Stoofer's 2nd Law

[Norinel]

Oh, but there is. Let's bring up another of Stoofer's Laws, if I may:

In a C9 game, a townie lynch on day one will have both scum on the lynchwagon.

He brought it up in a game I was in with him, and if we believe his statistics it has like an 80% success rate (sample size: 8 or so). The reason I put it out there is to see if other people have found it to be true or untrue in their experience.

It is OK that I say this, right Mr. Stoofer? I mean it's already sort of public knowledge when you posted it up in our game. If not, sorry

Turbovolver is quite right, This ought to be Stoofer's 1st Law in fact, since I have been propounding this for some time.

Note it only applies to C9 games, and therefore wouldn't apply to the invitational.

I just looked at half a dozen newbie games and

didn't

see one with both scum on a townie lynching Day 1 bandwagon. I would like to see the numbers run, as my inclination would be one on, one off to try to dissociate the mafia.

[Mr Stoofer]

If you exclude one game with a self-voter, its about 80% in finished games I've been in. I noticed that Newbie 182 was just lost by the town on day 3. If the town had applied the rule it would have won.

[Turbovolver]

If you exclude one game with a self-voter, its about 80% in finished games I've been in. I noticed that Newbie 182 was just lost by the town on day 3. If the town had applied the rule it would have won.

If the town had listened to me it would have won

...yeah, it's probably my own fault.

[W!nt3r]

it took spam off a long time...

but it wasa a mish mash

I think he was refering to discussion as opposed to spam Raj. In the case of spam-off every 8 page's is the equivalent of about 1 page of actual discussion in the terms of a ammount of brain cells used... unless of-course PJ add's to said discussion. in which case about 14 pages of spam-off would be needed for one PJ-page of discussion.

[rajrhcpfreak]

spam and discussion is the same thing... isnt it?

[Mr. Flay]

I'm inclined to agree with Norinel, but it should be pretty easy to lay to rest with a game analysis (just not right now for me, too stupid-busy).

[petroleumjelly]

it took spam off a long time...

but it wasa a mish mash

I think he was refering to discussion as opposed to spam Raj. In the case of spam-off every 8 page's is the equivalent of about 1 page of actual discussion in the terms of a ammount of brain cells used... unless of-course PJ add's to said discussion. in which case about 14 pages of spam-off would be needed for one PJ-page of discussion.

PJ as in me? Do I really talk

that

much?

[W!nt3r]

no but you talk in a complex manner, so most of the people have to spend extra braincells to comprehend...


It's a compliment in a way...

[Stewie]

I guess the stoofer equation is:

P = 1 - 1/n

Where P is the probability of a vote, and n is number of posts.

(waits for someone to make a thread with a vote on the first post to screw me over)

Ok, I suppose the following would be accurate:

P = 1 - 1/(n+1)

[zu_Faul]

I don't think that is right, because then you would have a 50% chance for a vote in the first post

[Stewie]

Yeah. The point is that the first post has a chance of a vote (two threads already made to "prove me wrong" on my previous equation) and that the probability aproaches one as more posts are made. I guess you have a point about it being too likely to have a post... Let's try again:

P = 1 - 19/(n+19)

That should work. First post there's a 1/20 chance of a vote. I can make the chance on the first post as small as I want, but I'll leave it there, since it seems reasonable.

[Norinel]

Well, maybe it only applies to games Stoof is in. *notes that scum Stoof lynches townies*

But here are the last 15 completed Newbie games where a townie was lynched Day 1: (If someone wants to go back further, the next 10 are 145, 144, 143, 142, 140, 138, 137, 135, 133, and 130)

182- 2 scum
175- 2 scum
169- 2 scum
164- 1 scum, deadline lynch
162- 2 scum
160- 2 scum
159- 1 scum
158- 1 scum
157- 1 scum
156- 0 scum
152- 1 scum
151- 1 scum
150- 1 scum
147- 1 scum
146- 1 scum

That's 5/14 for Stoof, although I admit I wasn't as careful checking for self-votes as I could have been. But more interesting than the statistics is the homogeneity- excepting 164 and 156, the games block fairly well. Does this mean the Newbie game metagame moves in waves?

I also find interesting the recent epidemic of lynching power roles day 1, but that deserves its own thread.

[Mr Stoofer]

The formula for Stoofer's 2nd Law is:

P=1-k/n

Where P = probablility of a vote in the thread
n = number of posts in the thread
k = the Stoofer constant, which has yet to be determined.

::edited due to being rubbish::

[Thok]

Assuming a random probaility of being on a lynch, you'd expect a lynch of a townie to have 2 mafia 40% (6/15) of the time, 1 mafia 53% (8/15) of the time and no mafia 7% (1/15) of the time.

The streakiness is interesting, but it could also be just random streakiness.

[Yosarian2]

Assuming a random probaility of being on a lynch, you'd expect a lynch of a townie to have 2 mafia 40% (6/15) of the time, 1 mafia 53% (8/15) of the time and no mafia 7% (1/15) of the time.

The streakiness is interesting, but it could also be just random streakiness.

(shrug) It's more a matter of stratagy then anything else. Some scum try to avoid ever being on a bandwagon with another scum; others don't really care, and others care only in certain situations. It's one of those see-saw effects where if most scum avoided being on a bandwagon with another scum, then people would stop looking on the bandwagon of scum 1 for scum 2, at which point it would no longer be a good stratagy for scum to avoid being on a bandwagon together, and so on. So basically, in reality, I think it has more to do with what stratagy the scum in question happen to be following at that moment in time then with any general rule.

[Stewie]

The formula for Stoofer's 2nd Law is:

P=1-k/n

Where P = probablility of a vote in the thread
n = number of posts in the thread
k = the Stoofer constant, which has yet to be determined.

k cannot be greater than one, because that would mean that the probability of a vote in the first post is negative (logically impossible).
k cannot be equal to one, because that would mean that the probability of a vote in the first post is zero (proved wrong).
Therefore, k must be a number lower than one, but considerably more than zero (or else the probability of a vote in the first post would be one, or pretty close to one). Just narrowing down your choices.

[Mr Stoofer]

My guess is that k is approximately 0.99283704157921304510793511709375923.
But this needs to be verified by experiment.

::edited due to being rubbish::

[Fiasco]

That would mean a 1% probability of a vote in the first post, and a 49% probability of a vote in the second post. The model just isn't very good. If the probability of a vote is the same in each post, then the right equation is:

1 - (1-p)^n

(with p the probability per post of a vote and n the number of posts in a thread).

If the probability of a vote depends on the post number, it's:

1 - ("product-with-t-running-from-1-to-n" of (1-p(t)) ),

where p(t) is the probability of a vote in post t given that there were no votes in any previous post.

Now all we need to do is get estimates for all the p(t)

[Mr. Flay]

It seems like there's a logarithmic function going on here, because the probability starts low and then scales upward sharply around page 3-4 for GD, maybe slightly later for MD. It never quite gets to 1, but it approaches it by page 7 or 8 pretty closely.

Unfortunately I've forgotten enough math to not be able to pull an example function up...

[Norinel]

vote: Stoofer

for changing the subject the moment he's proven wrong.

[VisMaior]

how is that for wishy-washy...

[Mr Stoofer]

Norinel, the "rule" applies to all pro-town roles, not just townies. I think your stats nin psts 36 are limited to vanilla townies, which is not the intention.

[Norinel]

unvote, FOS: Stoof

for trying to change what he was proven wrong about. And besides, as stated Stoof's II is

always

true, so I only needed to find one counterexample.

Anyway, from the same timeframe: (7 in 26 games? That's significantly worse than random!)

173- 2 scum (Newbie, didn't claim, scum laid final vote)
171- 2 scum (Newbie, claimed, scum laid final vote)
165- 1 scum (IC, quicklynched, scum laid final vote)
163- 1 scum (Newbie, didn't claim, scum laid final vote)
161- 1 scum (Newbie, claimed, scum laid final vote)
153- 1 scum, deadline lynch (IC, claimed, scum had first vote)
148- 1 scum (IC, didn't claim but strongly hinted, scum had third vote)

Not counting 153, that takes us to 7/20 for Stoof, which is still about average.

I had the extra notes so I could see why power roles get lynched Day 1. I'm surprised that there's a pretty good mix of newbies and ICs, and claims and no claims. But I will propose Norinel's first law: If a power role is lynched with four votes in Day 1 in a C9 game, the person to cast the last vote is more likely to be mafia than not.

[Mr Stoofer]

as stated Stoof's II is

always

true, so I only needed to find one counterexample.

In a C9 game, if a pro-town player is lynched on day 1, both scum were

probably

on the lynch.

Vote: Norinel

for getting the number of the Law wrong and misrepresenting the terms thereof (see: Stoofer's 1st Law). Even though, on your stats, it isn't true.

Although your Newbie Game, which just finished, obeyed the law .

[Commodore Amazing]

Mine didn't. But it was a deadline lynch, so maybe that's different.