[SETUP] Bonnie, Clyde, and the Other Guy

[mith]

This game fits the rules for the monthly challenge if you didn't notice mith.

Maybe you like the one currently on file there better though

I like the one I posted better. This was really just a single-cycle distillation of the idea, with actual flips.

[RadiantCowbells]

I think you're misunderstanding
Scum get to pick 2/3 of the scum pool as their 'players' so they are

on average

better.
That does not mean that they are by default the 2 best players in the game.

If you draft 3 people and pick the best 2 you're going to get players than if you just draft an arbitrary 2 of those 2/3 of the time
I think the sheer spread of scum winrates speaks for itself in terms of the fact that 2 stronger scum players are going to do better than 2 weaker ones?

Rather than looking at EV I like to judge mafia by exactly what proportion of hypothetical town the mafia need to be townier than.
Most (balanced) setups require scum to be townier than more than half of the townies.

[mith]

I'm not misunderstanding. But it's helpful to talk about simplified situations. I don't even believe that the two strongest players being scum would lead to a 65% EV necessarily (small, low info games tend to be more random than large, high info games); you're suggesting that scum

on average

would win 65%. The disconnect here seems to be the leap from "better scum winrate players will do better than 2 weaker winrate players, and the two scum left will be better on average than in a randomly generated 2:6 game" to "65% EV on average". It's just not a reasonable leap to make without evidence.

Here's a thought experiment for you, since you like looking at "townier" lists. (Never mind that this setup requires the scum pair to be townier than 2 of the 3 town pairs.)

Let's say there are 10 players, with a known ordering of player strength. We randomly allocate these players to the alignments - there are 120 possible scum teams (10 choose 3). Then we toss out the weakest scum player and the strongest town player. (Never mind that the strongest town player will be able to at least influence the D1 lynch.)

Of the 120 setups, 60 have the two strongest scum both in the top half of the strength rankings. That's a lot! Only 10 setups have both scum in the bottom half - that's not many!

Let's say individual player strength

really

matters in this setup. (It should matter much less, given the low information nature of the game, but who cares.) So let's say if the scum are both in the top half, they win a whopping 6 out of 7 games (~86%). And if the scum are both in the bottom half, they only win 1 out of 7. And in the other 50 cases, it's 50/50.

The overall EV in this hypothetical? 64.88%... Still not 65%, even granting a ridiculous and unsustainable winrate for a pair of top half players in a coin flip setup.

tl;dr; I already changed the setup, why are we even arguing about this anyway?

[RadiantCowbells]

If you assume the following

1) scums and town's towniness are distributed at random
2) scum correctly choose the scum player to exclude
3) scum correctly choose the top 3 towniest players to pair with scum and pair together
4) lynches are determined by average towniness of both relevant players
5) scum on average screw up and pair the two townier of the bottom four players together to create a more formidable opponent (partially counterbalancing the fact that 4 is excessive)

then this setup sims at 64.4%. I think the only point in contention there would be 3. I don't think scum make mistakes there that spectacularly often.
Perhaps I'm imposing my own awareness of the meta on everyone else but I'm rarely surprised by people having breakout town games

How often do you think that scum are going to be wrong on who is not going to be lynchable from the start of the game?

[RadiantCowbells]

And this all ignores the chilling effect that the essentially associationless gameplay is going to have on town players. I would expect people to perform below rand in this setup for that reason.

[RadiantCowbells]

By the way, order to be lynched in 3 way, BOTH townies have to scumread you over the other townie because if one townie scumreads the other over you, you win. Whereas you can hammer whoever you want if one scumreads the other.
That's 1/2*1/2 = 1/4 odds.

I'm keeping all the other voting aspects out of the sim but if I add them back in and plug this into my normal game simulator that skews the odds even further in scum's favor.

[chennisden]

I don't think 64.88 vs 65 percent really disproves RC's pt

[chennisden]

The new setup should be fine

[mith]

The point of the not quite 65% is not that I couldn’t quite get it to 65%. It’s that you need some pretty huge assumptions (6 out of 7 scum wins, even if the scum pair is “clearly” stronger, is just not realistic) to get close.

RC: The much bigger problem is 4. The stronger players don’t win 100% of the time! What your sim shows is that for your particular set of assumptions, the scum team will be strongest or second strongest 64.4% of the time? Which doesn’t guarantee they will win those games, any more than it guarantees they will lose all the games they are weaker. Mafia doesn’t work like that. (Never mind all the other assumptions in this method - that averaging strength is the best measure of team strength is debatable, for example... a very strong player is likely to drag their lover along if they’re bad.)

I have more I could say but I’m on my phone and tired of arguing about this.

The updated setup is flawed in the EV calculation, since town can telegraph their guesses in case the lone Mafia is lyched, bumping that case to 3/4. I can get it to 2/3 easily (for an overall EV of 1/2 again), but I’m not sure I’m satisfied with that idea yet.)

[popsofctown]

The argument seems mayhaps under my head
I feel like the argument the setup wouldn't be that fun to play is more straightforward.
1 Survivor 3 VT has perfect 50% EV balance but i have no desire to play it.
Actually maybe that's analagous to this setup precisely, not sure because i'm not sure how to grok the mixed pair, but I was trying to give a

different

example of I think fun and balance can be different. This setup is definitely novel I just don't think it has the pinatas and the birthday cake.

[mith]

I agree, pops, that’s why I modified it. Scum need incentive to protect the mixed pair (or at least the scum from that pair).

[popsofctown]

Does the town find out who the lover guessed? Because otherwise the lover's guess is going to win the games the town was already going to win, and not win the games the town wasn't going to win, assuming the lover's opinions about the game are similar to the town's. The lover can deliberately make a "stupid" guess and that's some EV but it's less EV than assuming the pair the lover guesses and the pair the town selects as first D2 lynch has a 1/4th chance of being the same, the chance of those two things being the same is much, much higher.
I'd want to see it buffed to an outright flag or like "just guess 2 town pairs and you win"

[popsofctown]

The lover can hypoclaim her guess before the lynch and break the setup for town, actually, can't she? Am I misunderstanding the setup?

[popsofctown]

Oh, no, that doesn't break it for town it just gives her really really good EV because the mafia have to mislynch every pair but the IC pair.
I kind of like that.
But you should make it "publically guesses" because pretending your town won't break your setup with hypoclaims is silly.

[popsofctown]

ICing the very pair that the town was likely to mislynch then requiring the mafia to mislynch every single other pair is like asymptotically close to saying it's black or white flag ( i can't remember what the flag colors mean) and the mafia has lost. So that is plenty of disincentive to bussing

[mith]

Yeah, see the end of post 33. Town can avoid hammering, get everyone to claim which pair they would guess if the lynch is the lone scum, and town gets three full chances, same as if the guess were revealed.

The easiest fix in the case of lone Mafia lynched is that the game goes to 2:6 Lovers Nightless as before but before D2 Mafia must confirm one pair as innocent (2:4:2 Lovers Nightless with IC is of course EV 2/3 for town, resulting in a 50-50 game overall.) Aside from punishing scum for a lone Mafia lynch, this also addresses some of RC’s scum pairing concerns.

[post-preview edit]What you said.