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Werewolves, Serial Killers and Demons (Murdergame: Modified rules) Round Four

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Borror0:

--- Quote from: Soulreaper77 on September 30, 2010, 10:03:11 PM ---So to sum it up:
1st person to be given a special role: 1/17*1/9 
2nd person to be given a special role: 1/16*1/8
....
Last person to be given a special role: 1/8*1/1

--- End quote ---

First, there are only special eight roles attributed at game start, not nine:
1. Werewolf
2. Serial killer
3. Demon
4. Sheriff
5. Paladin
6 Vigilante
7. Doctor
8. Vampire

Now that's cleared out, I can explain the problem with that methodology is that it does not even give a 100% chance (ie 17/17):

  1/17*1/8
+1/16*1/7
+1/15*1/6
+1/14*1/5
+1/13*1/4
+1/12*1/3
+1/11*1/2
+1/10*1/1
      0.2341

At that point, you have only 23.4% of all outcomes accounted for yet over 50% of the players have had their roles attributed to them. I'm not even sure how you'd calculate the probability of someone being an innocent (9/10, maybe? But then you'd be over 100%!) When you add all possible outcomes, and you don't come up with exactly 100% it means that you've done something as not all outcomes are accounted for.


Here's two mistakes you've committed:

1. You ignored previous events. For someone to make it to 1d15, he had to not be rolled on the two previous rolls (probability of 16/17 and 15/16). If you ignore that, you are not measuring the chance of someone being of a certain role. You're measuring the chance of someone having a special role on that particular die role. That's not what you're interested in.

2. You're measuring the chance of someone to land a particular role at a specific point in time, when it's not a relevant metric. The smaller die roll measure is used to determine which role someone gets, but you don't care about that. You only care about the likelihood of someone being any special role.


--- Quote from: tomoya-kun on September 30, 2010, 10:37:18 PM ---On the topic of werewolf, when can they attack?

--- End quote ---

On Day 1, and then every two nights (Day 3, Day 5, etc.).

Meomix:

--- Quote from: Soulreaper77 on September 30, 2010, 07:08:57 PM ---If he hadn't used strike-outs to invalidate his first vote it would have been so much more believable, his first vote was simply based on the fact that he wanted to even out the votes. Also his vote was made after the events of day 2 were posted and again there was no reason to change votes nor to deem them invalidated, and if you look at the times you'll see that his vote was 19 minutes after day 2. He had enough time to read, assess the situation and vote but he didn't. He just voted for the reason that he wanted to even out the votes. Then after changing his vote he realized that he was turned into a Newborn and had to vote on the target the Vampire specified so to fix his mistake he deemed his vote invalidated and had to vote again. After that we get an explanation that he felt bad to kill
--- End quote ---

Wo wo hold it. How do you know it was exactly 19 minutes? There are people that pop in, take afew seconds then vote on the first person they see. Only people who had special roles would know the time of revelation, care to explain this Soulreaper77?

Soulreaper77:

--- Quote from: Borror0 on September 30, 2010, 10:42:38 PM ---
--- Quote from: Soulreaper77 on September 30, 2010, 10:03:11 PM ---So to sum it up:
1st person to be given a special role: 1/17*1/9 
2nd person to be given a special role: 1/16*1/8
....
Last person to be given a special role: 1/8*1/1

--- End quote ---

First, there are only special eight roles attributed at game start, not nine:
1. Werewolf
2. Serial killer
3. Demon
4. Sheriff
5. Paladin
6 Vigilante
7. Doctor
8. Vampire

Now that's cleared out, I can explain the problem with that methodology is that it does not even give a 100% chance (ie 17/17):

  1/17*1/8
+1/16*1/7
+1/15*1/6
+1/14*1/5
+1/13*1/4
+1/12*1/3
+1/11*1/2
+1/10*1/1
      0.2341



At that point, you have only 23.4% of all outcomes accounted for yet over 50% of the players have had their roles attributed to them. I'm not even sure how you'd calculate the probability of someone being an innocent (9/10, maybe? But then you'd be over 100%!) When you add all possible outcomes, and you don't come up with exactly 100% it means that you've done something as not all outcomes are accounted for.


--- End quote ---

You forgot the Nurse but that doesn't matter.

That what I did didn't account for the innocents only the special roles. So if the chance that a random player will get a special role is 23.4% then the chance that a random player will get an Innocent role is 76.6%.


--- Quote from: Borror0 on September 30, 2010, 10:42:38 PM ---Here's two mistakes you've committed:

1. You ignored previous events. For someone to make it to 1d15, he had to not be rolled on the two previous rolls (probability of 16/17 and 15/16). If you ignore that, you are not measuring the chance of someone being of a certain role. You're measuring the chance of someone having a special role on that particular die role. That's not what you're interested in.

2. You're measuring the chance of someone to land a particular role at a specific point in time, when it's not a relevant metric. The smaller die roll measure is used to determine which role someone gets, but you don't care about that. You only care about the likelihood of someone being any special role.

--- End quote ---

How did I ignore previous events? I can't roll the same person twice, I cross them out hence the 1/17, 1/16, etc. What you are doing is calculating the chance that I pick a person on my Xth turn and assuming I can roll them multiple times. Or in die-terms, you're calculating the chance that I throw a number X and X-1 in a row and then throw a Y. But we want to know the chance that we get a role with Z amount of people. Hence the second die.
And in this particular problem only the first 9 people matter since the rest will be an Innocent anyways.

Example time ^^:
If I have a deck of cards the chance that I will draw an Ace on my first hit = 1/52. But that's only an Ace, I want to draw an Ace of Diamonds on my first hit = 1/52 (52 cards)*1/4 (4 suits). Now I want another Ace but this time I want it to be an Ace of Spades = 1/51*1/3. Now what is the chance that I draw those in a row? 1/52*1/4*1/51*1/3 = 1/31824 Now what would be the chance that I draw any other card combination on my next turn? 1 - 1/31824 = 31823/31824.
Now back to the game. Let's say we have only 3 roles, Werewolf and Demon and Innocent.  Chance that I draw a person is 1/X. Chance that I draw a person with the werewolf attribute is 1/X*1/3. Now I draw another person, the chance that he has the Demon attribute would be 1/(X-1)*1/2. Chance that I draw and a Werewolf and Demon in succession = 1/X*1/3*1/(X-1)*1/2 = 1/(6(X^2-X)) What is the chance I draw an Innocent next? 1 - 1/(6(X^2-X)) =
(6(X^2-X)-1)/(6(X^2-X)) and adding the chance that I draw the Werewolf + Demon on turn 1 and 2 + the Innocent on turn 3 will always result in a total chance of 1.
I only expanded those first turns to 9 and left out the Innocent chance.

Let me hear if you have any objections since I'll be needing these chance calculating skills very soon and this is helping me a lot :3



--- Quote from: Meomix on September 30, 2010, 11:52:04 PM ---
--- Quote from: Soulreaper77 on September 30, 2010, 07:08:57 PM ---If he hadn't used strike-outs to invalidate his first vote it would have been so much more believable, his first vote was simply based on the fact that he wanted to even out the votes. Also his vote was made after the events of day 2 were posted and again there was no reason to change votes nor to deem them invalidated, and if you look at the times you'll see that his vote was 19 minutes after day 2. He had enough time to read, assess the situation and vote but he didn't. He just voted for the reason that he wanted to even out the votes. Then after changing his vote he realized that he was turned into a Newborn and had to vote on the target the Vampire specified so to fix his mistake he deemed his vote invalidated and had to vote again. After that we get an explanation that he felt bad to kill
--- End quote ---

Wo wo hold it. How do you know it was exactly 19 minutes? There are people that pop in, take afew seconds then vote on the first person they see. Only people who had special roles would know the time of revelation, care to explain this Soulreaper77?

--- End quote ---

Because:


--- Quote from: Tiffanys on September 29, 2010, 01:52:19 AM ---                                                               Look here ^Day 2

Scene 1
Good morning BakaTown, we have some breaking news for you this morning. It seems a lot was going on at the police station last night. For that, we're going to go to our reporter in the field, Sally McFields.

(click to show/hide)Scene 2
Yeah, thanks Tiffany. As you can see behind me here, it looks like the police office got smashed up a bit and they've made an official statement saying that they'll have a crew coming in a couple hours to repair the damage. Now, like always, the Sheriff did choose to remain anonymous but they did make a statement that there was indeed multiple attacks here last night. It is unclear at this time whether their targets were the Sheriff or the suspect in for questioning, Chiyachan, but it would seem that everyone managed to make it out of this extremely stressful ordeal unharmed.
It is said that shots were fired but there are no suspects and anything else is just speculation at this time. Tiffany, back to you.

(click to show/hide)Scene 3
Thanks, Sally. While we were just live at the scene we've been receiving word here at the station of more gruesome events that occurred here in BakaTown sometime late last night.

(click to show/hide)Scene 4
It would seem OniSamurai committed Seppuku last night. Some of his friends and family were present at the time and said it came out of nowhere. He just stumbled around and his eyes glazed over, and then the next thing they knew he'd pulled out his katana and impaled himself mumbling some crazy nonsense.
Support workers rushed to his residence, but he was pronounced dead at the scene. Family members speculate that possession may have been involved.

(click to show/hide)Scene 5
We have some more breaking news coverage for you this morning and for that we're going to take you to our reporter on the scene, Tasha Pharoah.

(click to show/hide)Scene 6
Yeah, as you can see behind me it looks like 1000mAh was stabbed to death in their sleep after an apparent sex change operation. There doesn't appear to have been any struggle and there is only the single knife wound present. Authorities have found no evidence and suspect that this was the work of the Serial Killer. There's nothing else to report on this end, back to you Tiffany.

(click to show/hide)Scene 7
Thanks, Tasha. That's it for our breaking news coverage this morning. For any viewers at home that missed last night's news, the voting results of yesterday's lynching decision are in and it seems maddoctor was lynched yesterday after an overwhelming lynch vote in their favor. And now, a message from the Major.

(click to show/hide)Scene 8
Hey guys, we've received a lot of feedback here at City Hall about there not being enough hot near naked male bartenders. Well, that's just plain wrong. There's actually an entire quarter of the Town Hall facility itself dedicated to entirely female preferences of strip clubs, bartenders and bar themes.
It's a big facility and I guess people just get lost and confused, I know I do sometimes... But, just go to one of the Kiosks located throughout the facility and you'll be able to find directions to the all male entertainer section of the facility. You can't miss it... you're gonna know when you're there. I know I spend a lot of time there personally. Several of my latest se--.. um, oh... it looks like my assistant is signaling to me... What..? I can't read lips... "Dd-on't... talk... about... sex... tapes..."
Oohhh.. aha... ah... ahaha...
Right, well... there was still no clear decision last night on what drinks to serve. It seems that a "Wet t-shirt, no panties" contest has been proposed however, and that will be the sub-item of tonight's vote. Of course, the main topic is who to lyncharoo!
Huh..? What? Oh, I can't say that..? Oh, whatever... you guys are just a big bunch of party poopers!
You know what, I don't have to listen to you because I'm a Princess, and I can just call my mommy! And you're just a big bunch of meanies!---

(click to show/hide)Scene 9

(click to show/hide)Scene 10
--yeah, they are really big... I had this really sexy stripper last night. He pulled down his thong and omigod it was soooo-- Whoa!! We're back on?!
Ahem... Right, well... For our female and male preferential audience, it's really very simple. It's kinda confusing when you go in there, but when you get to the elevators if you look on there it's actually not just 2 floors. You can go down 1 level and that's the mixed male and female performer level and if you go down 2 floors, that floor's entirely dedicated to male performers and there are a ton of hotties down there.
There really are.
You go there, Hidea?
All the time.
Oh, wow... I didn't know that. Right, well anyways... We're going to go to a reporter in the field for today's lynch vote.
I swing both ways.
Oh, really?

(click to show/hide)Scene 11
Wow, really Hidea? That's hawt. Oh, thanks Tiffany! I'm here at Town Hall in the voting lounge. It looks like everyone's getting ready to cast their votes.
Sir, can I get your comments on who you'll be voting for next? Also, your thoughts on the "Wet T-Shirt, No Panties" contest also on the ballet tonight?

(click to show/hide)Whew! This one took me 4 hours.

Votes:
tomoya-kun = x
TightMuffin = xx
maddoctor = xxxxxxx
Arc Da Rat = x
Borror0 = x
harpy = x
shabutie = x
suhaib = x


Player List:
tomoya-kun
harpy
shabutie
maddoctor
Meomix
Arc da Rat
ilkaid
scotsman
1000mAh
flyawave
Soulreaper77
OniSamurai
TightMuffin
Borror0
vuzedome
suhaib
Chiyachan
[/spoiler]

--- End quote ---

and


--- Quote from: tomoya-kun on September 29, 2010, 02:11:12 AM ---I vote on tight muffin, as he had 2 votes in the last round.

This vote has been invalidated

« Last Edit: 29 September 2010, 05:32:03 by tomoya-kun »

--- End quote ---

It's actually more than 19 minutes. I accidentally took the post time and not the edit time.

Tiffanys:
Day 3

Scene 1
Good eve, subjects. Your Queen has arrived.
I trust little Mimina has treated you well. How cute she is.
Ah, well... It would appear there have become affairs which will have been dealt with soon enough.
Magics forbidden at the turn of the 13th century. Though, it would seem they had not been forbidden quite well enough.
Oh, it's a real bother... But, what's a Queen to do?
Oh! I know. How about we just kill them? That seemed to work pretty well in the past. Or did it..? Hmm... there does seem to be that little issue with it cropping up again.
Well, I suppose it can't be helped.
The Werewolf Chiyachan. Be taking that one, we will. Perhaps a public execution is in order? Those are always fun.
Doesn't everyone just love a little death in the morning? I know I do.
You humans are so drab... Lynchings? Uck! You'll have to get -5 style points for that one, little boys and girls. Where's the style? ugh... The world's not what it was 4 centuries ago.
Oh, it was nice... mass impaling... public torture, stretchings, crucifixions, iron maidens, witch burning... Ohh, witch burning... I think I like that one!
So, Ophelia dear, get on with it, would you?
Oh, and Mimi, sweetie... come play with mommy.

(click to show/hide)Scene 2
It is so, my Lord.
Chiyachan, you have been found guilty of high crimes against the Vampire Kingdom. You have been sentenced to death. Do you have anything to say in your defense?
AHHHHHHHHHHH!!!!!!!!!!!!!!!!!!
No? Very well. Let it be known, at 6:35 PT on September 30th, in the year of our Unholy Queen Dracul, your sentence has commenced. It shall go on until such a time that... Oh, who am I kidding? Everyone knows you can't burn a Werewolf to death. You're in for some fun.
Now Tiffany, the news?  :)

(click to show/hide)Scene 3
...................................

(click to show/hide)Scene 4
In other news... If you missed it yesterday, the lynching vote was extended and then canceled entirely by the Queen of the Vampire Kingdom to allow for an internal investigation by the Vampiric Secret Forces. Well, it appears their investigation has finished. But luckily for us, it turns out Chiyachan was a Werewolf. And... what you just witnessed was the execution of Chiyachan.
That was an execution, right?
Well, they're probably actually going to let Chiyachan burn like that until they get bored.
I'd just like to remind our viewers at home that you are subject to Vampiric Law and their punishments tend to be a lot more severe than human law. You can pick up a copy of the laws at the Book Store in Town Hall.
But, it looks like we have some more breaking news for you today, and for that we'll be taking you to our reporter live on the scene, Sally McFields. Sally.

(click to show/hide)Scene 5
Thanks Hidea. Well, as you can see behind me here, it looks like the adorable TightMuffin was murdered in her sleep last night. It definitely looks like the work of the Serial Killer. Hidea, back to you.

(click to show/hide)Scene 6
Thanks Sally. It looks like my co-anchor has regained her composure and will be joining me again.
Thanks Hidea. Well, it looks like there was no Demonic possession last night. But rumors would have it that there was quite a lot of activity going on at the ilkaid house.
In other news, Soulreaper77 was called in for questioning last night and despite the lynch vote being canceled yesterday, the "Wet T-Shirt, No Panties" decision passed almost unanimously and will be taking place later today. We're going to take you to Town Hall now live for that, where our Major, Princess Mimi Dracul will be covering that. Tiffany and I will be joining her shortly.

(click to show/hide)Scene 7
Mimi Dracul here, getting right into the action! We're all having a lot of fun here at the "Wet T-Shirt, No Panties" Contest. As you can see, I'm competing myself. There's a lot of familiar faces here like Arc Da Rat and others, and I'll be covering the event all night.
But, it looks like we're going to our only reporter not participating in the contest for coverage of tonight's lynching decision. After that, we'll be broadcasting the contest live nationwide for the rest of the evening. Ilya, over to you.

(click to show/hide)Scene 8
Hey, you. Hurry up and vote so I can go play with my onee-chan. If you don't, my Berserker here might accidentally kill you.

(click to show/hide)Votes:
N/A
Chiyachan admitted to game manipulation by having forum Staff change signatures. As such, they have been removed from the game. I don't want to ever see anything like this again or I'll just stop hosting games all together.

Further gameplay will proceed as usual.

Player List:
tomoya-kun
harpy
shabutie
maddoctor
Meomix
Arc da Rat
ilkaid
scotsman
1000mAh
flyawave
Soulreaper77
OniSamurai
TightMuffin
Borror0
vuzedome
suhaib
Chiyachan

scotsman:
So now 3 vampires, 1 werewolf?, a serial killer and a demon. I would say poor Muffin and apologize for suspecting you but you probably deserved it....

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