going to add this to the above post, but got quote sniped:

Investigative roles are a nightmare even at small counts, because of the addition of claiming strategies and fake claiming and so on. Killing roles are slightly better (counter claims aren't as effective if the real role can just kill the claimer). You can simplify these roles by making them non-counterable, though - that is, a Cop that can choose to claim at any time, and is then confirmed to be the Cop by the Mod.

And yes, having a baseline for EV is useful, that's why I started the Vanilla Variants thread and try to expand on it whenever I get in the mood.

I see. I am going to try and take another look at the EV threads to try and figure out what is going on there.

Game didn't run because no one wanted to play it which gives me the sads.