[SETUP] Bonnie, Clyde, and the Other Guy

[mith]

3 Mafia
7 Town

Pre-game, the Mafia pair all the players as Lovers so that one pair contains 2 Mafia. The goal of the town is to lynch this pair.

The 2 Mafia pair does not have a nightkill. If the 1 Mafia pair survives Day 1, this Mafia kills their lover and flees town; if the 1 Mafia pair is lynched Day 1, the game proceeds as nightless.

EV is exactly 1/2. (1/5 * 1 + 1/5 * 1/2 + 3/5 * 1/3)

Updated version: If the lone Mafia is lynched, their lover gets to guess the Mafia pair, secretly - if correct, town wins, otherwise game proceeds as Nightless. If the lone Mafia's lover is lynched, the lone Mafia gets a nightkill before fleeing/dying.

EV is now 119/240 (1/5 * 1 + 1/10 * 5/8 + 7/10 * 1/3)

[mith]

Mafia can make it difficult for town to lynch successfully day 1, but risk giving them a lot of information going into day 2. "D2 Lylo" sounds rough out of context, but an EV of 1/3 in the worst case isn't that bad. I would actually expect this to be a little townsided, honestly.

Quick and swingy, but it's basically a 5 player game in disguise. (1 Mafia, 1 Traitor, 3 Town with Traitor fleeing if not killed day 1 is equivalent, EV-wise, though the lover version gives more potential for information due to third Mafia.)

[mith]

Disagree; Mafia can make it difficult for town to lynch successfully day 1, but risk giving them a lot of information going into day 2.

Mafias best play is to pair their weakest scum with the strongest town and just out as scum and lalalalalalala spam the thread. No associations will realistically be made with that slot. Scum get to hard defend each other due to mechanical reasons so there won't really be associatives there. It's difficult to tell scum apart from town in this game and with the strongest townie absolutely only impacting 1 lynch and scum having complete control over who gets paired with who, they should realistically win nearly all the time unless two scum players are completely unable to play scum.

If the lone scum outs and town lynches that pair, the 2 Town pairs effectively become Mason Lovers to each other. The two scum players have no advantage whatsoever in this case - it reduces to a 1:3 Nightless Hydra game, really.

[mith]

It's a huge deal

Say that a lobby contains NSG Creature and Sakura Hana followed by a bunch of weaker players. Most games, that's enough to win. But in this one, NSG gets paired with the weaker scum to silence her and Creature and Sakura Hana get paired together so neither can independently townspew their slot. Scum choosing the pairings doesn't show up on EV but it massively changes the game if you have meta on the players.

If the lone scum outs and town lynches that pair, the 2 Town pairs effectively become Mason Lovers to each other. The two scum players have no advantage whatsoever in this case - it reduces to a 1:3 Nightless Hydra game, really.

They're going to become Mason lovers to each other D2 anyway and the difference here is that scum are choosing exactly who is hydrad with who.

You're going to have to use people I know to make a compelling meta argument...

There is actually no reason for town to lynch a scum claim. If they ignore that slot, the game reduces to 2:6 Lovers Nightless immediately

with the now confirmed town player still alive to steer the discussion

on day 1. The claimed scum can be ignored and will exit the game regardless. Quite the opposite of silencing a strong player - arguably scum would be better off pairing scum with the weakest town player.

(Your argument also assumes that two of the three strongest players in the game are scum, which would happen only 17.5% of the time, and that there is a significant gap between the top three and the bottom seven in the first place. Strong players tend to win more than weak players, whatever alignment.)

The EV is what the EV is. If there is a strong scum strategy, it can be met with a town strategy.

[mith]

So, there are two different things here:

1. Can scum assure themselves a higher win percentage by having the weakest scum paired with town and claim immediately? My contention is that, on average, no, not substantially. (65% is completely absurd.)
2. Does scum lose anything by claiming immediately? No, and that's an actual problem.

The latter can be fixed though by having a single player lynched and a different outcome for lynching the lone scum player vs. lynching that player's lover. I'll have to play around with this. A quick attempt:

If the Mafia pair is lynched, town wins (1/5, EV 1)
If the lone Mafia is lynched, their lover gets to (secretly) guess the scum pair; town win if successful, otherwise game proceeds without nightkill (1/10, EV is 1/4 + 3/4*1/2 = 5/8)
If the town paired with scum is lynched, lone scum gets a nightkill before fleeing/dying. (1/10, EV 1/3)
If any other town is lynched, lone scum must kill lover and flee (3/5, EV 1/3)

EV = 1/5 + 1/16 + 1/30 + 1/5 = 119/240 (49.58%)

[mith]

RC: Well, you're wrong, but ok.

65%

might

be reasonable if the two strongest players left at 2:6 are the scum pair... if you ignore how town would view the two clearly strongest players (in your example) being paired. For the sake of argument, let's say that happens 20% of the time, and the other 80% of the time the EV is just 1/2 as expected. That gets us to an overall EV of 53% for scum (47% for town). That ignores that town may do better if scum are weaker players, of course. Or that town may be able to get some small bit of information out of how the players are paired.

There just isn't evidence that even the strongest players would do significantly better as scum in such a small, low info game (effectively 1:3 Nightless with no prior game to base decisions on). The onus would be on you to demonstrate that advantage (and that such an advantage is purely or mostly scumsided).

[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.

[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?

[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.)

[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).

[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.