U-Pick Mafia Vol 1 - Game Over

[Kylemii]

I have many thoughts on number 6.

for me and a lot of people I think early game ends and the real game starts as soon as we've cracked that eggshell just a little and lynched our first mafia. triple-lynch could hypothetically do that for us, and at the same time help with narrowing the PoE a little bit.

however... that only happens if we can have our shit together tomorrow. with 3 players lynched there's a decent chance the mafia uses the opportunity to get rid of someone they don't want around, or saving their teammate who's in second or third place by voting or unvoting someone, which could lead to interesting votal analysis. if guided properly tomorrow we could use #6 to sweep away some inactives but that sort of thing would require a lot of cat herding.

worst reasonable scenario with #6 is 3 town lynches, mafia shenanigans may lead to town leader types getting lynched over others which benefits mafia, also gives us something to analyze though....

best reasonable scenario is we get one mafia out of it, maybe 2 if we're *extremely* lucky and the two players are on opposite teams but I think hoping for 1 is more realistic. if we catch even just one mafia tomorrow i think #6 would be worth it.

so I guess its... yeah. very high risk high reward. but I think even the risks can be educational. I agree that 6 goes much more smoothly with epignosis around.

[Kylemii]

@Quin if I send you some beeroots will you play a game with me?

The compromise was to be resolved before EoD. But this is Night 1, so I will forgive it.

Yes, Kyle. I will play a game with you.

any requests?

[Golden]

if we catch even just one mafia tomorrow i think #6 would be worth it.

If you catch one mafia for every three lynches town loses.

For this to be successful we HAVE to catch two.

[JaggedJimmyJay]

I'll use numbers in your 5 vs 3 situation, Jay, since that's your 'town-leaning' one. I can't possibility demonstrate it with the complex numbers required for 31 players.

You have 5 civilians. On day one, each has a 0.428 shot at being right about who a mafia is. If they need to find two mafia on that day, they have a 0.286 probability of successfully identifying a second one.

However, if you kill one at a 0.428 probability and allow a nightkill, ending at 4 v 2 the next day, your odds of catching the second mafia increase from 0.286 to 0.333

That's the most basic illustration I can provide to demonstrate how catching two mafia on one day rather than on consecutive days is less likely and provides lower odds for the civilians.

~~~~~~~~~~~~~~~~~~

The numbers absolutely live on a curve, and depends on the numbers. I can't compute the numbers because I don't know exactly what is out there. What I can say is that it sits on a curve, so while odds might increase from 1 to 2, they'd dramatically drop from 2 to 3, because you are diluting civilians too far.

You're ignoring the multi-day element.

The probability on Day 1 at .428 must be multiplied by the Day 2 probability of .333 = .143 to be an apt comparison. You have to convert on the .428 and then on the .333. The vantage point in question is always Day 1 -- From that point, what is the raw probability of a correct read/vote/lynch of two mafia members, either in one motion, or in consecutive lynch attempts? This the point I was trying to make when I spoke of the necessity for multi-cycle perfection -- a requirement which does not exist when multiple people are lynched.

I do agree that dilluted votes can be an issue in certain scenarios wherein the civilians don't have the numbers necessary to overcome the mafia influence. Is that going to be an issue on Day 2 of this game?

[colonialbob]

We could just put dunya/jjj/Golden in the top 3 to cut down on the reading required in this game

[colonialbob]

I'll use numbers in your 5 vs 3 situation, Jay, since that's your 'town-leaning' one. I can't possibility demonstrate it with the complex numbers required for 31 players.

You have 5 civilians. On day one, each has a 0.428 shot at being right about who a mafia is. If they need to find two mafia on that day, they have a 0.286 probability of successfully identifying a second one.

However, if you kill one at a 0.428 probability and allow a nightkill, ending at 4 v 2 the next day, your odds of catching the second mafia increase from 0.286 to 0.333

That's the most basic illustration I can provide to demonstrate how catching two mafia on one day rather than on consecutive days is less likely and provides lower odds for the civilians.

~~~~~~~~~~~~~~~~~~

The numbers absolutely live on a curve, and depends on the numbers. I can't compute the numbers because I don't know exactly what is out there. What I can say is that it sits on a curve, so while odds might increase from 1 to 2, they'd dramatically drop from 2 to 3, because you are diluting civilians too far.

You're ignoring the multi-day element.

The probability on Day 1 at .428 must be multiplied by the Day 2 probability of .333 = .143 to be an apt comparison. You have to convert on the .428 and then on the .333. The vantage point in question is always Day 1 -- From that point, what is the raw probability of a correct read/vote/lynch of two mafia members, either in one motion, or in consecutive lynch attempts? This the point I was trying to make when I spoke of the necessity for multi-cycle perfection -- a requirement which does not exist when multiple people are lynched.

I do agree that dilluted votes can be an issue in certain scenarios wherein the civilians don't have the numbers necessary to overcome the mafia influence. Is that going to be an issue on Day 2 of this game?

The same math applies to the single day version though

[JaggedJimmyJay]

If the mafia teams just try to combine their votes to ensure command of #2 or #3 spot without regard for their actual suspicions (or the suspicions being promoted by civilians), then... that should be something we can see, right?

[ColinIsCool]

We could just put dunya/jjj/Golden in the top 3 to cut down on the reading required in this game

For the record, I posted this in a slightly more serious way and you hounded me for it.

[JaggedJimmyJay]

The same math applies to the single day version though

The probability of a single civilian correctly identifying two mafia members out of 7 players (5v3 minus self) in one try is .286 -- the number Golden reported. There is no multiplication.

[colonialbob]

We could just put dunya/jjj/Golden in the top 3 to cut down on the reading required in this game

For the record, I posted this in a slightly more serious way and you hounded me for it.

A) I'm 100% sarcastic
B) I'm not saying anything about their alignments just how much they post
C) hounded is a strong word

[JaggedJimmyJay]

Also please consider that these probabilities are raw and do not respect context (reads and game development primarily). Also, I don't think LyLo concerns are applicable to a Day 2 with 30-31 players alive.

[Quin]

@Quin if I send you some beeroots will you play a game with me?

The compromise was to be resolved before EoD. But this is Night 1, so I will forgive it.

Yes, Kyle. I will play a game with you.

any requests?

None.

[Golden]

I'll use numbers in your 5 vs 3 situation, Jay, since that's your 'town-leaning' one. I can't possibility demonstrate it with the complex numbers required for 31 players.

You have 5 civilians. On day one, each has a 0.428 shot at being right about who a mafia is. If they need to find two mafia on that day, they have a 0.286 probability of successfully identifying a second one.

However, if you kill one at a 0.428 probability and allow a nightkill, ending at 4 v 2 the next day, your odds of catching the second mafia increase from 0.286 to 0.333

That's the most basic illustration I can provide to demonstrate how catching two mafia on one day rather than on consecutive days is less likely and provides lower odds for the civilians.

~~~~~~~~~~~~~~~~~~

The numbers absolutely live on a curve, and depends on the numbers. I can't compute the numbers because I don't know exactly what is out there. What I can say is that it sits on a curve, so while odds might increase from 1 to 2, they'd dramatically drop from 2 to 3, because you are diluting civilians too far.

You're ignoring the multi-day element.

The probability on Day 1 at .428 must be multiplied by the Day 2 probability of .333 = .143 to be an apt comparison. You have to convert on the .428 and then on the .333. The vantage point in question is always Day 1 -- From that point, what is the raw probability of a correct read/vote/lynch of two mafia members, either in one motion, or in consecutive lynch attempts? This the point I was trying to make when I spoke of the necessity for multi-cycle perfection -- a requirement which does not exist when multiple people are lynched.

I do agree that dilluted votes can be an issue in certain scenarios wherein the civilians don't have the numbers necessary to overcome the mafia influence. Is that going to be an issue on Day 2 of this game?

The probability is multiplied either way. You still are hitting on two lynches. so its .143 vs .171. One-cycle perfection is harder than multi-cycle perfection.

To your second point - YES, it is going to be an issue, because at least at lylo the civilians have a lot of data to work with. On day 2, we have nearly nothing. As I said, think of it through the lens of being a mafia. If I was mafia in this game, this would be my wet dream. I'd absolutely back myself to control both the second and third lynches. So where you might hit mafia on days three and four, here I believe I could make sure you only hit mafia (tops) with your top-voted player... which you can do anyway.

The more civilians there are, the more the odds reduce that they're actually on the same page as well. So while you could feasibly have 6 civs across three people, the reality is that if we have 18 civs you'd be lucky to get 12 of them actively on the same page. At four votes on each of three, chances of the civs actually having control of the lot are extremely low.

This is why I'm saying it's living on a parabola. At lynching the top two, I might agree with you. At lynching the top three, the numbers are definitely bad. The curve is against you. Civ influence is too diluted. Once you meaningfully control one lynch, getting either of the other two is probably too difficult.

[Golden]

Also please consider that these probabilities are raw and do not respect context (reads and game development primarily). Also, I don't think LyLo concerns are applicable to a Day 2 with 30-31 players alive.

It's not a 'lylo concern'.

It's me pointing out with a simple example how your description of what is 'town-leaning' is factually incorrect. You have a biased lens on this.

[Golden]

The same math applies to the single day version though

The probability of a single civilian correctly identifying two mafia members out of 7 players (5v3 minus self) in one try is .286 -- the number Golden reported. There is no multiplication.

No, that was my probability of getting the second, not both. You do have to multiply it.

[Kylemii]

1) Each player must vote for two people

boring but practical, forces everyone to give more thoughts, though in practice it might not actually do that, and would realistically lead to a few big leads

2) The poll will only have 8 people on it, selected randomly

interesting but dangerous, may enforce focus on 8 players who hadn't been spoken about yet which could be good.

3) Votes will be unchangeable

boring and lame. doesn't change anything.

4) Votes will also count for the people either side of the person you voted for

actually horrible. pointless and unnoticable at best. troublesome at worst.

5) The final vote cast will be worth 3

interesting I guess. only actually meaningful if the end of phase has a couple of close lynches, and even then it's not that meaningful. biggest change is that there's gonna be a bunch of hooligans trying to vote last and I'll have to tell them to stay out of my swamp

[Jackofhearts2005]

Bop it.

Shout it.

So the day ended four hours early? I’m confused

Bop it.

Strange device, do you gain advantages should someone pull or bop you?

Such a device is surely worthy of being added to your storehouse.

(What I would give to see a Bop-It flying out of one of those big golden portals)

It is a mere imitation.

My vault holds the original.

[Sloonei]

HEY THERE BUCKAROOS .MY SON RICHARD SETUP THIS COMPUTER IN THE DEN FOR GERALD AND I . WE ARE SO PROUD OF HIM AND OUR GRANDSON BENJAMIN, 8. IS THIS WHERE I GO TO CATCH SCUM...?

[ColinIsCool]

I can’t believe we’re doing statistical analysis in a meme game

[colonialbob]

The same math applies to the single day version though

The probability of a single civilian correctly identifying two mafia members out of 7 players (5v3 minus self) in one try is .286 -- the number Golden reported. There is no multiplication.

Incorrect.

The chance of hitting 2 successes out of a sample of 2, population size of 7, and success population of 3 is just over 14%. If you split that up over two days, the chance goes up to 17%, because of the kill.

Now obviously those numbers assume totally random decisions, but they are pretty clear.

[Sloonei]

Effective immediately Kenway has been replaced by someone.

it's @Sloonei isn't it? I saw teh Sloon lurking.

THANK YOU FOR THE WARM WELCOME DEARY, ITS WONDERFUL TO BE HERE

[Jackofhearts2005]

Also please consider that these probabilities are raw and do not respect context (reads and game development primarily). Also, I don't think LyLo concerns are applicable to a Day 2 with 30-31 players alive.

Right. They don’t take into account that that have been no baddie flips, yet.

[colonialbob]

I can’t believe we’re doing statistical analysis in a meme game

Gonna be 100% honest here, I'm now more invested in illustrating the stats than convincing people option 2 is better than option 6

[Golden]

I can’t believe we’re doing statistical analysis in a meme game

[ColinIsCool]

I haven’t done math more complicated than multiplication in about 5 years and stats was a year before that, so it’s all going over my head a bit but I appreciate it.

[colonialbob]

Also please consider that these probabilities are raw and do not respect context (reads and game development primarily). Also, I don't think LyLo concerns are applicable to a Day 2 with 30-31 players alive.

They also don't consider that mafia is an informed block vote

[Sloonei]

WHATS ALL THIS HOGWASH ABOUT NUMBERS? YOU KIDS THESE DAYS AND YOUR FANCY MATHEMATICS. BACK IN MY DAY IT WAS SIMPLE ARITHMETIC ! I DON'T KNOW WHERE WE WENT WRONG ... HAVE A LOVELY DAY!

[Marmot]

Simple scenario regarding the maths. I will make some assumptions on this. One player will die each night, and that one player who will die flips civilian. Also, that there are two teams of 4 mafia each, and that all independent players count as civilian here, leaving 8 mafia and 23 civilian roles in the game.


SCENARIO 1 - We lynch 3 players in one day.

We lynch three players tomorrow. Assuming there are 30 players alive after Night 1, the following odds result from this.

• Lynching 0 mafia = 37.9%
• Lynching 1 mafia = 45.5%
• Lynching 2 mafia = 15.2%
• Lynching 3 mafia = 1.4%

SCENARIO 2 - We lynch 1 player tomorrow ( I won't get into the math of the other options now).

We lynch one player each of the next three days, allowing two nightkills to happen in the process (2 more dead civilians over those three lynches). The following odds result over that span.

• Lynching 0 mafia = 36.3%
• Lynching 1 mafia = 46.0%
• Lynching 2 mafia = 16.2%
• Lynching 3 mafia = 1.5%

Addendum: yes this requires assumptions. The odds are pretty similar, slightly edging having the tri-fecta lynch. Additionally, Scenario 2 requires that two players are nightkilled by the time the third player is lynched, adding two additional deaths to the toll.

[colonialbob]

WHATS ALL THIS HOGWASH ABOUT NUMBERS? YOU KIDS THESE DAYS AND YOUR FANCY MATHEMATICS. BACK IN MY DAY IT WAS SIMPLE ARITHMETIC ! I DON'T KNOW WHERE WE WENT WRONG ... HAVE A LOVELY DAY!

[ColinIsCool]

5 is not that bad an option honestly. Scum are kind of in a damned if, if not situation and the lynch is otherwise normal.

[Marmot]

Oh hi Sloonei, you like numbers?

[JaggedJimmyJay]

The same math applies to the single day version though

The probability of a single civilian correctly identifying two mafia members out of 7 players (5v3 minus self) in one try is .286 -- the number Golden reported. There is no multiplication.

Incorrect.

The chance of hitting 2 successes out of a sample of 2, population size of 7, and success population of 3 is just over 14%. If you split that up over two days, the chance goes up to 17%, because of the kill.

Now obviously those numbers assume totally random decisions, but they are pretty clear.

Yes I just went back through it, and you're both correct (3/7 times 2/6). In a 5v3 scenario, the raw numbers oppose the triple lynch. If we find ourselves in that position and a triple lynch is offered, I will think twice.

On Day 2 with 30 people? I will need substantial convincing. Perfection is not relevant because it is not necessary, and the destruction of three suspects at once is an incredible accelerant. Consider that in this non-LyLo scenario, we are being gifted with two free lynches -- the most basic means by which civilians are able to eliminate mafia members. We can have maybe 10-13 of them, or we can have 12-15.

I will listen.

[Kylemii]

if we catch even just one mafia tomorrow i think #6 would be worth it.

If you catch one mafia for every three lynches town loses.

For this to be successful we HAVE to catch two.

mathematically sure, but mafia isn't 100% math.

catching the first mafia member of a team opens up avenues for finding the rest of them.

linki oh god you guys are doing actual mathematics

[Golden]

If the mafia teams just try to combine their votes to ensure command of #2 or #3 spot without regard for their actual suspicions (or the suspicions being promoted by civilians), then... that should be something we can see, right?

Why would they need to do that? I doubt they'd have to block vote.

Look at the day one poll. Third place got 2 votes. There were lots of them. Is it really hard to drop one vote at a timely point to ensure someone gets to three that isn't on your team, without it being obvious?

Do you not believe in your own skill to do this if you're bad? I fully believe in mine.

[Marmot]

if we catch even just one mafia tomorrow i think #6 would be worth it.

If you catch one mafia for every three lynches town loses.

For this to be successful we HAVE to catch two.

mathematically sure, but mafia isn't 100% math.

catching the first mafia member of a team opens up avenues for finding the rest of them.

linki oh god you guys are doing actual mathematics

It was all fun and games while we talked about math.

Then someone actually did math...

[JaggedJimmyJay]

Thank you Marmot. I have a feeling your alignment guesses are off, as 23-4-4 would be highly civilian slanted. Still, the basic concept of what you are saying is apt.

The question here must then be: going one at a time offers a slight improvement in raw probability while also increasing the probability of night killed civilians during the nights between those one-at-a-time lynches. One can also say to be fair that the increased time frame adjusts the raw probability further in an ideal world, to some unknowable degree.

Is it an agreeable trade?

I will stop screaming and allow others to pipe in.

[Sloonei]

Oh hi Sloonei, you like numbers?

I am 73 years old

[Sloonei]

WHATS ALL THIS HOGWASH ABOUT NUMBERS? YOU KIDS THESE DAYS AND YOUR FANCY MATHEMATICS. BACK IN MY DAY IT WAS SIMPLE ARITHMETIC ! I DON'T KNOW WHERE WE WENT WRONG ... HAVE A LOVELY DAY!

How do I make a video on the page ?
thanks.

[Marmot]

The same math applies to the single day version though

The probability of a single civilian correctly identifying two mafia members out of 7 players (5v3 minus self) in one try is .286 -- the number Golden reported. There is no multiplication.

No it's not. 2 mafia members out of 7 is .286 of the players. The probability of selecting 2 mafia members from a group of 7 players is .0476 (4.76%), a much lower rate.

[Golden]

On Day 2 with 30 people? I will need substantial convincing. Perfection is not relevant because it is not necessary, and the destruction of three suspects at once is an incredible accelerant. Consider that in this non-LyLo scenario, we are being gifted with two free lynches -- the most basic means by which civilians are able to eliminate mafia members. We can have maybe 10-13 of them, or we can have 12-15.

I will listen.

The assumption that you are making is that having a lynch is town-leaning.

It's not. Controlling a lynch is town-leaning, if the town controls it. If the mafia controls a lynch, it's mafia-leaning. I would say a triple lynch could be at best vaguely similar to a double lynch and a mafia vig shot. At worst (and in my opinion most likely), it's like having your normal lynch and giving each mafia team a vig shot.

Imagine you got a free lynch but only a third of the town votes would count but every mafia vote would count. Would you take that lynch? Or would you see it as too much of a risk of just being an extra mafia kill?

[JaggedJimmyJay]

If the mafia teams just try to combine their votes to ensure command of #2 or #3 spot without regard for their actual suspicions (or the suspicions being promoted by civilians), then... that should be something we can see, right?

Why would they need to do that? I doubt they'd have to block vote.

Look at the day one poll. Third place got 2 votes. There were lots of them. Is it really hard to drop one vote at a timely point to ensure someone gets to three that isn't on your team, without it being obvious?

Do you not believe in your own skill to do this if you're bad? I fully believe in mine.

I believe that is as plausible as any other strategic vote in any lynch. I don't understand why this is different. There are three wagons that die instead of one. Everyone who votes in those wagons (or doesn't) is responsible for what they've done and open to questioning accordingly.

In this case, the potential to evade a lynch of one's own teammate requires dancing around three wagons instead of just one.

[colonialbob]

Thank you Marmot. I have a feeling your alignment guesses are off, as 23-4-4 would be highly civilian slanted. Still, the basic concept of what you are saying is apt.

The question here must then be: going one at a time offers a slight improvement in raw probability while also increasing the probability of night killed civilians during the nights between those one-at-a-time lynches. One can also say to be fair that the increased time frame adjusts the raw probability further in an ideal world, to some unknowable degree.

Is it an agreeable trade?

I will stop screaming and allow others to pipe in.

It also allows us to see the flips before making additional lynch decisions, is the crucial bit I feel isn't being given enough weight.

Tbh the only reason I'm not calling triple lynch flat out bad is double mafia, and even then I'm not sure if the increased pool of good lynches outweighs the fact that there's more informed anti-town votes in the pool. Obviously mafia size affects that.

[Kylemii]

[mention]Quin[/mention] do you want bread?

[Golden]

One can also say to be fair that the increased time frame adjusts the raw probability further in an ideal world, to some unknowable degree.

This is the other thing I'd say. I'd actually be more inclined to option 6 later in the game. The raw probability of a successful lynch is more likely to improve in the civilians favour later. If this option came along when we actually had a pool of decently agreed suspects, it might be worth the risk. As it stands, we don't have a strong enough collective view on who the suspects are to rely on that.

[Sloonei]

I DO NOT KNOW WHO YOU PEOPLE ARE OR WHY I SHOULD TRUST YOU WITH 3 LYNCHES. HAVE TWO VOTES FOR ALL I CARE !

[Quin]

@Quin do you want bread?

No. I have bread.

[Scotty]

At this juncture this game has more posts than Turf Wars and Talking Heads combined had AT THE CONCLUSION OF NIGHT 1.

You’re inflating your own game to further the cause





(I just wanted to be part of the shit list so I don’t feel left out

please love me)

[ColinIsCool]

As much of a fuss I have caused over option 6, JJJ saying “three wagons” just now almost makes me want it to pass do that I can vote for none of them and avenge myself in Ancient Greece.

[colonialbob]

WHATS ALL THIS HOGWASH ABOUT NUMBERS? YOU KIDS THESE DAYS AND YOUR FANCY MATHEMATICS. BACK IN MY DAY IT WAS SIMPLE ARITHMETIC ! I DON'T KNOW WHERE WE WENT WRONG ... HAVE A LOVELY DAY!

Spoiler: show

How do I make a video on the page ?
thanks.

Spoiler: show

[Marmot]

Thank you Marmot. I have a feeling your alignment guesses are off, as 23-4-4 would be highly civilian slanted. Still, the basic concept of what you are saying is apt.

The question here must then be: going one at a time offers a slight improvement in raw probability while also increasing the probability of night killed civilians during the nights between those one-at-a-time lynches. One can also say to be fair that the increased time frame adjusts the raw probability further in an ideal world, to some unknowable degree.

Is it an agreeable trade?

I will stop screaming and allow others to pipe in.

I can crunch numbers, but I can only conjecture on whether it's better for town to have 2 extra days of discussion while those three players are lynched, or to get as much information as possible as quickly as possible, or some other benefit that either option will provide.