Open 705: Polygamist - Game Over

[sheepsaysmeep]

pagetop

[DiamondSentinel]

Huh. The amount of accord between Sky and me is unreal, especially considering our planning during the pre-game phase was "Hey, I have no idea what to do, do you?" "Nope" "Oh cool. Well, let's just wing it"

[Mathdino]

A. Can you please explain why you disagree that vote count analysis, vote analysis, and holding people accountable for their vote, are worthwhile scumhunting tools in this game.

I do not mean to say that you are 'not good'. I think your idea is a poor one, in that it adversely impacts town, but it does not mean I think poorly of you. I just think that any idea that asks us to trade our experience and scumhunting tools for the random hand of fate, is more likely to come from a scum player than a town player.

I would love for this to be an ordinary game.

B. Then treat it as such. This is no different to a regular game where the setup is known and night phase is skipped.

I'm saying that scum MUST disagree with it.

C. No, they don't. Scum can agree with it all the way up until we actually roll a dice and it happens to come up with a scum name. They'll happily go along with it as long as it's a towny being lynched and we'd never known until game over. I think statistically the dice roll favors scum - the first roll is 8/12 in hitting town, and the second roll is 6/12. That's a better than 50% chance, if my napkin math is correct, of scum winning off the rolls.

Lettered your points to respond to them.

A. I reviewed the evidence. Open setups are often designed around a theoretical winrate that results from random lynching. For example, in a 2 scum vs 7 townies game, assuming mafia shoots every night, the theoretical winrate is 37.2%. Adding power roles increases that, and allowing real life towns to play the game as it's intended to be played (scumhunting) increases that further.

This open setup has a 60% theoretical winrate. Its actual winrate? 36%. That's

fucking abysmal

. And my opinion of the last game is that town only won because scum played like shit. The fact that 2/3 of the other town wins were the first couple times this setup was even played supports that hypothesis.

So either one believes that previous towns are horrible and "oh man, my scumhunting is so much better, I can do better than that", or you realise that

non-random lynching actually hurts town's winrate.

From the wiki:

At the end of Open 88 it was proposed that this setup inherently favors Town. By randomly lynching, the Town has a 60% chance of winning. However,

truly random lynches will not occur in practice because scum cannot and will not lynch themselves

; further, it was noted that scum voting each other up to L-1 would make them consistently look great under vote analysis. It was also discussed that massclaim should occur either early Day 2 or very late Day 1 to keep scum Lover claims as implausible as possible. See also White Flag Gambit.

Emphasis mine. I believe that town's low winrate from a strategy of real scumhunting is due to the fact that most towns lynch town early on due to scum manipulation, and in my experience, only come to their senses in LyLo. We can't afford to clown around going through the motions of scumhunting, being wrong, and correcting later on.

We have 2 days

.

I can understand why you might think that. Look at this from a scum-me point of view.

I, as scum, come in and read up on the setup and previous games (unless you think I didn't do this, but I'm pretty sure I've shown that I have), and see that classic scumhunting gives scum a 64% winrate. I'm in general a pretty difficult-to-early-lynch player (you can factcheck me on this one) when I play like I normally do. So the scum-me narrative requires me deciding, "fuck that 64% winrate and fuck my own ability to not get lynched, I'm gonna suggest a plan that objectively has a 60% chance of fucking my team over, a plan that's clearly unpopular and might get me lynched even trying to implement it, and I'm gonna carry that plan through the game". Doing this would literally be not playing to my wincon to the best of my abilities.

Now you could argue that this is all WIFOM and I'm only doing that for towncred. But I wasn't saying "don't lynch me". I was saying "random lynching is a better strategy for town than lynching based on scumreads".

B. This is different to a regular game, because we only have 1 mislynch available. Most games, we'd have more flips to analyse. This is essentially 2v4 Mountainous Nightless where the 2 scum hydrae are lovers. Odds are bad.

C. If scum do that, then it'll be pretty obvious that they're scum. And no, the dice roll doesn't favour scum, you're doing your math wrong.

The probability of scum winning this by random lynch is 8/12*6/10 = 2/3*3/5 = 2/5 = 40%. Thus the probability of town winning is the inverse, 60%.

I'm happy to talk math with you all day but understand that probability/game theory is literally my specialty, and I've calculated all this beforehand.

[Sky_Paladin]

8/12*6/10 = 2/3*3/5 = 2/5 = 40%

Day 1 - 8/12 chance of the lynch randomly favoring scum.
Day 2 - 6/10 chance of the lynch randomly favoring scum.

Yes, I accept that if you multiply out the 'day 1 and day 2' value, it's a 40% win rate for scum.

I cannot explain using maths why this is a bad idea because my math is not strong enough.

However, on day 1, it's 75% chance of town mislynching (random miss).
On day 2, it's 60% chance of town mislynching (random miss).
I would take those odds as scum every time.

I don't really understand how a 75% chance and a 60% chance works out to a 40% chance and I am prepared to learn about this after the game.

However for the purposes of this game I am not persuaded that a random dice roll is in town's favor, and even if it was, I would still be disinclined to employ that as a strategy.

[RedFlavor]

There is 4/12 chance that scum was chosen as dice roller so you have to multiply 60 percent with 8/12 which makes it %40 (you can townread someone but they can be wolf)

Scumhunting seems better

[RedFlavor]

It should be like this:
8/12 dice roller is town
4/12 dice roller is scum

If dr is scum(4/12) scum wins

If dr is town (8/12)
Since they wont be lynching themselves it will be
4/10 chance lynching scum at d1
6/10 (lynching town d1) x 4/8= 3/10 chance lynching scum at d2

When we add d1 and d2 it makes 7/10 and we should multiply this with 8/12 which makes it 46% of lynching scum with dice rolling

It is still lower than 50
Btw just realized day 1 is longer than 3 weeks

[Lalendra]

To respond to a couple things in particular:
"He even says that if he were confirmed town he would still choose randomly, but I don't believe that's true": Then you're just wrong, and you don't know enough about how I think to know you're wrong. Feel free to leaf through my open games if you're actually interested in sorting me (I won't expect it of you, but if it eases your mind, whatever). Sun shines, grass grows, Mathdino breaks setups. The main things that stop me are in the set of {obstinate townies, scared scum, D1 going majorly off the rails in some way}.

This isn't the first time I've played with you. And no, I don't believe that as town you would be espousing this kind of strategy. Feel free to disagree, but that's my opinion.

"The "I know this is scummy but we should do it anyway" just feels like backpedaling": I think you skimmed/missed the point in some way. IN A NORMAL GAME, what I'm doing would be massively scummy, because scumhunting increases town's winrate in normal games. In this game, scumhunting literally decreases our winrate, so I'm uninterested in scumhunting. I do believe I can come up with at least one townread, and I'm basing my entire game around that. Because that's where the math leads me.

Speaking in terms of probability, yes, scumhunting decreases our winrate. HOWEVER, I am far more comfortable with the idea of scumhunting, and coming up with meta/associative/scummy tells, than I am with picking random targets.

On that note, let me ask - if you had a scumread on someone, would you still be using this approach? i.e., would you forgo your scumread and trust the dice? Because that seems like playing against your wincon imo.

I don't really have much more response to Diamond, but for those of you interested in actual scumhunting, notice how neither Sky_Paladin nor Diamond are sure on how to scumhunt in this situation, so they both default to discrediting my solution

which is specifically to solve the "no real way to scumhunt" problem

. So they're probably scum. Or maybe this is me confbiasing because they disagree with me. Dunno. At the very least I have no reason to townread them, so I'm sticking to sheep/Tora as my locktown team.

I like that you at least acknowledge the fact that you're scumreading people just for not agreeing with you, but I still think you should be a little more open-minded. Just because people don't agree with you doesn't mean they're scum.

MathDino, that's a big strawman. Town can completely disagree with your idea because it's a pants idea. I'm not calling you bad or stupid for it, I'm saying it's scum to push the agenda that it's too hard to scumhunt so we should just roll a dice instead, and that's why I'm voting you.

Exactly.

To more specifically respond to this, I know that town CAN disagree with it. That's beside the point: I'm saying that scum MUST disagree with it. So I naturally must consider that anyone who disagrees with it could be scum.

Wait...but above you said that you were scumreading Sky/Diamond for disagreeing with you. Yet here, you acknowledge that people can disagree with you and still be town?

However, on day 1, it's 75% chance of town mislynching (random miss).
On day 2, it's 60% chance of town mislynching (random miss).
I would take those odds as scum every time.

I'm not big on doing the math in setups because I feel that math only works in a vacuum where you don't take into account unpredictable and unquantifiable things such as people's opinions, behavior, psychology, willfully doing things that they otherwise wouldn't just to throw people off their meta, etc. However, Sky's example above is pretty much exactly why I'm not comfortable with Math's approach.

[Mathdino]

smh i've failed my town at communication

Spoiler: me arguing with people (SkyPaladin and RedFlavor) about math

Day 1 - 8/12 chance of the lynch randomly favoring scum.
Day 2 - 6/10 chance of the lynch randomly favoring scum.

Yes, I accept that if you multiply out the 'day 1 and day 2' value, it's a 40% win rate for scum.

I cannot explain using maths why this is a bad idea because my math is not strong enough.

However, on day 1, it's 75% chance of town mislynching (random miss).
On day 2, it's 60% chance of town mislynching (random miss).
I would take those odds as scum every time.

I don't really understand how a 75% chance and a 60% chance works out to a 40% chance and I am prepared to learn about this after the game.

However for the purposes of this game I am not persuaded that a random dice roll is in town's favor, and even if it was, I would still be disinclined to employ that as a strategy.

You would be wrong to take those odds. You're looking in the face of correct calculations and saying "nah that's unconvincing".

Here's an example. If you got the opportunity to play a game where if you hit a 8/12 diceroll and then a 6/10 diceroll, you won a dollar, and if you lost either, you lost a dollar, would you play?

The key is that scum has to win BOTH of those (the 75% AND the 60%) and it's unlikely they do. Looking at past games, it seems a better strategy for scum is literally just to scumhunt.

It should be like this:
8/12 dice roller is town
4/12 dice roller is scum

If dr is scum(4/12) scum wins

If dr is town (8/12)
Since they wont be lynching themselves it will be
4/10 chance lynching scum at d1
6/10 (lynching town d1) x 4/8= 3/10 chance lynching scum at d2

When we add d1 and d2 it makes 7/10 and we should multiply this with 8/12 which makes it 46% of lynching scum with dice rolling

It is still lower than 50
Btw just realized day 1 is longer than 3 weeks

I understand what you're doing here. I just want to nip that idea in the bud real quick.

The dice roller cannot be tampered with.

Just because I roll the dice doesn't mean I can say "alright guys I'm rolling the dice to lynch anyone other than me, [scumpartner X], [scumpartner Y], [scumpartner Z]". If I did that, I would be super obvious scum.

Now you could (and I am) making an argument that the dice roller should be town and should randomise their target as anyone other than themselves and their own lover. I've done the odds on this already. If dice roller is town and comes up with 2 random lynches other than themselves, our winrate is 70%. If dice roller is scum and comes up with 2 random lynches other than themselves, our winrate is 30%. Since dice roller has a 25% chance of being scum, this expected probability comes out to

30%*25% + 70%*75% = 0.3*0.25 + 0.7*0.75 = 0.6 = 60%

The aforementioned 60% winrate.

Also your math doesn't even take into account the lovers mechanic, that lynching anyone also lynches their partner.
Someone else pointed out that we can basically treat this game as 6 hydrae with 2 scum hydrae. Try the math that way if it's easier for you; it's effectively equivalent.

[RedFlavor]

Dice roller has a 4/12 chance of being scum which is equal to 33%

[Mathdino]

This isn't the first time I've played with you. And no, I don't believe that as town you would be espousing this kind of strategy. Feel free to disagree, but that's my opinion.

I have a response to this that I can't use because that game is ongoing. This is a perfect example of why you shouldn't use or talk about ongoing games. Do the meta on me. Realise how my play might vary game to game depending on
A. the setup
B. my role
Again, you're literally suggesting that as scum, I would be espousing the kind of strategy that creates a 40% winrate for my team, rather than playing the game normally and winning like

the majority of my predecessors in this setup

. THAT would be idiotic. And to suggest I would do that is kind of insulting to my intelligence. The ONLY argument I would accept for why I'm doing this as scum is "oh he's telling everyone the objectively optimal town strategy just for the towncred", and even doing that would be hilariously risky. But doing this does not create an edge for scum.

Speaking in terms of probability, yes, scumhunting decreases our winrate. HOWEVER, I am far more comfortable with the idea of scumhunting, and coming up with meta/associative/scummy tells, than I am with picking random targets.

On that note, let me ask - if you had a scumread on someone, would you still be using this approach? i.e., would you forgo your scumread and trust the dice? Because that seems like playing against your wincon imo.

Yes. My scumreads have a long sad history of being wrong on D1 and D2. I'm a fantastic LyLo player and an okay early player (my main strength as an early player is not getting myself lynched). The dice have a better chance of being right than I do. This does not apply to other setups. I would not suggest this in other setups. But in this setup, it's correct.

Notice that I'm doing something that's effectively equivalent to picking a random target, which is saying "Hey guys, sheep/Tora are town, I'm just gonna sheep their vote". If we model their scumreads as essentially random, I get what I want, which is 2 somewhat arbitrary lynches, and you guys get what you want, which is someone who's actually theoretically scumhunting (just not me).

I like that you at least acknowledge the fact that you're scumreading people just for not agreeing with you, but I still think you should be a little more open-minded. Just because people don't agree with you doesn't mean they're scum.

Wait...but above you said that you were scumreading Sky/Diamond for disagreeing with you. Yet here, you acknowledge that people can disagree with you and still be town?

I don't know how I can be clearer on this.
- Town CAN disagree with it. Towns are generally bad.
- Scum MUST disagree with it. Scum would have to be monumentally bad to go along with this idea.
So if someone agrees with the idea, that to some extent shows they're probably town (unless everyone agrees in which case scum is just acting like they agree for the towncred). If someone disagrees with the idea, they could be either, but it makes it slightly more likely they're scum.

I don't know how I'm being inconsistent here. I was asked to come up with scumreads, and I can do that to the best of my ability, but I still don't actually trust my scumreads so fuck it.

I'm not big on doing the math in setups because I feel that math only works in a vacuum where you don't take into account unpredictable and unquantifiable things such as people's opinions, behavior, psychology, willfully doing things that they otherwise wouldn't just to throw people off their meta, etc. However, Sky's example above is pretty much exactly why I'm not comfortable with Math's approach.

I completely agree with you. Unfortunately, this is why scumhunting lowers town's winrate. Taking into account all of those things, scum tends to win over town by not lynching other scum, and convincing people to lynch town. Town would literally have a better winrate if they were all robots or computers. That vacuum BENEFITS TOWN. That's why I'm trying not to take into account all of those things.

[Mathdino]

Dice roller has a 4/12 chance of being scum which is equal to 33%

You're right, of course. This doesn't change the outcome because of how combinatorics works, but I did make a mistake on how I showed that outcome.

Redone expected value calculation:
33% chance dice roller is scum: For scum to win, they have to mislynch town D1 (8/10) and then D2 (6/8).
8/10 * 6/8 = 3/5 = 60%
Town winrate here is 40%.

66% chance dice roller is town: For scum to win, they have to mislynch town D1 (6/10) and then D2 (4/8).
6/10 * 4/8 = 3/10 = 30%
Town winrate here is 70%.

Expected value:
1/3 * 40% + 2/3 * 70% = 0.6 = 60%

The 60% winrate as expected.

[Mathdino]

If anyone doesn't believe me on the math side of things, I can write a script in Python (or any programming language that someone else here can verify) that simulates 100 games and shows the winrate.

I'm bored and I could use the programming exercise so Imma go do that now.

[manrock]

If anyone doesn't believe me on the math side of things, I can write a script in Python (or any programming language that someone else here can verify) that simulates 100 games and shows the winrate.

I'm bored and I could use the programming exercise so Imma go do that now.

question

If we go down the math route can you guys let me make 100 posts this game regardless, so i can go into speakeasy?

[DiamondSentinel]

If anyone doesn't believe me on the math side of things, I can write a script in Python (or any programming language that someone else here can verify) that simulates 100 games and shows the winrate.

I'm bored and I could use the programming exercise so Imma go do that now.

question

If we go down the math route can you guys let me make 100 posts this game regardless, so i can go into speakeasy?

1. Just make the posts with actually god damned content or post elsewhere. 100 posts in a game is easy.
2. Why the fuck do you want to join the speakeasy? It’s the shittiest part of the forum, filled with horrible drama political arguing, and just general shiftiness.

[DiamondSentinel]

Shittiness*

[RedFlavor]

Dice roller has a 4/12 chance of being scum which is equal to 33%

You're right, of course. This doesn't change the outcome because of how combinatorics works, but I did make a mistake on how I showed that outcome.

Redone expected value calculation:
33% chance dice roller is scum: For scum to win, they have to mislynch town D1 (8/10) and then D2 (6/8).
8/10 * 6/8 = 3/5 = 60%
Town winrate here is 40%.

66% chance dice roller is town: For scum to win, they have to mislynch town D1 (6/10) and then D2 (4/8).
6/10 * 4/8 = 3/10 = 30%
Town winrate here is 70%.

Expected value:
1/3 * 40% + 2/3 * 70% = 0.6 = 60%

The 60% winrate as expected.

There is no reason for scum to roll a dice, they could just say lynch A and lynch B who are actually town members

[Mathdino]

There is no reason for scum to roll a dice, they could just say lynch A and lynch B who are actually town members

Original Roll String: 6d10

6 10-Sided Dice: (7, 3, 9, 3, 4, 1) = 27

Here's 6 random numbers. Use the dice tag, put "1d10" inside it, and that was the original dice rolling plan.

[RedFlavor]

There is no reason for scum to roll a dice, they could just say lynch A and lynch B who are actually town members

Original Roll String: 6d10 (STATIC)

6 10-Sided Dice: (4, 10, 7, 7, 1, 9) = 38

Here's 6 random numbers. Use the dice tag, put "1d10" inside it, and that was the original dice rolling plan.

Oh I did not know about this feature lol

Original Roll String: 7d8

7 8-Sided Dice: (2, 3, 1, 5, 7, 5, 7) = 30

[Lalendra]

There is no reason for scum to roll a dice, they could just say lynch A and lynch B who are actually town members

Or they could fake a dice roll and doctor the results to pick town members, which is what I suspect is happening here. Now I am not familiar with the dice mechanic as I haven't seen it used in a game before, but I think I understand what Math is saying; I just disagree with his statement that town can do something with the dice that scum can't or wouldn't. Math says they can't be tampered with, but then immediately after he says that the dice roller should make sure the dice doesn't hit them or their lover:

The dice roller cannot be tampered with.

Just because I roll the dice doesn't mean I can say "alright guys I'm rolling the dice to lynch anyone other than me, [scumpartner X], [scumpartner Y], [scumpartner Z]". If I did that, I would be super obvious scum.

Now you could (and I am) making an argument that the dice roller should be town and should randomise their target as anyone other than themselves and their own lover.

He says he'd be super obvious scum if he chose to eliminate 4 people instead of 2, which is true, but how do we know he's not just playing the odds by saying "even if I eliminate myself and my lover, the odds are still in my favor (i.e. 8/10 or 80%) that I will still hit town"? If the dice rolled and chose either him or his

scumbuddy

lover, would he still go along with this approach? The only motivation I can see to the dice approach is a scum-driven one, and Math is using statistics to prove that he has a town motivation for it, but I'm just not buying it.

[Mathdino]

I'm not suggesting that I be the one to roll the dice.

I'm suggesting sheep/Tora do it.

[Toranaga]

If anyone doesn't believe me on the math side of things, I can write a script in Python (or any programming language that someone else here can verify) that simulates 100 games and shows the winrate.

I'm bored and I could use the programming exercise so Imma go do that now.

question

If we go down the math route can you guys let me make 100 posts this game regardless, so i can go into speakeasy?

1. Just make the posts with actually god damned content or post elsewhere. 100 posts in a game is easy.
2. Why the fuck do you want to join the speakeasy? It’s the shittiest part of the forum, filled with horrible drama political arguing, and just general shiftiness.

he is in it for the horrible drama

it's my fault even

[Toranaga]

I'm not suggesting that I be the one to roll the dice.

I'm suggesting sheep/Tora do it.

elite powerwolfing my friend

wish your lover was playing though

I haven't read anything but I think I'll be around tonight to do some solving and hopefully pick a wolf for us to lynch

[sheepsaysmeep]

mathdino, what do you think is the probability that the ppl arguing against you are actually the town who think the strategy is bad, and the scum who think it does help town are just staying silent?
that's what i think the situation is rn

diamond's self consciousness about his coordination with his lover is slightly pingy

[Mathdino]

mathdino, what do you think is the probability that the ppl arguing against you are actually the town who think the strategy is bad, and the scum who think it does help town are just staying silent?

Well, you're town, and RedFlavor's team is town. So Lalendra/cy and Sky/Diamond each should have a 2/3 chance of being town?

From your perspective, if you still don't think I'm town, should be 2/4 for each of them.

If you wanna lynch the silent team, go ahead. I'll literally sheep whatever your vote is. I'm just telling you I specifically have more of a problem with those teams, and I think it'll be easier to get a lynch on someone who disagrees with me than someone who agrees with me.

[manrock]

If anyone doesn't believe me on the math side of things, I can write a script in Python (or any programming language that someone else here can verify) that simulates 100 games and shows the winrate.

I'm bored and I could use the programming exercise so Imma go do that now.

question

If we go down the math route can you guys let me make 100 posts this game regardless, so i can go into speakeasy?

1. Just make the posts with actually god damned content or post elsewhere. 100 posts in a game is easy.
2. Why the fuck do you want to join the speakeasy? It’s the shittiest part of the forum, filled with horrible drama political arguing, and just general shiftiness.

1. What content? apparently the best idea in this setup is too randomly lynch, so what am I supposed to talk about? "Oh random lynch a is better than random lynch b for no absolute reason"
2. Someone linked me a thread there and I need to read it