Solve this problem

[Sasaki Kojiro]

Since we often talk about logic in mafia games I thought I'd post some puzzles. Here's a starter problem:

Four cards are presented: E, C, 2, and 5. There is a letter on one side of each card and a number on the other side. Which card(s) must you turn over to determine whether the following statement is false? "If a card has a vowel on one side, then it has an even number on the other side."

*******

If you've heard the problem before, give other people a chance to answer.

[Lord Winter]

Spoiler Alert, click show to read: 

It would have to be the E, right? Since all others would prove nothing. Seems to simple though

[Gaius Scribonius Curio]

Spoiler Alert, click show to read: 

E, obviously.

And I think 5 as well. If its reverse is a vowel that would prove the statement false.

[Askthepizzaguy]

Spoiler Alert, click show to read: 

You must turn over E, C, and 5

If ANY of the cards have a vowel (besides the 2) on the OTHER side, then the statement is false,
and if the 2 does not have a vowel on the other side, it doesn't matter. It only asks about the status of the vowel cards, and if the card with the 2 has a vowel, that wouldn't prove the statement false either.

You need to determine what the status is of all the cards that do not have an even number facing up to determine if the statement is false.



Edit: Nevermind I was wrong, it states that all the cards have a vowel on one side and a number on the other

[Sasaki Kojiro]

Three replies three different answers

One of you is right...here is the problem in a different form:

Let the cards show "beer," "cola," "16 years," and "22 years." On one side of each card is the name of a drink; on the other side is the age of the drinker. What card(s) must be turned over to determine if the following statement is false? "If a person is drinking beer, then the person is over 19-years-old."

[Strike For The South]

Spoiler Alert, click show to read: 

beer and 16 years

[Askthepizzaguy]

Three replies three different answers

One of you is right...here is the problem in a different form:

Let the cards show "beer," "cola," "16 years," and "22 years." On one side of each card is the name of a drink; on the other side is the age of the drinker. What card(s) must be turned over to determine if the following statement is false? "If a person is drinking beer, then the person is over 19-years-old."

Spoiler Alert, click show to read: 

beer - unknown age (side opposite)
must turn over to prove false.

cola - unknown age (side opposite)
do not need to turn over to prove false (only concerned with beer drinker's ages)

16 years - unknown beverage (side opposite)
must find out what they are drinking

22 years - unknown beverage (side opposite)
Does not matter what they are drinking, because they are over the proper age.



So.... The beer card and the 16 year old card.

[Yoyoma1910]

E & 5, Beer & 16.

[Sasaki Kojiro]

Yup, you guys got it. Posted it because my instinct was to make a snap judgement of "A and 4", which seems perfectly correct until you take a second look. Peoples instinctive method of testing the rule is to look for examples that would fit the pattern when actually they should be looking for examples that disprove the rule. Seems to relate to mafia on some level.

[GeneralHankerchief]

Problem of induction all over again.

[Askthepizzaguy]

Ya know, if I had only read the danged instructions properly the first time, I might have gotten that.
I mistakenly thought that the cards could have had anything on the other side of them. Read, read, read...

There is a letter on one side of each card and a number on the other side

[boudica]

Yup, you guys got it. Posted it because my instinct was to make a snap judgement of "A and 4", which seems perfectly correct until you take a second look. Peoples instinctive method of testing the rule is to look for examples that would fit the pattern when actually they should be looking for examples that disprove the rule. Seems to relate to mafia on some level.

Interesting point. So while looking for 'scummy' behaviour perhaps what we should really be doing (as townies) is beginning the game by assuming that EVERYone else is mafia and seeking out evidence that disproves that assumption.

Sorry if that's stating the obvious... I'm still new to mafia

I didn't get the question right until the second example btw. I thought I was being clever by only turning over 'E'.

[Sasaki Kojiro]

Interesting point. So while looking for 'scummy' behaviour perhaps what we should really be doing (as townies) is beginning the game by assuming that EVERYone else is mafia and seeking out evidence that disproves that assumption.

Sorry if that's stating the obvious... I'm still new to mafia

I didn't get the question right until the second example btw. I thought I was being clever by only turning over 'E'.

Really what I think it says is to watch out for confirmation bias. If you think someone is scum and you read over your posts and just look for things that would confirm your assumption--things they've done that are scummy--you might miss something that makes them look innocent.

For example, looking at andres and saying:

1) Andres seems innocent
2) If andres was mafia he would try and appear innocent and is capable of doing so
1) If Andres were mafia he would still be alive because he can't nightkill himself
2) Andres is still alive

3) Therefore Andres is mafia.

When really you should be looking at:

1) Mafia don't usually put themselves on the chopping block
2) Andres didn't break the tie when he was tied

Of course in mafia there is much less certainty. The second set doesn't disprove the rule, and the first two arguments taken together (that Andres appears innocent and yet hasn't been killed) still counts as a legitimate argument. But you have to weigh everything together, not just look at the arguments against.

[Askthepizzaguy]

What about a dual approach?

If you take the strategy of assuming everyone is possibly guilty, and then trying to find stuff that makes them appear innocent, then a clever mafioso will do whatever they can to appear innocent and be no longer considered a top suspect.

If however, you ALSO take the strategy of looking for telltale scummy behaviors, behaviors you can question and pressure someone about, then you could specifically target those who are acting out of sorts, even if they are making a big show of being a townie.

I am not blind to the lesson; indeed Sasaki's approach has at least as much merit as the opposing method. I do suggest that both approaches are not foolproof, and even better might be to do both. Read the thread from a "reduce the number of suspects" point of view, make your suspect list, and then read the thread from a behavioral/analytical standpoint looking specifically for scummy behavior to add a person to the list (starting at the standpoint of everyone is possibly guilty, but innocent until proven so)

Then, you could merge the two lists and go after certain people; using context of the thread and your experience to prioritize the suspects.

Any merit to this approach?

EDIT: Apparently I just reworded your argument, Sasaki... lol so of course you agree.

[Yoyoma1910]

Comrade Pizza, to the Gulag with you.

[Pannonian]

Really what I think it says is to watch out for confirmation bias. If you think someone is scum and you read over your posts and just look for things that would confirm your assumption--things they've done that are scummy--you might miss something that makes them look innocent.

For example, looking at andres and saying:

1) Andres seems innocent
2) If andres was mafia he would try and appear innocent and is capable of doing so
1) If Andres were mafia he would still be alive because he can't nightkill himself
2) Andres is still alive

3) Therefore Andres is mafia.

When really you should be looking at:

1) Mafia don't usually put themselves on the chopping block
2) Andres didn't break the tie when he was tied

Of course in mafia there is much less certainty. The second set doesn't disprove the rule, and the first two arguments taken together (that Andres appears innocent and yet hasn't been killed) still counts as a legitimate argument. But you have to weigh everything together, not just look at the arguments against.

Have there ever been any double takes in org Mafia games? Ie. people making themselves look scummy because real mafia don't look that scummy. In my first TWC game, out of 4 guesses, I managed to identify the 3 scum, using fairly standard parameters. Conversely, in my last GH game, I didn't bother to make myself non-scummy, and got my only execution, resulting in my user title. Have there been any real scum who deliberately made themselves look scummy?

[Sasaki Kojiro]

I don't recall. It's certainly not common on the org, because we quickly lynch people who act scummy. This in turn makes it less likely that a mafiosos would try, which increases the reward if they did try it and got to the position ylc did last game--but it's still a lower percentage play than just doing it straight.

If you take the strategy of assuming everyone is possibly guilty, and then trying to find stuff that makes them appear innocent, then a clever mafioso will do whatever they can to appear innocent and be no longer considered a top suspect.

I don't think you should do that though, I'm just saying you have to consider both the evidence against someone and the evidence in favor of them. When you reread someone's posts it's because you think they're guilty, and confirmation bias would be just picking out the posts that fit your theory.

[Askthepizzaguy]

Acting scummy, as a scum:

I intentionally made myself a top suspect as a mafia in Prometheus, and after I died, I went into full on scummy mode. What I did was I played the talkative, accusatory inquisitor and even under repeated threats of death I did not alter my strategy. It took 4 turns before town decided I was more trouble than I was worth.

I never intended to survive the game, my intention was to be a distraction, and that's where I succeeded. Early on people had locked onto seireikhaan as a suspect, Ichigo in particular, and others followed suit. I forget when, but Reenk Roink had also become a suspect in many people's minds, and both had come close to being lynched.

I accused seireikhaan of being mafia, and I had an adversarial relationship with Reenk Roink. Finally, town lynches me, and I "reveal" that I am the leader of this cult, and that we are a cult of virtue and enlightenment. My argument was so convincing, a townie decided to seriously entertain my stated explanation for the game, and instead of seireikhaan that round there was a huge bandwagon on Chaotix.

Later, YLC had started to tell the town to look for clues in my posts, and that immediately made him a suspect too, and he was the final lynch.

My teammates deserve most of the credit; seireikhaan had asked me to be my usual supertownie self and gave me good advice, and had been one of the masterminds behind Reenk's role reveal which kept him alive for an astounding number of rounds after we had died, and Reenk's solo performance was outstanding. My small part was simply this: Distract town as long as possible, and after my death, use the powers of persuasion to get town to kill themselves even though they knew I was a scum. I had no idea if it would work, but amazingly it did for at least one townie, and that did delay seireikhaan's death for a few rounds.

Here's some of the quotes in the early game:

Spoiler Alert, click show to read: 

Re: pizzaguy: if a maff would go to the lengths this guy has gone to camouflage his true role, we have a new, excellent player/liar. I'd leave him alone for awhile.

Pizza is being awfully helpful for a townie in day 1. I really hope you are just a helpful townie.

Damn. Talk about walls and walls o' text. Pizzaguy's going overboard...

Dont know who to vote. But I doubt its Pizza.

I said I dont think its pizza guy.. Theres no reason to change my vote just yet.. I could go for TB but I wanna actually make my vote count.

Wasnt it Pizza guy in first place who brought up the idea that mafia has been converting people? Thus there should be three mafia supporters? If pizza man is one of the baddys why bring it up? Sure it could be reverse psychology and for that he must be lynched eventually, but why lynch a guy whos been at least providing ideas more then most of you when more then half of us are still alive?

If we can avoid the woggs then I say we wait few more phases before we decide the fate of the Pizza guy.

YLC's reaction when I finally died... town chose between me and chaotix for the tie, and was frankly surprised I was scum.

Spoiler Alert, click show to read: 

Hmm, well, now it's my turn, I had my suspicions while I talked to him, but that was it. I'll understand if the town comes down on me for being unwittingly involved, I happily accept your votes in any attempt to clear my name . I just wish I listened to my mafia sense when he first began mentioning a cult, I know he plays ballsy, and I even called him out on it several times, just wish I had followed my instincts. Remember that from now on, Pizzaguy plays ballsy from now on...

And my postmortem speech;

Spoiler Alert, click show to read: 

A letter is found, written in the blood of Askthepizzaguy

To all who seek knowledge;

The harmonious order of the universe will never accept the continued destruction propagated by the land rapists. Polluters and thieves, your time is at an end. Your crimes against the light are greater than you could ever possibly imagine. From out of the light you were conceived, and from that light you were granted food, shelter, and a land which yielded everlasting harmonious life to you. From these glorious gifts, you have taken, and taken, and now you take more than you deserve. You have upset the natural order, come into conflict with the harmonious light, the logic and wisdom of the universe itself. With every rock you disturb, every ounce of water you pollute, every cubic centimeter of poison you spew into the air, and every resource you plunder from nature, you take for yourself that which does not belong to you. You have altered the climate and unbalanced the ecosystem, and now you seek to spread your selfish and chaotic system into other spheres, other untouched places. Like a virus, a plague, a mass of locusts, you take all that there is to take from an environment and then when everything has been harvested, raped, and destroyed, you move on, leaving nothing of value in your wake. You do not even thank the natural world for the things which you consume and destroy.

But fear not, for you will be purified by the light. It is inevitable, and that is what gives me peace. I know that my body and my soul have become one with the harmonious order, and that even in death, my place is part of nature. You may struggle, but your inevitable death brings you closer to the light, closer to the harmony of the universe. It is not too late for you. You can still join the glorious light voluntarily, if you so choose. All you have to do is remain still, remain passive. No harm will ever come to you. The others who struggle in their madness will be calmed, and become at peace. Then they will join you. If you stay inside your quarters and do not speak, and do not take up arms, and do not continue to resist us, the forces of logic and nature will overcome the cluttered minds aboard this vessel. The ones who follow the ways of selfishness, who take without giving back, who contaminate the natural order and who spread the illogical vision of a humanocentric universe, who are so single-minded as to continue on their journey towards the harmonious moons of Jupiter, on a mission to steal and take what does not belong to them... they will become enlightened, or they will be swallowed up by the glorious light.

I have so much more to teach you, but my shell is about to be captured. It will rejoin the glorious light soon enough. My followers will help me spread the teachings of logic, of harmony with nature, and of our great faith, well beyond the existence of my own mere consciousness. I trust that those with an open mind will hear what I have to say, and take my wisdom to heart. It is with love and with open arms that I welcome you all into the glorious enlightenment. I will wait patiently for you all to see the light.

All my love and logic are yours. Share in the light with me.

Note the bolded part. The entire speech is a subtle argument to let the mafia win. And then:

Okay, everyone. I have been speaking with the scum ATPG, and I believe I have learned something from his words, although he mentioned nothing directly and I was left to infer this for myself. No, I have not been converted.

In the very first sentence of this thread, Crazed Rabbit mentions that there is a gameplay mechanic that is not found in traditional mafias. This could simply be the convert mechanic that the mafia employs, however this has happened in other mafia games. Rather, I think that it is possible that there's no town victory condition. That if, in the event we do defeat the mafia, our load of precious chemicals will wind up being used for nukes or something, and we'll blow up the Earth. Then there'll be no winner, cause we'll all be dead. Perhaps the only way there can be a victory is if it is for mafia. And in that case, it would be in our every interest to join the mafia.

Now, I'm not saying that you should believe this, or even that I necessarily believe it myself. It's just, the more I think about it, the more it seems likely that CR would play a sick trick on us in the event that we won . That, and ATPG left me with a cryptic comment, although he could just as easily be lying: "If you would just lay down your arms, you would attain victory."

I think that we need to discuss this, and whether or not we want to follow it or not. Maybe we should have a vote on it.

And town's reaction:

Vote: Chaotix

You may be right that by saving the crew, we are dooming our planet BUT I'd rather stay alive then be killed by agents.
I intentionatly didn't read the Pizzaguy's testimony as I suspected it could be used to confuse us. Chaotix, you just jumped on it like a fly on rotten greens. Naive or a deliberate action? Quite frankly I don't care.

Unvote: Khaan Vote: Chaotix

Im sorry but way you talk.... Means that you are either agent or extremely unhelpful townie. You may be right about how we create something which could harm others. But that doesn't give the agents any reason to kill us. Some of us here are genuinely innocent. I know the oracle with out the weapon will always be ignored but still.. I really dislike your method.

Massive bandwagon, and chaotix dies instead of khaan. And for a time, Chaotix redeems himself because he is now convinced of my partner's guilt, but due to the fact that no one believed he was innocent anymore, they ignored khaan and Reenk.

And somehow, khaan and Reenk are let off the hook once again.

For future reference: what Aries is doing is just his play style. He's a joker/spammer, and you can never really be sure if he wants his side to win. He's doing exactly the same thing in the Simpsons Mafia.

YLC is the next to suggest people listen to my words, even if they don't believe them;

Spoiler Alert, click show to read: 

I'd like to voice something that has bothered me from the beginning, yet was never able to put words to it.

If the ecofreaks are able to convert, then why kill? Killing eliminates a possible convert, and incites said dead townie to become angry at them. A converted townie helps with voting and increase numbers, allowing the mafia to achieve their goal FASTER.

To me, this means several things -

The mafia either may only recruit so many,
The mafia actually lacks the ability to convert,
The mafia only has a chance to convert, where as they are guaranteed the elimination of a townie by killing them,
The mafia are highly experienced players, and are weeding out possible townie who would be bad for conversion based upon their lack of experience and susceptibility to being exposed, and expsoing those they associate with,
The mafia is highly inexperienced, and hasn't thought analytically about their position.

Also, reading through Pizzaguy's posts, I have come to a handful of conclusion, although I admit RR beat me to most of them.

1 - Do not bother trying to tell innocence from the write ups, where dealing with a cult like behavior who believe in something higher then themselves. As far as they are concerned, they will win, and that any sacrifice they make is better for the whole, thus they will be just as willing to be cyro-ed as town would.
2 - The words "Order, Balance, Harmony" continue to crop up in Pizzaguy's writings. Why? From what I gather, they hold significant importance. No other words are as repeated, for little or no reason, as these are. Pizzaguy is one to try to imbed clues, even if it is detrimental to his own side, in his writing.

3 - Also, as noted by Seamus and Reenk, Pizzaguy's tone changed significantly midway through the game. This leads me to believe he is a convert, and could have possibly been a protown role, which would explain his rather...revealing lynching. Thus, a thorough reading of Pizzaguy's posts, just before and just after, may reveal much information...if the town is willing to work for it.

And town's reaction:

*sighs* not another Chaotix please....YLC you just got FoS for talking about hippie-based crap....1 and 2 MIGHT be true but 3 is worthless....because Pizza guy being a Pro-town role? (then why kill shlin?) Just ignore all of Pizza guys posts....he only wants to confuse you....He is VERY tricky....and only wants his side to win by any means necessary

YLC and White_Eyes have an argument, and White eyes is convinced for the rest of the game that YLC needs to go. On the final lynch, the town chooses YLC over Reenk Roink, even though Reenk had revealed as a detective some 5 turns earlier and was still alive and "unable to investigate".

Like I said, most of the credit goes to my teammates, because all that bluffing wouldn't have done diddley squat had they not taken the ball and run with it to the endzone. Eventually the town had finally decided to ignore me, so I was only partly and marginally responsible for the win.

Still, there are times when acting scummy, as a scum, is to your advantage.

I think that was the second game I ever played in.

[Sasaki Kojiro]

OK here's another problem that mafia lessons can be drawn from:

"Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?"

Don't look it up...but don't bother putting your answers in spoilers.

[GeneralHankerchief]

Okay, looking at it logically... the second, unknown child has a 50% chance of being a boy, assuming no outside factors. However, we haven't accounted for the first (boy) child yet. It should come out to 75%, but I'm sure I'm missing something.

[Kagemusha]

50% If i flip a coin once. I have a 50% chance of getting heads. If i throw it twice. I still have the same odds.

[Andres]

Two children, only three possibilities: 1 girl, 1 boy, 2 boys, 2 girls.

At least one of them is a boy, so 2 girls is not possible. Only two possibilities left are: 1 girl, 1 boy or 2 boys.

50 % chance that it's two boys.



* Making abstraction from hermaphrodites.

[Reenk Roink]

0

It was predestined from eternity that Mr. Smith would have one boy, and probability was a false construct.

[Greyblades]

How about a riddle?

I am around long before dawn.
But by lunch I am usually gone.
You can see me summer, fall, and spring.
I like to get on everything.
But when winter winds start to blow;
Burr, then it's time for me to go!
What am I?

[Sasaki Kojiro]

Reenk is closest...lol.

[Chaotix]

Acting scummy, as a scum:

I intentionally made myself a top suspect as a mafia in Prometheus, and after I died, I went into full on scummy mode. What I did was I played the talkative, accusatory inquisitor and even under repeated threats of death I did not alter my strategy. It took 4 turns before town decided I was more trouble than I was worth.

I never intended to survive the game, my intention was to be a distraction, and that's where I succeeded. Early on people had locked onto seireikhaan as a suspect, Ichigo in particular, and others followed suit. I forget when, but Reenk Roink had also become a suspect in many people's minds, and both had come close to being lynched.

I accused seireikhaan of being mafia, and I had an adversarial relationship with Reenk Roink. Finally, town lynches me, and I "reveal" that I am the leader of this cult, and that we are a cult of virtue and enlightenment. My argument was so convincing, a townie decided to seriously entertain my stated explanation for the game, and instead of seireikhaan that round there was a huge bandwagon on Chaotix.

Later, YLC had started to tell the town to look for clues in my posts, and that immediately made him a suspect too, and he was the final lynch.

My teammates deserve most of the credit; seireikhaan had asked me to be my usual supertownie self and gave me good advice, and had been one of the masterminds behind Reenk's role reveal which kept him alive for an astounding number of rounds after we had died, and Reenk's solo performance was outstanding. My small part was simply this: Distract town as long as possible, and after my death, use the powers of persuasion to get town to kill themselves even though they knew I was a scum. I had no idea if it would work, but amazingly it did for at least one townie, and that did delay seireikhaan's death for a few rounds.

Here's some of the quotes in the early game:

Spoiler Alert, click show to read: 

YLC's reaction when I finally died... town chose between me and chaotix for the tie, and was frankly surprised I was scum.

Spoiler Alert, click show to read: 

And my postmortem speech;



Note the bolded part. The entire speech is a subtle argument to let the mafia win. And then:



And town's reaction:





Massive bandwagon, and chaotix dies instead of khaan. And for a time, Chaotix redeems himself because he is now convinced of my partner's guilt, but due to the fact that no one believed he was innocent anymore, they ignored khaan and Reenk.



YLC is the next to suggest people listen to my words, even if they don't believe them;



And town's reaction:



YLC and White_Eyes have an argument, and White eyes is convinced for the rest of the game that YLC needs to go. On the final lynch, the town chooses YLC over Reenk Roink, even though Reenk had revealed as a detective some 5 turns earlier and was still alive and "unable to investigate".

Like I said, most of the credit goes to my teammates, because all that bluffing wouldn't have done diddley squat had they not taken the ball and run with it to the endzone. Eventually the town had finally decided to ignore me, so I was only partly and marginally responsible for the win.

Still, there are times when acting scummy, as a scum, is to your advantage.

I think that was the second game I ever played in.

NOOOOOOO!

My inglorious past, back to haunt me again!



If it redeems me, I also was the one to peg Reenk for mafia early on, and kept having a scummy feeling about him long after his detective reveal.

EDIT: to answer Sasaki's second question, there's a 50% chance. Easy probability.

[Greyblades]

Edit: nevermind

[A Very Super Market]

Forgets it.

[Strike For The South]

33%

[Pannonian]

How about a riddle?

I am around long before dawn.
But by lunch I am usually gone.
You can see me summer, fall, and spring.
I like to get on everything.
But when winter winds start to blow;
Burr, then it's time for me to go!
What am I?

Shadow?