tyler.durden
Well-Known Member
Wow, I'll bet you're right, but I still can't see how it works. Can someone explain it to me like I'm six?
Critical Thought Experiments
- Thread starter Heisenberg
- Start date
Wow, I'll bet you're right, but I still can't see how it works. Can someone explain it to me like I'm six?
cannabineer
Ursus marijanus
This one is conceptually very tough, because it violates a deep-seated bit of common sense that muddles our ability to correctly assign probabilities in a perturbed system. The hinge of it is, if you hold, you're gaining nothing from the discard. If you switch, you gain something. The discard is not random and is perturbing the outcome.
If you switch:
your first choice has one chance in three if being the winner.
If it is, you'll lose.
If however your first pick is a loser (chances two out of three), the remaining two boxes are one good, one dry. The leprechaun WILL discard the dry one. That's the kicker.
If your initial choice was dry, and you switch, you have a unity chance of getting the prize.
Thus, switching as a matter of routine raises your win chances to 2 out of 3.
The Wikipedia entry is informative imo. cn
https://en.wikipedia.org/wiki/Monty_Hall_problem
PeyoteReligion
Well-Known Member
Ah fuck, i was thinking along the same longs as tyler. It makes enough sense. Because i made my choice when three options were available, and sticking with that choice even though one was removed still leaves me with the same odds.
But like I said, that fucker is supposed to pay up just for catching him.
But like I said, that fucker is supposed to pay up just for catching him.
tyler.durden
Well-Known Member
Thank you, gentlemen, my mind is blown! This is the graph from your link, Neer, that finally simplified it enough for me to comprehend:
[TABLE="class: wikitable"]
[TR]
[TH]behind Door 1[/TH]
[TH]behind Door 2[/TH]
[TH]behind Door 3[/TH]
[TH]result if staying at door #1[/TH]
[TH]result if switching to the door offered[/TH]
[/TR]
[TR]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[/TR]
[TR]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[/TR]
[TR]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Car
[/TD]
[/TR]
[/TABLE]
It's amazing that thousand of Ph.Ds could not see this. I guess I was in somewhat good company. Good, stupid company
cannabineer
Ursus marijanus
Thank you, gentlemen, my mind is blown! This is the graph from your link, Neer, that finally simplified it enough for me to comprehend:
[TABLE="class: wikitable"]
[TR]
[TH]behind Door 1[/TH]
[TH]behind Door 2[/TH]
[TH]behind Door 3[/TH]
[TH]result if staying at door #1[/TH]
[TH]result if switching to the door offered[/TH]
[/TR]
[TR]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[/TR]
[TR]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[/TR]
[TR]
[TD]Goat[/TD]
[TD]Goat[/TD]
[TD]Car[/TD]
[TD]Goat[/TD]
[TD]Car
[/TD]
[/TR]
[/TABLE]
It's amazing that thousand of Ph.Ds could not see this. I guess I was in somewhat good company. Good, stupid company
Not stupid. I think this is a brilliant puzzle (and I'd +rep Heis for it if I could, but I need to suck off a few more unicorns first ... horny bastards) because it "catches" on a glitch in our ability to think probabilistically. cn
tyler.durden
Well-Known Member
Yeah, I can't rep the guy anymore, either. I haven't been this challenged in years, thanks for the lesson. I love this sub-forum...
PeyoteReligion
Well-Known Member
It's just counter intuitive. Damn preconceived notions! You guys would love this YouTube guy, his channels is called Veritasium. He covers tons of misconceptions that people have about all sorts of things, like where trees get most of their mass from. This guy wrote his phd on how to educate people with videos. He found that just telling someone "trees get most of their mass from air" they just to oh yeah I knew that, and the misconception strengthens. Instead he asks them, and most everyone forgets that plants inhale co2. Good videos if anyone is interested.
http://m.youtube.com/watch?v=RQaW2bFieo8
http://m.youtube.com/watch?v=RQaW2bFieo8
Heisenberg
Well-Known Member
Neer not only gave the right answer, he also saw the lesson behind it. Humans are great at pattern recognition, and terrible at probability assessment. The problem is, because of intuition, we feel we are skilled at judging probability. I am glad this sparked some conversation. It's nice to see people handle disagreement without taking it personally or feeling insulted.
I have not viewed the wiki page, but this is how my mind breaks it down.
When you pick the first box your chances are 1/3. The leprechaun takes one choice away. At this point we are more or less given a new choice, it's a new game. If you stay, you still have 1/3 chance because you are still playing the old game. If you switch, your new choice is governed by 1/2 odds. If during my new choice I pick the same box (essentially stay with my original) I am also staying with the 1/3 odds.
Another way to see it is, the leprechaun is essentially giving you a choice between a single box or a pair. He is saying you can have box 1 (1/3 chance) or you can have box 2 AND box 3. (2/3 chance) The fact that he showed one of the pair is empty offers no new information, you already knew that.
I have not viewed the wiki page, but this is how my mind breaks it down.
When you pick the first box your chances are 1/3. The leprechaun takes one choice away. At this point we are more or less given a new choice, it's a new game. If you stay, you still have 1/3 chance because you are still playing the old game. If you switch, your new choice is governed by 1/2 odds. If during my new choice I pick the same box (essentially stay with my original) I am also staying with the 1/3 odds.
Another way to see it is, the leprechaun is essentially giving you a choice between a single box or a pair. He is saying you can have box 1 (1/3 chance) or you can have box 2 AND box 3. (2/3 chance) The fact that he showed one of the pair is empty offers no new information, you already knew that.
Heisenberg
Well-Known Member
Lets see if you learned anything. You meet an old high school friend on the bus. You ask if He has any children, and he says he has two. You ask if he has any daughters, and he says yes. You now know that he has two children and one is female. What are the chances that he has two daughters?
I expect not all will agree on this one.
I expect not all will agree on this one.
PeyoteReligion
Well-Known Member
Fuck you got me again. Intuition tells me 50/50 boy girl. But clearly that didn't work before for me.
The only thing that makes me think he has TWO females is that you said "has any daughters, and he said yes." Daughters implies more than one, so that means 100% two girls?
UncleBuck
Well-Known Member
the part in bold seems to try to semantically preclude the next two parts.
but you could have a variety that seems to dabble in inside information from all areas, and the volume can be limited enough to preclude pure chance.
you are trying to assert an 'a priori' that can be explained by 'a posteriori'.
take that bullshit and go elsewhere.
i said good day sir.
I SAID GOOD DAY!
Heisenberg
Well-Known Member
You are right, the question is ambiguous, and it's meant to be. I am attempting show that numbers have their own internal logical consistency which sometimes conflicts with our logic. He may have meant daughters plural, but easily could have meant single. Say your life depended on it, would you think it's safer to assume he meant daughters plural, or forgo that assumption in favor of odds based on what you can know for sure?
PeyoteReligion
Well-Known Member
Ok help me with this guys. I told cannabineers situation to a friend, the island that catches on fire one that I solved. After I tell her that I start another fire on the island and take cover behind the new burn line, she points out that the size of the island was never specified and she assumed that it was small and thus not large enough to do such a task. I tell her the island size was not specified and that if you limited the size of the island to the point where setting a backfire is not safe, then you fail the puzzle.
Is this correct, or was she safe in assuming that the island was too small for that task? I think she failed because she assumed the size of the island. This is where over thinking comes into play, and I'm sure that's what stopped her from solving the problem.
Is this correct, or was she safe in assuming that the island was too small for that task? I think she failed because she assumed the size of the island. This is where over thinking comes into play, and I'm sure that's what stopped her from solving the problem.
UncleBuck
Well-Known Member
that possibility is not ruled out a priori.
you have not given me a four sided triangle or a woman taller than herself yet.
PeyoteReligion
Well-Known Member
I assume that he would say daughters if he had two. But we all know what assumptions make...
Also I'm making this assumption off very little evidence, so it is risky anyways.
Heisenberg
Well-Known Member
I had the same thoughts. The size of the island does seem to come into play. At some point it would be too small for a burn line to work, but then we wouldn't need to ask the question. The problem is, we the listener do not know that a small island moots the question.
UncleBuck
Well-Known Member
i was right. this scenario, however unlikely, is not ruled out a priori.
just semantical fapping.
your puzzle was bad and you should feel bad.
just kidding, i still love you.
Heisenberg
Well-Known Member
Well he just answered 'yes'. The question was, do you have any daughters. The only thing you can safely assume from that is he has at least one. You could infer he has two, and the chances of you being right would be...
PeyoteReligion
Well-Known Member
I think you nailed it, I was unable to point it out. If the island was too small it's a baited question. So we must assume its large enough for any situation. That's why I said she failed; because she failed to take into account that the island me be large. Seems she forgot Australia is an island/continant.
PeyoteReligion
Well-Known Member
Always 50/50. Unless he wears a fur cod peice that raises his average testicle temperature, making him more likely to have females.
