Mafia has a nightkill. Town has a lynch. Town no-lynches at even numbers to maximize EV. Given S scum, how many townies should you add to the game to get a winrate as close to 50% as possible?
Well I wrote a simple program and then I made the data:
And here is the graph of the number of town you add for the number of mafia:
And the graph of the winrate is very interesting but hard to display because it gets really small, but the pattern alternates between spiking up and down and a curve every 5-10 data points, as it slowly converges to 0.5. The spikes and curves lose magnitude for each repetition. Very cool.
When I find a line of best fit for the data,
r = 0.999999984
T = 4.08766637 S^2 + 1.318112 S - 0.9068
Then round T to the nearest integer such that T + S is odd.
So next time you and your friends want to play a nice simple easy to understand 5-mafia game, just get your closest 107 friends and PLAY!!!!
you could reduce any game of mafia to a series of integers (VTs, VTs with inno checks from cop1, mafia with guilty checks from cop1, ......) but what a pain dude
It's usually (always?) the most powerful single basic town role as far as EV is concerned, of course. But it doesn't take much town power to make the balance much more reasonable.
This completely depends on your assumptions about lynch accuracy btw. You get some weird shit if you're assuming random lynching all the way through; long-term (i.e. in a game where there's a bunch of day phases), town's lynch accuracy SHOULD be > rand. Just on an easy model, I'm pretty sure that town wins well over 33% of 2v1 LYLO's, for instance.
How far above =rand town is able to lynch, btw, is pretty vital when it comes to figuring out site norms for setup balancing (the shorthand of "find a stack of setups with ballpark 50% win rates; find setups with < 50% town win rates and adjust to help town; find setups with > 50% win rates and adjust to help wolves" gets you there too).
Simple example?
Take a 14/3 mountainous setup, mandatory lynching, mandatory kills (not the only way to model it but it's simpler). Town wins on three correct lynches, wolves win on six mislynches. With no other power roles around, you can reasonably guesstimate that it's in the ballpark of balanced for MS site meta.
So what assumptions would make it balanced? Basically, random lynching but where wolf lynches are relatively likelier than town lynches. In particular, you assume that each wolf is 60% likelier to be lynched than each villager each day phase (which is too high early game, and too low late game). So you get:
Day 1: 74% mislynch odds (which is probably a touch too low, but probably not WAY too low)
2/1 LYLO: 56% mislynch odds (and I'd say this is probably too high; once you get two wolf lynches, town probably has enough information to create a POE that isn't complete garbage, and should be well above 33% lynch accuracy)
3/2 LYLO: 71% mislynch odds (I'd say this is probably also too high)
4/3 LYLO: 79% mislynch odds (in fairness, a town that has been that crap is probably gonna lose so that probably isn't wildly unreasonable)
5/2: 61% mislynch odds (probably reaosnable?)
8/1: 83% mislynch odds (probably too high since 2 mislynches and 2 wolf lynches suggests a town doing well enough to probably close it out before long)
etc
Like, I'm not sure that the calculation I've done and the assumption of each wolf being 1.6 times as likely as each villager to be lynched each day phase is exactly right, but it doesn't strike me as broadly unreasonable given site meta.
http://wiki.mafiascum.net/index.php?title=Mhsmith0
Conq: you, sir, are great at being town.
BATMAN: Only jugg was the only one we didn’t scum read at least not me
Quick: There is little to no chance this slot is Power-Wolfing.
SR: I want to give him a day
Life is simply unfair, don't you think?
The EV we generally calculate in this forum is based on random lynches and nightkills (at least in simple Vanilla Variant setups; with roles, there are Nash equilibria and the like to calcluate). The reason for making this assumption is that it corresponds to the EV of an optimally played game
by both sides
. (The short version of the argument: Town's optimal play can be no worse than random lynching; if it were they would just lynch randomly to improve their EV. Mafia playing optimally can also do no worse than the lynches being random - at worst, their optimal play would be "play exactly like you don't know you're Mafia". QED)
In real life, we typically assume that town does better than random; this appears to be generally true (though there is limited data to actually back this up, since most games run on this site are not Vanilla Variant setups and thus have EV that are more difficult to calculate, if not intractable), except in the case of Vanilla games themselves. One reason for this, I suspect, is that in the absence of power roles to hunt for, Mafia can fall back on picking off stronger players, making the later stages of the game closer to random, and worse if Mafia are able to exercise their voting bloc during the day without too much punishment in the form of scumhunting. (This is only true for forum games - face-to-face games tend toward more scum slip-ups and easier scumhunting through reading people's body language and such.)
That said, I think the approach of adding a new parameter for "increased likelihood of scum lynch" is interesting... and I also suspect you didn't pull that 1.6 number out of nowhere, since it corresponds almost exactly to a balanced EV for 3:14 Vanilla (49.94%), though some of the individual mislynch percentages in your post are wrong.
Perhaps a better model would be to assign an additional likelihood for the team as a whole to have a member lynched, to mimic the effects of adding information as buddies are listed (that is, if the team as a whole has an (M+1)/(T+M+1) chance of someone on the team getting lynched, when the game starts it's not all that increased for any given member because it's spread out, but as you lynch buddies the last scum standing is much more likely to go down, since they are the whole team at that point). This particular model with parameter 1 has the nice property of 1:2 lylo being a 50-50 split, and 3:14 is again close to balanced (50.79% this time), as is 2:7.
Whether either model matches the data we would get over a large number of games under a given site meta... difficult to say without the data.
Fwiw I’d actually goalseeked what would reach balance at 14/3, and iirc it was like 1.602. Possibly I misread my tables in xl tho, I have file at work so I can’t quickly check.
I do think, though, that optimal play as scum is HARDER to achieve to bring down the lynch accuracy rates compared to optimal town play for increasing it. How much so is hard to measure, of course, but that’s part of the fun
http://wiki.mafiascum.net/index.php?title=Mhsmith0
Conq: you, sir, are great at being town.
BATMAN: Only jugg was the only one we didn’t scum read at least not me
Quick: There is little to no chance this slot is Power-Wolfing.
SR: I want to give him a day
Life is simply unfair, don't you think?
Yeah, you're remembered and reading correctly. I think it's a little dangerous to pick a setup, assume it's balanced, and then generate an increased lynch probability for scum based on that - but in the absence of sufficient data to compare to, it's hard to argue with.
Optimal scum/town play is impossible. I do agree though that "good" scum play is harder than "good" town play, up to a point. Good scum play tends to be more powerful though, in my experience.
(And FWIW, I think town's bad results in Vanilla may be tied heavily to Vanilla being run almost exclusively - at least on MS and predecessors - with 2 scum. With 3 scum, I would guess they would swing the other direction, though not as far as making 3:14 balanced; a 27.79% EV is a lot to overcome.)
I think that in a world where you're just looking at mountainous (i.e. PR's and PR influence are irrelevant) it's probably reasonable to use something that looks balanced-ish as a baseline, calculate out what the lynch probabilities would need to be presuming it's balanced, and then look back at resulting odds amounts (such as what I calc'd for various LYLO and early/mid game states) and see if it's broadly reasonable.
I think I'd also disagree with you about the relative merits of good/bad scum/town play. Good town play tends to be EXTREMELY powerful; a few good townies finding each other and creating a strong set of mutual town-read and back and forth engagement on solving other slots is utterly brutal for wolves to deal with. The reason you don't see it that often is that most townies are bad/dumb/lazy/etc, and so it's fairly rare to see a stacked town steamroll a game.
Like, I can think of two games in particular which were absolute roflstomps by town in setups that would be considered highly wolfsided around here:
1) Rio
Town: 3-shot doctor, 2-shot odd night tracker, 2-shot even night watcher, 7 vt's
Scum: roleblocker, 1-shot strongman, 1-shot ninja
Town mislynched day 1, lynched wolves the next three days, and the only PR help was the last wolf getting tracked on n3.
2) MU staff game
Town: cop with no n0 check (n0 checks are common by cops), 2-shot doctor, 1-shot vig, 16 vt’s
Scum: godfather, goon, goon, godfather sympathizer (didn’t know wolf team, endgamed when his teammates died)… and scum got DOUBLE factional kills while at least two of the main pack was alive.
Town lynched the godfather d1 (hilariously, the two counterwagons were the doc and cop, both of whom claimed PR late d1, neither of whom were shot n1, as the wolves shot for strong players instead), sympathizer d2, goon d3, and d4 the last goon conceded (she was a plausible wagon that day, and we basically told her she was gonna get policy vigged that night if we mislynched [we didn’t know vig was just one shot lol] ). The vig shot a vt n1, otherwise was a perfect stomp.
Admittedly in neither game were wolves really playing well, but at the same token they weren’t really playing BADLY (particularly in staff game), it was much much more that the town just did a really good job finding each other, establishing overall thread control, creating a solid POE, and figuring out decent lynches outside the POE (the only meaningful wagons on town during the game were on the cop/doc d1, and the vt who got vigged d2 [and the three d2 wagons were sympathizer/goon/vt] ). I’ll note, in case this reads as an ego thing, that in neither case was I close to the best townie in the game (though I was decently above the WORST townies in both games). But yeah, good townies can find each other, make good reads, power through the game state, and make major impacts even if they die early (like most good townies do).
Effective wolfing is strong too… but well playing towns will defeat well playing scum teams much more often than not. Games are won or lost more by the town than by the wolves; some wolf wins can be traced to good wolf plays, but most are mainly due to town play that ranges from poor to outrageously awful.
http://wiki.mafiascum.net/index.php?title=Mhsmith0
Conq: you, sir, are great at being town.
BATMAN: Only jugg was the only one we didn’t scum read at least not me
Quick: There is little to no chance this slot is Power-Wolfing.
SR: I want to give him a day
Life is simply unfair, don't you think?
I mean, there are a lot of lynch probabilities in your model that might be considered "broadly reasonable". The question is whether it is broadly reasonable on its own merits, or whether it's being considered reasonable because you have already assumed the setup is balanced. "Exactly as likely as town" and "Twice as likely as town" are both "reasonable" depending on how you view the good town vs. good scum question, but cover a big range of EVs for a particular player count (27.79% up to 61.37% for the 3:14 setup, for instance).
As for the rest, we'll probably have to agree to disagree at some point. For every argument on one side ("good town with mutual town reads = bad news for scum") there is a trivial counter ("good scum who are read as town = bad news for town"). (And you kinda blow up your own argument by admitting that most townies are bad/dumb/lazy/etc. - in which case, why would the assumption be that they get lynches right considerably more often than random?) Cherry-picked examples of easy town wins in scumsided (for the sake of argument) games don't tell us much about the overall model - town steamroll in some games and get steamrolled in others, EV takes into account the whole range of possibilities.
Ultimately, your argument hinges on "it would be reasonable for town to do this well, and this is my experience with town doing this well, and if town isn't doing this well it's because town is playing poorly"... to which I would say, in my experience with Vanilla games specifically: "it's reasonable for scum to do this well, and my experience is scum doing this well, and if scum aren't doing this well it's because scum are playing poorly".
In post 10, mhsmith0 wrote:Effective wolfing is strong too… but well playing towns will defeat well playing scum teams much more often than not. Games are won or lost more by the town than by the wolves; some wolf wins can be traced to good wolf plays, but most are mainly due to town play that ranges from poor to outrageously awful.
Disagree quite a bit with this on principal.
A single scum player playing well enough can win the game singlehandedly. If a town has a PoE pool that includes all of the scum and very few town, then yes, that's a sign that the town has played well... but it is also a sign that the scum have played poorly. Against a town that relies heavily on PoE, it isn't good scum play to fly somewhat under the radar and be middling for the entire game. It's good scum play to actively play up to your town meta, and get PoE'd out as a possible suspect. And if no scum manage to do that... they're playing poorly. "good play" and "bad play" in a social deception game is all comparative to how the other side is playing. There is no objective "good play." Even with optimal play as mith described it you can in practice do better by exploiting mistakes from the other side.
Good scum play is also EXTREMELY powerful; it's possible (and in a mountainous setup, straightforward modulo nightkill analysis worries) for a single good scum player to win the game singlehandedly. The reason you don't see *it* often is (speculatively) because it takes a lot of hard work that fewer players are willing to put in as scum than are willing to put in as town.
play as mith described it you can in practice do better by exploiting mistakes from the other side.
I think maybe you don't understand what that word means.
Otherwise, I agree. The best that can be said about play in a game is how the team performed relative to the other side and its EV. (You can perhaps make finer distinctions for how the game was won - that is, a clean scum victory would be more impressive than a scum victory where one was lynched - but even that is questionable; it may be that for a particular game, scum were better off bussing a buddy to make their win more certain, rather than going for the clean win and introducing a greater chance of giving the whole team away.)
In terms of balancing EVs against actual results, I still believe that 2:9 vanilla is more townsided than 2:11 vanilla in practical games. (The issue is that in 2:11, the extra mislynch hardly helps town because they have a small target to aim at, but the extra nightkill is very useful to scum as they can get rid of a strong townie before the game gets small enough for scum to be easy to find.) In fact, doesn't 2:7 (which was a Newbie queue variant for a short time) actually have a fairly noticeable town win percentage in practice? (Much less than 50%, but high enough that the setup clearly isn't unwinnable.)
2:7 was never a Newbie variant on its own, as far as I'm aware - but it was one of the possible setups in F11 (with the slight difference that Mafia had a useless Roleblocker and had to account for the possibility that there was a Cop and Doc in the setup). According to Newbie Data, town won ~32%, which is better than EV (but close enough that it's not statistically significant).
I meant subsetup, rather than variant. Sorry if I was being ambiguous.
You're right that scum wouldn't immediately know that the setup was vanilla, but it's hard to play around a Cop. Perhaps the setup favours town slightly due to scum needing to play around a potential Doctor (which may imply killing less attractive kill targets).
I suspect the bigger impact would be in scum trying to protect the Roleblocker D1 (which is huge in the Cop-Doc setup). Hard to say from the data though, and in fact towns in those setups lynched the Roleblocker 12 times and the Goon only twice. (And a 10/3 split in the Cop-Doc setup, as well. That's probably the weirdest stat in that data set, the probability of 22 Roleblockers out of 27 scum lynches is less than a tenth of a percent if Roleblocker and Goon were equally likely.)
