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 [quote="Dan"]Quick math problem because it's too late for me to think math and I should be writing a paper anyway: In Game Show Mafia Jadesmar made the 100th post. As a prize he got to pick a box, inside it was a new role. After assigning his role, the mod (LoudmouthLee) rolled a d3 for his allignment. LML explained that jadesmar had a 2/3 chance of being town and a 1/3 chance of being mafia. Mackay suspects that jadesmar's likelihood of being mafia is much greater now, estimated around 50%. I estimated that his initial odds of being evil were 6 roles out of 20 (4 maf, 2 SKs) which is roughly 1/3, giving him just a slightly higher chance of being mafia, not nealy 50%. The point is, we want to know what jadesmar's likelihood of being mafia is. We don't know much about the structure of the game yet, so here are some assumptions. Fact: The game started with 20 players. Assume: 1. That there are four mafia (for simplicity) 2. That there is at least one SK (possibly two) Not sure if this is a red herring but: It has been hypothesized that i00f jadesmar were mafia to begin with, he would remain mafia no matter what (switching to town would make no sense since he knew who all the mafia were), so the d3 role would be just for show, and he would in fact have the chance to change alignment only 80% of the time.[/quote]
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Lucky Wizard
Posted: Fri Apr 01, 2005 2:08 am    Post subject: 1

Furthermore, SKs tend to be on their own, so there's not necessarily anything stopping an SK from becoming Mafia later in the game. (The wiki at mafiascum.net , which is maintained by a number of GLers, has a page on them: http://www.mafiascum.net/cgi-bin/wiki.pl?Serial_Killer .)

In the other thread, Dan later said:

Dan wrote:
Um, I was trying to get you GOOD odds on being town, I still don't buy the odds the thread in VSP gave, because I'm not sure I explained the question well.

Hmm, the math looks like it fits the situation. Taking dybeck's second calculation: if we assume four mafia, that serial killers may switch, and that the roll is just for show if jadesmar is mafia, then we have three mutually exclusive possibilities:

-Mafia that remains mafia. This is simply 4/20, the probability that he was mafia before.
-Non-mafia that remains non-mafia. This is 16/20, the probability that he wasn't mafia, times 2/3, the probability that a non-mafia remained non-mafia, so we have 8/15.
-Non-mafia that becomes mafia. This is 16/20, the probability that he wasn't mafia, times 1/3, the probability that a non-mafia remained non-mafia, so we have 4/15.

If you want to also consider the possibility that he may be a serial killer whose role didn't change, then you can split up the "remains non-mafia" case into "remains serial killer" and "remains good guy"; in such a case, you'd be multiplying the probability that he was a non-mafia who remained non-mafia, times the probability that a given non-mafia would be a serial killer (possibly 1/16) or that a given non-mafia would be good (possibly 15/16).

This of course assumes that mafia can't become town; a later comment Dan made in the game thread,

Quote:
I think jadesmar currently has about 1/3 chance of being evil because the mod rolled a d3, simple as that.

would be true if the assumption was false, since the effect of the die roll would then be independent of his previous role.
LoudmouthLee
Posted: Thu Mar 31, 2005 5:23 pm    Post subject: 0

Tahnan wrote:
Ah, 14.5/20, right. Mind you, I have positively no idea what "SK" means, which is why I didn't factor its details into my calculations.

SK means Serial Killer, another evil role.
Tahnan
Posted: Thu Mar 31, 2005 5:08 pm    Post subject: -1

Ah, 14.5/20, right. Mind you, I have positively no idea what "SK" means, which is why I didn't factor its details into my calculations.
Posted: Thu Mar 31, 2005 1:35 pm    Post subject: -2

Ooh, my name in lights.

Anyhow, I have it on good authority that I'm not mafia. Thus, the probability of me being mafia is precisely 0%
dybeck
Posted: Thu Mar 31, 2005 12:15 pm    Post subject: -3

If there was an equal chance of one or two SKs, the numerators would still have to add up to 20 though...

(5.5/20) + (14.5/20)(1/3) = 31/60?

Having said that, I'd disagree that him being an SK before would preclude the idea of him switching alignment to a mafia family. I'd lay out a probability of

(4/20)+ (16/20)(1/3) = 7/15
Tahnan
Posted: Thu Mar 31, 2005 9:38 am    Post subject: -4

Urm?

If the roll necessarily mattered--and if what LML was announcing was the table he'd drawn up before rolling, as opposed to some sort of Monty-Hall-omniscient commentary on the result of the roll--then jadesmar's chance of being Mafia is now 1/3.

If the roll was just for show in the case that jadesmar was Mafia before--again assuming that LML was announcing the chances of the roll, as opposed to some post-roll result or the like--then his chances of now being Mafia, if you're right that it was previously 6/20, are (6/20) + (14/20)(1/3) = 8/15, slightly better than 50%.

If there's an equal chance that there was one SK or that there were two SK, then it'd be (5.5/20) + (14/20)(1/3) = 61/120, not quite as good but still better than 50%.
Dan
Posted: Thu Mar 31, 2005 8:04 am    Post subject: -5

Quick math problem because it's too late for me to think math and I should be writing a paper anyway:

In Game Show Mafia Jadesmar made the 100th post. As a prize he got to pick a box, inside it was a new role.

After assigning his role, the mod (LoudmouthLee) rolled a d3 for his allignment. LML explained that jadesmar had a 2/3 chance of being town and a 1/3 chance of being mafia.

Mackay suspects that jadesmar's likelihood of being mafia is much greater now, estimated around 50%. I estimated that his initial odds of being evil were 6 roles out of 20 (4 maf, 2 SKs) which is roughly 1/3, giving him just a slightly higher chance of being mafia, not nealy 50%.

The point is, we want to know what jadesmar's likelihood of being mafia is. We don't know much about the structure of the game yet, so here are some assumptions.

Fact: The game started with 20 players.

Assume:
1. That there are four mafia (for simplicity)
2. That there is at least one SK (possibly two)

Not sure if this is a red herring but: It has been hypothesized that i00f jadesmar were mafia to begin with, he would remain mafia no matter what (switching to town would make no sense since he knew who all the mafia were), so the d3 role would be just for show, and he would in fact have the chance to change alignment only 80% of the time.