General Mafia theory discussion

[~ Gheb ~]

Town has to outplay the opposing factions in order to win ... OUTRAGEOUS.

 

[Overswarm]

So essentially what you're saying is that mafia is Metaknight?

I knew I was correct in my analogies.

Only in the sense of what you consider the "core". Interpreting Night Actions is part of Mafia just like using projectiles/items is part of the core of Smash.

The most common setups for mafia involve a mafia NKill and a town Protect or Investigate as the "vanilla" game. Adding more roles is an extension of that same process. Smash starts out with items and is most commonly played with them, and even when you remove them they exist in the form of Peach's turnips/saber/bob-omb, and many projectiles act as items as well.

What you meant by core was more what you personally feel is the most important part of the game, not necessarily what is.


But yes, Mafia is Meta Knight in the sense that town's only real hope of winning is mafia messing up.

Town has to outplay the opposing factions in order to win ... OUTRAGEOUS.

No, not outplay. Overcome. There's a stark difference between the two. It's one thing to start a baseball game at 0-0 and then be down 0-3 in the 3rd inning and having to overcome your opponent. That's an earned advantage they have.

Simply getting a role PM that says "mafia" and having the ability to kill and communicate outside of the thread has proven to be more effective than a standard "we have a numbers advantage" that town has. Town has to fight itself and mafia to beat mafia, and mafia generally wins vanilla games.

 

[#HBC | Laundry]

They are if you're looking for a strictly balanced game given a finite set of numbers. If you played a game of 12 players with 3 scum goons and 9 VTs, you'd lose two people every revolution. 12 on D1 to 10 D2, to 8, to 6, to 4 on D5 for Lylo. This gives you 5 chances to kill 3 players, meaning you can only mess up twice unless you get a chain going. Given optimal play by scum, D1 should result in a town lynch nearly 100% of the time. Unless scum messes up there really ISN'T a possibility of town "catching scum". You have no evidence or history, so its just blind luck unless you know the player personally (which can't be something you account for in balance) or the scum member makes a large mistake.

Your only options in scenarios such as that are to either A) add something like a Doctor or B) add more town players. Power Roles just fit better than mathematically finding a middle ground.


Although it would be interesting to have like a 50 man mafia game of nothing but VTs with maybe 6 mafia goons go on for a year.

This. So much this.

 

[#HBC | Mac]

I forget where it was, I think mafiascum, sighted and proven with results that all VT games were resulting in a larger win for scum % wise over town.

Even looking at it I can completely understand why.

Just run the random-lynching numbers.

Guys, the mafia win % has to be higher than the towns win %. If it isn't than town could literally just random lynch the entire game and win more than half the time. Mafia balance 101

a 50/50 split win % is skewed in towns favor (imo)

 

[#HBC | ZoZo]

If it's a 50/50 split then Town can random lynch and win more than 50/50!

 

[#HBC | Mac]

50% of the time -_-

you don't want town to be able to random lynch and win half the time...

 

[vanderzant]

The idea of playing an OS mafia game IRL sounds so exciting to me. It'd be stupid to mod, but a helluva good time!

 

[#HBC | Gorf]

You're a helluva good time.

 

[Overswarm]

50% of the time -_-

you don't want town to be able to random lynch and win half the time...

I don't mean numbers-wise winning 50% of the time. I mean actual win % at the end of the game winning 50% of the time. As in if town and mafia both play a good game town and mafia both win equally.

The idea of playing an OS mafia game IRL sounds so exciting to me. It'd be stupid to mod, but a helluva good time!

I thoguht about how it'd be possible. Determined that the only way to really do it would be to give everyone a piece of paper where they were forced to write down their top scum picks each Night. Scum would instead be writing their Night actions down. Everyone's name on the top of the paper/index card. I take it back up, tally night results, reveal.

 

[#HBC | Mac]

yea os, that wasn't directed towards you

 

[adumbrodeus]

Guys, the mafia win % has to be higher than the towns win %. If it isn't than town could literally just random lynch the entire game and win more than half the time. Mafia balance 101

a 50/50 split win % is skewed in towns favor (imo)

Well, the existence of PRs means that this isn't even a question, random lynches will never produce a 50% winrate in a balanced PR game.

At the same time, I have a substantially better then 50% win rate, and I'm sure that a fair chunk of players in dgames do as well, why would I go for something where I have an average of 50% winrate when I can go for something where I have a substantially higher winrate?

Because of this, and scum's natural advantage, you need to tilt the game beyond 50% town win rate in a game without PRs, otherwise scum will win 90% of the games at least.

Why? Information gap, mafia is naturally less balanced then random numbers suggest because scum has a lot more information then town. That's why a good game leans towards TOWN, not scum.


And yes, I think it's quite possible that mountainous reaches the point where in order to be balanced, town needs to have such a strong average advantage that they're better off just random lynching.

 

[vanderzant]

Adum I think what Mac is saying is that games shouldn't be balanced to the point where Town win 50% of the time by random lynching. Like, if you run a computer simulation in which all lynches/night kills and power roles are randomized, if a game is about 50/50 for either side in reality it is imbalanced in scums favour.

In theory random lynching should result in scum winning most of the time if a game is properly balanced. That's the point of Town having to generate information during the day; to try and overcome the natural scum advantage through scum hunting and what not.

Because of this, and scum's natural advantage, you need to tilt the game beyond 50% town win rate in a game without PRs, otherwise scum will win 90% of the games at least.

No, because if this was true Town should just use a random lynch method and they'd win more than 50% of games on average.

 

[adumbrodeus]

Adum I think what Mac is saying is that games shouldn't be balanced to the point where Town win 50% of the time by random lynching. Like, if you run a computer simulation in which all lynches/night kills and power roles are randomized, if a game is about 50/50 for either side in reality it is imbalanced in scums favour.

In theory random lynching should result in scum winning most of the time if a game is properly balanced. That's the point of Town having to generate information during the day; to try and overcome the natural scum advantage through scum hunting and what not.

The thing is, that just like town can work to overcome it, good scumplay makes it more confusing. Scum can generate information too, information that misleads town, and they have a large advantage in doing so.

Saying that scum should be able to win when they play significantly worse then town is simply not acceptable in a skill-based game, scum should have to outplay town.

So random lynches should not result in town winning the majority of the time, random role use however should. This is because you can't optimize it due to it requiring trust, also it significantly changes the relative power of certain roles, specifically protective roles.


And keep in mind, why would I random lynch for a 50% win if I could play it out for better then 50%?

No, because if this was true Town should just use a random lynch method and they'd win more than 50% of games on average.

And the fact that to be balanced to the point of being reasonable for town to win, mountainous requires town to be significantly ahead in terms of odds of random-lynching, is exactly why mountainous seems to be a poor setup.

 

[vanderzant]

The thing is, that just like town can work to overcome it, good scumplay makes it more confusing. Scum can generate information too, information that misleads town, and they have a large advantage in doing so.

Saying that scum should be able to win when they play significantly worse then town is simply not acceptable in a skill-based game, scum should have to outplay town.

So random lynches should not result in town winning the majority of the time, random role use however should. This is because you can't optimize it due to it requiring trust, also it significantly changes the relative power of certain roles, specifically protective roles.

I'm not sure what you're arguing. Random role use should result in Town winning the majority of the time? How?! A cop or vigilante or doc should NEVER pick their targets randomly. Information should almost always result in Town PR's making better choices. I can see why Scum would NK randomly, but a Town PR acting randomly is basically a complete shot in the dark with a very low chance of success.

Ignoring power roles, the Day phase is Town's ONLY method of generating intelligent information. If scum win around 60% of games through random lynching, then it's in Town's interest to scum hunt and generate information. However if they have a 50% chance of winning, why potentially jeopardize that win ratio and play into scums hands? This is why random lynching should always favour scum, even if only slightly.

Maybe we have different opinions of what is balanced, but something like Vengeful Mafia is what I consider balanced when played in a forum mafia scenario, and if it's played randomly scum win's 60% of the time.

[collapse=Vengeful]Assuming all lynch and vengeance decisions are made randomly, mafia will win 60% of games and town will win 40%.
The mafia's win odds are:
20% chance of godfather lynch D1 * 0% chance of mafia win in this case +
20% chance of second mafia lynch D1 * 75% chance to survive final four * 67% chance to survive final three +
60% chance of townie lynch D1 *
(50% chance of vig kill targeting a townie +
50% chance of vig kill targeting mafia * 67% chance to survive final three)[/collapse]

And keep in mind, why would I random lynch for a 50% win if I could play it out for better then 50%?

In the same way that Mafia can reduce the odds of Town winning by playing smart. You claim earlier that Mafia have a large advantage in being able to generate misinformation. Why should Towns allow that if they already have a decent shot (50/50) at winning?

And the fact that to be balanced to the point of being reasonable for town to win, mountainous requires town to be significantly ahead in terms of odds of random-lynching, is exactly why mountainous seems to be a poor setup.

Could you link to this mountainous set up? I'm not sure what it is.

 

[#HBC | marshy]

http://wiki.mafiascum.net/index.php?title=Mountainous

boring as ****

EDIT unless you quicklynch all daily!

 

[#HBC | Laundry]

I could imagine some pretty funny games if we quicklynched regardless of their play and just lynched for humor effects.

 

[vanderzant]

Geez after that link, I clicked on the CV project thing and I've been crunching numbers for set ups like an hour >.<

 

[adumbrodeus]

I'm not sure what you're arguing. Random role use should result in Town winning the majority of the time? How?! A cop or vigilante or doc should NEVER pick their targets randomly. Information should almost always result in Town PR's making better choices. I can see why Scum would NK randomly, but a Town PR acting randomly is basically a complete shot in the dark with a very low chance of success.

What I'm arguing is that power roles are more about statistical odds of success when added or removed from a game, because they CAN'T be randomly plotted effectively.

Ignoring power roles, the Day phase is Town's ONLY method of generating intelligent information. If scum win around 60% of games through random lynching, then it's in Town's interest to scum hunt and generate information. However if they have a 50% chance of winning, why potentially jeopardize that win ratio and play into scums hands? This is why random lynching should always favour scum, even if only slightly.

Because individual skill overcomes the inherent advantages in the setup. Just because scum have an inherent advantage in the day phase doesn't mean


That and the majority of town PRs (as you stated before) lose the vast majority of their effectiveness when randomly plotted, as stated before.

90% of doc's power is that it forces mafia to pick secondary targets, allowing a stronger endgame for town.


Basically, to get a balanced game, you're looking for intelligent play to result in a 50% average win rate for town and scum in a 2 faction game.

In practice this means giving town a slightly stronger overall setup then scum to account for information advantage.

Maybe we have different opinions of what is balanced, but something like Vengeful Mafia is what I consider balanced when played in a forum mafia scenario, and if it's played randomly scum win's 60% of the time.

[collapse=Vengeful]Assuming all lynch and vengeance decisions are made randomly, mafia will win 60% of games and town will win 40%.
The mafia's win odds are:
20% chance of godfather lynch D1 * 0% chance of mafia win in this case +
20% chance of second mafia lynch D1 * 75% chance to survive final four * 67% chance to survive final three +
60% chance of townie lynch D1 *
(50% chance of vig kill targeting a townie +
50% chance of vig kill targeting mafia * 67% chance to survive final three)[/collapse]

I think that's obvious, and no I would not call this balanced.

In the same way that Mafia can reduce the odds of Town winning by playing smart. You claim earlier that Mafia have a large advantage in being able to generate misinformation. Why should Towns allow that if they already have a decent shot (50/50) at winning?

Again, because skill of the players trumps natural advantages of the faction.

This will, as a side effect, naturally make it so that the people who would be expected to say "no, lets not randomly lynch" are the people who are in the best position to convince people not to randomly lynch because they have the highest winrates.


Of course this is really only relevant in open games where you can get an expected winrate from actions.

 

[Overswarm]

Speaking of accounting for balance, the FF6 experiment of "giving town a ton of legit information" does so much damage.... to town. Totally blew my mind. I had suspected it as a possibility, but similar things happened twice even with FF6's fairly complex design with completely different player groups.

 

[ranmaru]

Interesting. Can you show the repeating patterns overall the diff player groups?

 

[Overswarm]

I could!



but I won't

 

[Overswarm]

So has anyone else read the paper from 2010 that basically says "random lynching is town's best chance to win against mafia, assuming no detective"?

 

[Orboknown]

wut.
would be interested in reading it.

 

[Overswarm]

http://arxiv.org/pdf/1009.1031v2.pdf

It found a mathematical model for balance (50% chance of mafia/town winning with 50 mafia and 10,000 players)

w(n, m) ∝ m/√n is the formula for mafia's winning chance. n & m are nonmafia and mafia.


TL;DR paper = if town has more players than mafia that align with a balanced game, random lynching gives town a > 50% chance to win while under normal circumstances mafia would have a larger chance to win simply by their ability to swing momentum and group votes giving them one "alpha" strike that can flip the game in their favor.

When you incorporate the psychological aspect the best strategy for mafia is to buddy with a townie of sorts to increase mafia's net pull without being obvious, allowing for the alpha strike to come a full phase sooner.

 

[Overswarm]

Also, fun thing:

4 town and 1 mafia member gives mafia a 0.375% chance to win

9 town and 1 mafia member gives mafia a 0.406% chance to win

XD


This doesn't account for the power roles we use though, which actually make the game more focused on lynching scummy people rather than straight up math in an online presence, given that we don't have physical tells.

 

[#HBC | ZoZo]

But wouldn't 9v1 eventually result in 4v1 :v (if mafia is indeed on the path to victory)

 

[Orboknown]

how in the hell...
wait, i think i get that math sort of. the more townspeople, the more people mafia can misconstrue as being scummy and get mislynches through.

 

[Overswarm]

But wouldn't 9v1 eventually result in 4v1 :v (if mafia is indeed on the path to victory)

Yes, and the win % changes for the mafia member as the game goes on given the real state of the game. Given a mathematical model of 9v1 or 4v1, they aren't assuming 9v1 to 8v1 to 7v1 etc., etc., they're assuming the game in its entirety.

Like saying you have a 50% chance of completing a mile in under 6 minutes but a 90% chance of completing half a mile in under 6 minutes doesn't mean you have a 90% chance once you hit the half mile marker.

 

[#HBC | ZoZo]

Right, I see how it is. Makes sense when there are so many targets to mislynch.

 

[Overswarm]

The actual win rate for mafia wouldn't change much, it's just an extreme example he gave to illustrate how the formula works. Both groups would give mafia roughly a 40% chance to win.

 

[~ Gheb ~]

I heard that to get a 50% balance between a town of only VTs and mafia of only goons you'd need 49 VTs and 2 Goons. Wouldn't be surprised if that was actually the case. Should be noted however that "Vanilla" roles are not limited to VT and Goon only. Warlock for example is a Vanilla role for all intents and purposes.

 

[Overswarm]

In the study and the other two referenced the only special roles used were 1 vanilla cop role.

 

[~ Gheb ~]

In a game with only Vanillas? 0_0

 

[Overswarm]

yes

10yesses

 

[adumbrodeus]

OS, we actually discussed that quite a bit.

 

[vanderzant]

Oooh maths. Gonna read that later!

 

[vanderzant]

Also, fun thing:

4 town and 1 mafia member gives mafia a 0.375% chance to win

9 town and 1 mafia member gives mafia a 0.406% chance to win

Only had a quick skim, but I find it funny that the model doesn't account for a MYLO strategy of No Lynching to change the probability of lynching scum from 1/4 to 1/3 .

I assume this is because No Lynching is not common practice irl?

Mathematically speaking, adding another Town player should always increase the chance of a Town win, even if only slightly, because an extra lynch always adds another chance for a successful lynch to occur.

Another thing that occurred to me is that as Town approaches ridiculous numbers to get the 50/50 balance (i.e Gheb's scenario of 49 VT 2 Goons), the value that each VT contributes to Town's overall chance of winning is very small. I.e. 39 VT vs 2 Goons is probably very close to 50/50 balanced, it's just that the last 10 VT's add soooooo little in terms of successful lynch probability.

 

[vanderzant]

Hmm, his model for determining Mafia's win chance (in a single Mafia game) is a bad approximation as well. He showed the correct way to determine it initially (at the start of page 4) but he then tried to change it to take into account his bad MYLO strategy, and average it out to make a straight line equation.

He's even inconsistent with what he chooses the variable 'n' to be >.<. In some cases it's the total number of players, in others it's the number of townies.

This is how the Maths should be:

For a game of 4 Town 1 Mafia

Pr(Mafia Win) = Pr(Mislynch Day 1) * Pr(Mislynch Day 2) = 4/5 * 2/3 = 0.536

For a game of 9 Town 1 Mafia, there are two scenarios based on how town treats MYLO. I won't type out the calcs (it's the same process as the other game) but Mafia's win chance is 0.492 if Town choose to lynch on MYLO and 0.433 if they No Lynch, let mafia kill someone and then lynch in the 2v1 LYLO scenario.

I don't know how he got those numbers of .375 and .406 either

 

[#HBC | ZoZo]

Different subject; do any of you guys plan far ahead as either alignment (past night kills/night actions)? I kinda work very impulsively as either alignment and post whatever I "feel" is approperiate etc. So, hbu?

 

[Swiss]

Different subject; do any of you guys plan far ahead as either alignment (past night kills/night actions)? I kinda work very impulsively as either alignment and post whatever I "feel" is approperiate etc. So, hbu?

Plan what you can, but your optimal night action will often be dictated but he day just gone. I had most of my night actions planned since D1 in Britches but I marker so had to.