ESPIONAGE: Round Three (Spies & Informants Win)

[Fujiwara]

Ooh, math!

Math ahead, skip my post if you don't care about that anyway 8D

Well, it's certainly getting very lively now.

Also, in your calculation, the detective dies 2x :x One for getting voted (1/11) and once getting killed by the spy (1/9) :x Which you can't add up just like that.

Ah, you're right. It's been a while since I did this sort of stuff. The calculation for non-mutually exclusive events is
P(A or B) = P(A) + P(B) - P(A and B)
Which means I'd have to amend my calculation as follows:
P(arrest or kill) = 1/11 + 1/9 - 1/99 = 19/99 = 19%

I just noticed, you're calculating P(A and B) = P(A) * P (B)? But you can't do that, since P(A) and P(B) need to be independent, which isn't the case here (as long as you don't throw the arrested detective back into the "Team pool" and let him get a killed too XD)

I think you need the Bayes formula... but that would be way too much to calculate :V (at least I dun feel like it XD)

But P(A) and P(B) are independent, since the detective getting arrested and the spy deciding to kill the detective are in no way conditional upon one another. Just because we arrest the detective doesn't mean he can't be the kill target. And it also doesn't change the probability of him being the kill target, since - given random voting - the spy won't know that he'll get arrested and thus won't avoid him on purpose. So I'd say the detective is very much back in the 'team pool' and thus the calculation doesn't call for Bayes, as far as I can see. ^_^

[Kleene Onigiri]

No, they are conditional.
Because if the spy knows that for example, team 1 get's voted most likely, when someone just mentiones his random vote, he won't send a kill for that team (or at least, the chance that he'll try to kill them will sink dramatically) So the vote on a random team is influencing the chance of killing a team.

Also, as I said, it's not totally random :x Considering the spy didn't even kill at all, that chance that this would happen wasn't calculated at all in our calculations D:

[Iwamoto Yuri]

Hey, quit the math talk! No maths will be allowed in my round from this point on.
meh... my head is spinning already. (gee, I'm doing a language study for a reason )

[Kamite]

I have a quick announcement.

Spoiler:

2 + 2 = Fish

That is all.

[Fujiwara]

No, they are conditional.
Because if the spy knows that for example, team 1 get's voted most likely, when someone just mentions his random vote, he won't send a kill for that team (or at least, the chance that he'll try to kill them will sink dramatically) So the vote on a random team is influencing the chance of killing a team.

Also, as I said, it's not totally random :x Considering the spy didn't even kill at all, that chance that this would happen wasn't calculated at all in our calculations D:

These calculations were made on the basis of a random vote and I mentioned as much in my original post. If everyone votes randomly without telling us who they'll vote for, there's no way of knowing who will get arrested and in that case the two are completely independent. I'll agree that this will change if people say who they'll vote for, making it less likely for the spy to kill those people that are mentioned. But here's the thing: Giving the spy information to let him avoid killing the person who'll be arrested will decrease P(A and B), i.e. the probability of the detective getting arrested and being the kill target. Reducing P(A and B) however will increase P(A or B) = P(A) + P(B) - P(A and B), so what you're actually saying here is that my estimation for the detective being arrested or killed was too low.

Regarding the non-randomness of the vote: You say it's not completely random because people vote from their lists, but the lists, too, are random, with a slightly higher chance for the both the detective and the spy in comparison with the other players. Again, this was a fact which I mentioned in my original post as something which I didn't include in my calculation, but just like the revealing of votes, this actually increases P(A), the chance of the detective being arrested, because he has a higher chance of being on any given list, thus he has a higher chance of being voted.

Also, I'll admit that I didn't include the chance of the spy not killing, since I expected him to kill, so just imagine the following preface to my calculations: Given a random vote and the spy actually killing a person

Anyway, I don't mean to say the calculations were perfect. I already admitted yesterday that I forgot the possibility of a tie occurring naturally, for example. Nonetheless, I'm sure that they're pretty close to the truth, and most of the adjustments I made (neglecting announced votes and increased chances of the detective and spy being on the list) actually kept my calculations on the conservative side, instead of trying to embellish the results and erring on the side of making the probabilities too high.

In any case, maybe we should try to return to the actual game now and think about our next steps. XD

[Memesu]

That was nice coincidence :x

what is?

Mine and Kleene´s vote :x
I´ll try to think of something more relevant to say later

[Jd-]

After conferring with KL, the team we'd like to hear more from is KainTheVampire/Jellitto. They've been the quietest team so far, and judging from the lack of a kill on the first day that otherwise doesn't benefit the Spy team at all, I find it at least a bit interesting. On that same token, I'd say they're highly likely not the Informants since they've posted almost nothing, but it's also possible that they were just both inactive for the first day and didn't have time to really respond to identify themselves.

Actually... Now that I think about it: It is possible (as someone else pointed out earlier I think) that the Spy team didn't kill because their Informants didn't identify themselves in time. While I'd question the full logic of leaving a kill on the table for that, it does make a little bit of sense if only to avoid the fiasco that happened last round in a round with a lot fewer targets and thus higher likelihood of killing an allied party.

There are a few possibilities, but hearing from Kain/Jellitto will at least give us an idea of what's happening with each team to some degree.

[Kleene Onigiri]

More math, response to Fuji :3

Spoiler:

I wasn't trying to blame you or saying you're wrong XD I find it fun to talk with you about the probabilities and see if those calculations are right or something is missing or not XD

But you still can't say it's random. Because it could be possible that team 1 isn't on anyone's list for example.
So your P(A)= 1/11 would actually be P(A)= 1/10 because no one would vote for team 1 if they go random based on their list. This again would increase your P(A and B) chance. But would totally decrease it if team 1 is actually the detective team. Because then your P(A) would be P(A)= 0 :x
Then again, if people see team 1 acting suspicious, a lot of people would "randomly" vote team 1 D: So there is no real randomness here, since people can't be totally random like a dice (as long as they don't use a dice to actually vote someone)

So your calculations would just work under very strict conditions: People are actually voting random, People won't tell who they vote, the lists in the game have Detective and Spy on them equally, P(A) and P(B) are actually unconditional, Spy is actually killing.
That's why I said that this isn't 20%. There are many factors that aren't counted into it, since this isn't a perfect scenario.

Using math to calculate something can actually manipulate people into doing something :x Because people will think it's true and follow your solution (what actually happened XD) So it' important to analyze it *_*

but people are annoyed by our math, Fuji ;_; *hugs fuji*

[Kleene Onigiri]

After conferring with KL, the team we'd like to hear more from is KainTheVampire/Jellitto. They've been the quietest team so far, and judging from the lack of a kill on the first day that otherwise doesn't benefit the Spy team at all, I find it at least a bit interesting. On that same token, I'd say they're highly likely not the Informants since they've posted almost nothing, but it's also possible that they were just both inactive for the first day and didn't have time to really respond to identify themselves.

Actually... Now that I think about it: It is possible (as someone else pointed out earlier I think) that the Spy team didn't kill because their Informants didn't identify themselves in time. While I'd question the full logic of leaving a kill on the table for that, it does make a little bit of sense if only to avoid the fiasco that happened last round in a round with a lot fewer targets and thus higher likelihood of killing an allied party.

There are a few possibilities, but hearing from Kain/Jellitto will at least give us an idea of what's happening with each team to some degree.

What if the order from the spy was that the Informant isn't supposed to say anything?

[Jd-]

Math. MAAAAATHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH!

Spoiler:

When it comes to making decisions for game-based properties, I've never gotten into probabilities so much (primarily due to my lack of interest in statistical properties). Instead, I tend to rely more on hard inferences drawn from induction of related (but not necessarily statistical) events. You'll see me using inductive reasoning quite often in situations like this.

Ahem. So!

What if the order from the spy was that the Informant isn't supposed to say anything?

An interesting order to say the least! It's certainly one that could be used in this sort of situation, since you could tell both members not to say anything when it's likely (but of course not definite) that at least one player on the other teams is going to say something.

[Jecka]

Nooo guys, stop. D:
It's too early for math. *currently in math class actually :V *

[Jellitto]

After conferring with KL, the team we'd like to hear more from is KainTheVampire/Jellitto. They've been the quietest team so far, and judging from the lack of a kill on the first day that otherwise doesn't benefit the Spy team at all, I find it at least a bit interesting. On that same token, I'd say they're highly likely not the Informants since they've posted almost nothing, but it's also possible that they were just both inactive for the first day and didn't have time to really respond to identify themselves.

Actually... Now that I think about it: It is possible (as someone else pointed out earlier I think) that the Spy team didn't kill because their Informants didn't identify themselves in time. While I'd question the full logic of leaving a kill on the table for that, it does make a little bit of sense if only to avoid the fiasco that happened last round in a round with a lot fewer targets and thus higher likelihood of killing an allied party.

There are a few possibilities, but hearing from Kain/Jellitto will at least give us an idea of what's happening with each team to some degree.

Well, sorry for being quiet but I really haven´t had anything to say and apparently it is the same for Kain too.

Your post just reminds me of round 2. At day 2 I didn´t post anything and the Spy, Raiden, accidentally didn´t kill anyone. So at day 3 Fujiwara nominated and voted me because I had been inactive in the topic on the same day when no one died. In the end I was just a civilian though.

That is why I was a bit irritated when I read your earlier post where you said something similiar about us being inactive but we really should post more I think.

It´s not impossible for the Spy not to kill anyone because of inactivity of course, but me not posting isn´t because of lack of time, but lack of ideas.

What if the order from the spy was that the Informant isn't supposed to say anything?

An interesting order to say the least! It's certainly one that could be used in this sort of situation, since you could tell both members not to say anything when it's likely (but of course not definite) that at least one player on the other teams is going to say something.

That is completely something I haven´t even thought about, I always thought that the Informants have to identify themselves by posting something that the order said, not by not posting. So, not posting is a possibility too? Seemingly it isn´t against the rules?

[Kleene Onigiri]

@Jellitto: I think it's not against the rules? It doesn't say you can't command them to be silent :V XD

[Jd-]

Well, sorry for being quiet but I really haven´t had anything to say and apparently it is the same for Kain too.

Your post just reminds me of round 2. At day 2 I didn´t post anything and the Spy, Raiden, accidentally didn´t kill anyone. So at day 3 Fujiwara nominated and voted me because I had been inactive in the topic on the same day when no one died. In the end I was just a civilian though.

That is why I was a bit irritated when I read your earlier post where you said something similiar about us being inactive but we really should post more I think.

It´s not impossible for the Spy not to kill anyone because of inactivity of course, but me not posting isn´t because of lack of time, but lack of ideas.

Basically, the major problem that arises from civilians being quiet and inactive is that they create hiding place for the Spies. The Spies can always hide within those inactive ranks, while the active civilians are forced to reason it out amongst themselves. By all civilian teams being active, we diminish if not eliminate that hiding place and force them out into the open one way or the other. It's not perfect, but it's at least a starting point, wouldn't you say so?

I'd also like to note that the Day 2 fiasco of last time was a pretty special case and wasn't really the fault of any one player. We had to go with what information we had at the time, so that's just how it shook out.

I think the way most players reason, at least in these first three rounds, is that inactive civilians make it a lot harder to effectively proceed and thus why they are so often the first ones nominated for vote discussions. In essence: An active civilian dying/being arrested is a lot more detrimental to the civilian effort than an inactive one dying/being arrested. Imagine if the active civilians were all the first ones to die/be arrested. The game would just be the Spies picking people off while the inactive civilians cast random and likely ineffective votes until the Spy team nearly inevitably gets away on account of never really being in any real danger.

That is completely something I haven´t even thought about, I always thought that the Informants have to identify themselves by posting something that the order said, not by not posting. So, not posting is a possibility too? Seemingly it isn´t against the rules?

The only real restriction on orders is that they must be post-related. Like, you can't order them to change signatures or something like that, but if it's anything fair and reasonable relative to posts within the game topic--including not posting--it should be legal.

[Iwamoto Yuri]

@Jellitto: I think it's not against the rules? It doesn't say you can't command them to be silent :V XD

It's not, it can be done if the spy sends that order.