Just like the simulations

[MURDERCAT]

Lol

[Jake The Wolfie]

Yeah I just did. 48%

What are some sample games? What assumptions were made?

[MURDERCAT]

I am joking that would be way too hard

[Jake The Wolfie]

So the assumption was that we'd believe you if you lied?

How insidious. You sir, are a heinously evil and wicked man. Shame on you!

[Gamma Emerald]

Can you balance a randomly generated great idea game

[MURDERCAT]

Yeah that I could do

[Gamma Emerald]

(I won’t do this but you could technically do every conceivable setup in a row and find an EV for the entire setup)

[MURDERCAT]

Yes but I'd have to code all of it

[Gamma Emerald]

Yeah that’s why I’m not gonna make you do that

[Awoo]

I tried coding this one as an exercize in haskell, but then I remembered that haskell is completely unreasonable to use when you need to work with numbers, and I resolved to never touch haskell again.

Circus Dictatorship

13 Players

2 Mafia Goons

2 Clown Lovers

1 Town Loyal Doctor
8 Vanilla Townies

• Clowns do not have a nightkill, instead they have a factional loyal protect or a factional killblock.
  
• If the Clowns survive till Day 4, they win.
  
• If the Mafia are eliminated before Day 4, Town wins and Clowns lose.
  
• Traditional win conditions apply on the death of a Clown. (Town wins when Mafia are eliminated, Mafia wins when number is equal to town)

I SWEAR I posted this yesterday but apparently not

Please help me balance it, I had Day 3 originally but thought it might be too hard?

[Awoo]

That being said, the pattern matching in haskell is SUPER nice for coding setups, you literally just write out one endgame per line and everything Just Works (TM). Shame about the fromIntegral nonsense.

[MURDERCAT]

I played around with haskell a bit but was never any good at it. I usually use python or R depending on exactly what the simulation involves.

This looks like what Gypyx submitted to this month's setup challenge

[Jake The Wolfie]

Could you simulate this game?

[MURDERCAT]

I will have to think about how to do this one, as it's not clear when the game "ends." There's also a ton of abilities, so I'm not sure if random usage of them will really capture the setup well. But I can give it a shot this weekend.

[Awoo]

Well, typically I use python too, but I use it to calculate the expected value to an exact number, not by approximation. Which can be done very easily using recursive DP + memoization for simple setups without a ton of roles. Every new role or faction adds an extra dimension of complexity to the space you need to enumerate over.

[Gypyx]

This looks like what Gypyx submitted to this month's setup challenge

well that's because it's the setup i got my inspiration from x)

also cool thread while i'm at it

[Infinity 324]

Wondering about the limit of the EV of X:2 mountainous as x approaches infinity. Like what's the EV of 35:2 mountainous for example?

[Gypyx]

Well, if x literally approaches infinity there is no EV i think

But good question for 35:2

[MURDERCAT]

This is a fun one, I will make a plot. 31-2 is only ~60% town win according to the EV project, which is surprising at first but also makes sense. 98-2 mountainous viable?

[MURDERCAT]

The numbers may be hard to see depending on your theme, if so you may need to download the figure. The x axis is the number of town players and the y axis is town win %

[Infinity 324]

Wow that's interesting, looks like it does approach infinity but very slowly. Looks like it doesn't get up to 90% winrate until 700:2 lol

[MURDERCAT]

I'm sure there is some smart person like implosion or Ircher who knows or could figure out the exact formula. This is the relationship you'd expect though because at very high numbers of townies adding a single townie doesn't really do much to change the odds of hitting scum. Compared to lower numbers where obviously there is a big difference between 7:2 and 9:2.

[Awoo]

This is already a solved problem. Town winrate always goes to infinity in mountainous as number of townies approaches infinity. There is no known closed form solution, only a recursive function. In order to balance mountainous, the number of townies is bounded quadratically in proportion to the number of mafia.

The approximation I found is: T ~= 4.08766637 S^2 + 1.318112 S - 0.9068
Then round T to the nearest integer such that T + S is odd.

viewtopic.php?f=115&t=75528
viewtopic.php?p=8088743#p8088743
viewtopic.php?p=10027427#p10027427

Somewhere on Google scholar, someone mathematically proved a more interesting result that holds for things like nightess, double day, etc, but I can't find it right now.

[Awoo]

Here it is. This one asymptotically solves all setups that are like double day / double night / 3 days and two nights / etc...

https://arxiv.org/pdf/0804.0071.pdf

by proving this conjecture from a previous paper:



It's worth noting that these papers have one dumb assumption that does not affect asymptotic behavior: namely that EV(1 town, 1 mafia) = 0.5, because "when there is a tie in votes you kill randomly" (mathematicians seem to want to skirt around the concept of NLing because they need the game to terminate). And for some examples that we all know and love that are known to satisfy that equality are mountainous (d/r = 1/2 -> mafia proportional to square root of town), nightless: (d/r = 1/1 -> mafia is linear to town, see nightless expectation rule), double day: (d/r = 2/3 -> .. etc... )

[MURDERCAT]

I love that there is a literature on this