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Author Topic: Random Stuff Part IV  (Read 139437 times)

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GendoIkari

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Re: Random Stuff Part IV
« Reply #225 on: August 14, 2018, 06:00:46 pm »
0

Paul Erdos refused to believe the solution to the Monty Hall problem.

A lot of academics refused to believe it as well:
http://marilynvossavant.com/game-show-problem/

I didn't accept it at first either, but I at least wasn't a petulant little dick about it.

I ate crow when someone suggested expanding the puzzle to 1000 doors. Made me re-examine the math while acknowledging my blinders.

I still think it makes much more sense to ask what the probability is when you first pick, and realize that that probability doesn't change when the host opens another door.

But the exact problem is that so many people's intuition tells them that the probability does change as a result of getting new information. The trick is to make them realize that they didn't actually get new (meaningful) information.
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Donald X.

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Re: Random Stuff Part IV
« Reply #226 on: August 14, 2018, 06:36:34 pm »
+1

But you can just iterate through the cases. However counterintuitive it is, there's your answer. Why wasn't that enough for Erdos? It's a sad comment on how people work.
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ConMan

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Re: Random Stuff Part IV
« Reply #227 on: August 14, 2018, 07:29:43 pm »
+3

The one that I prefer is to rephrase the problem - you pick a door, then Monty asks you whether you want what's behind your door, or what's behind both other doors. Assuming the goat has zero value to you, then it winds up being the same result, which means you definitely get twice the chance of winning if you swap.
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Re: Random Stuff Part IV
« Reply #228 on: August 14, 2018, 07:54:42 pm »
+4

The funny thing is that, if the door that is revealed to have a goat was chosen randomly, then it doesn’t make any difference whether you swap doors or not, you have a 50% chance either way. It’s only because the host guarantees that he will open a door with a goat behind it that the odds are skewed in favour of swapping doors.
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Witherweaver

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Re: Random Stuff Part IV
« Reply #229 on: August 14, 2018, 09:08:22 pm »
+4

I once had an internship at this tech company, and the IT guy was trying to convince me that since it could either rain or not rain (two outcomes), the chance of rain was always 50% and weather reports were nonsense.
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Re: Random Stuff Part IV
« Reply #230 on: August 15, 2018, 03:08:11 am »
+2

The funny thing is that, if the door that is revealed to have a goat was chosen randomly, then it doesn’t make any difference whether you swap doors or not, you have a 50% chance either way. It’s only because the host guarantees that he will open a door with a goat behind it that the odds are skewed in favour of swapping doors.

*upvote*

That's exactly right. And if it is unspecified how the door was chosen, the problem actually doesn't have a right answer. Wikipedia acknowledges this (at least by now).

infangthief

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Re: Random Stuff Part IV
« Reply #231 on: August 15, 2018, 07:50:16 am »
0

I once had an internship at this tech company, and the IT guy was trying to convince me that since it could either rain or not rain (two outcomes), the chance of rain was always 50% and weather reports were nonsense.
You can extend that kind of reasoning to prove that there is life outside our galaxy.
Chance of Cows outside our galaxy? Don't really know, two options, call it 50%.
Chance of Pigs? 50%
Chance of Trees? 50%
...
Chance of lifeform n? 50%

Chance of none of them? Well that would be (0.5)^n, which tends to 0 as n increases.
Therefore it's pretty much certain there's at least one lifeform existing outside our galaxy... what do you mean 'they're not independent'?!
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Kuildeous

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Re: Random Stuff Part IV
« Reply #232 on: August 15, 2018, 09:14:54 am »
0

The funny thing is that, if the door that is revealed to have a goat was chosen randomly, then it doesn’t make any difference whether you swap doors or not, you have a 50% chance either way. It’s only because the host guarantees that he will open a door with a goat behind it that the odds are skewed in favour of swapping doors.

*upvote*

That's exactly right. And if it is unspecified how the door was chosen, the problem actually doesn't have a right answer. Wikipedia acknowledges this (at least by now).

There are reasonable assumptions you can make though. The puzzle presumes that this always happens in all scenarios. Since 2/3 of the scenarios would involve having the car behind one of the two doors, the revealed goat cannot be randomly chosen.

But if the scenario is such that the car can be revealed by the host, then that does imply that the door is chosen randomly.

It boils down to whether there are reasonable assumptions for the puzzle. Since this is based on a real event, has there ever been a case where the host reveals the car?
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Kuildeous

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Re: Random Stuff Part IV
« Reply #233 on: August 15, 2018, 09:19:08 am »
0

I still think it makes much more sense to ask what the probability is when you first pick, and realize that that probability doesn't change when the host opens another door.


I agree that it makes sense, but it isn't intuitive for many people. Even I refused to believe it. The math was right in front of me, but I was so certain I was right that I was ignoring what made sense and looked for evidence supporting my belief (so pretty much human politics). It took the hyperbole of several doors to make me question those beliefs and re-examine the probability. I was a lot more accepting of it at that point.
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infangthief

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Re: Random Stuff Part IV
« Reply #234 on: August 15, 2018, 09:57:22 am »
+1

The funny thing is that, if the door that is revealed to have a goat was chosen randomly, then it doesn’t make any difference whether you swap doors or not, you have a 50% chance either way. It’s only because the host guarantees that he will open a door with a goat behind it that the odds are skewed in favour of swapping doors.

*upvote*

That's exactly right. And if it is unspecified how the door was chosen, the problem actually doesn't have a right answer. Wikipedia acknowledges this (at least by now).

There are reasonable assumptions you can make though. The puzzle presumes that this always happens in all scenarios. Since 2/3 of the scenarios would involve having the car behind one of the two doors, the revealed goat cannot be randomly chosen.

But if the scenario is such that the car can be revealed by the host, then that does imply that the door is chosen randomly.

It boils down to whether there are reasonable assumptions for the puzzle. Since this is based on a real event, has there ever been a case where the host reveals the car?

It's the difference between the host saying:
(i) "I'm going to open this door here... oh look, there's a goat, that's interesting."
(ii) "I'm going to open this door here which has a goat behind it."

True, the host does always reveal a goat, so they are in fact doing (ii), but it might not be clear to a first-time viewer whether the host is doing (i) or (ii).
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sudgy

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Re: Random Stuff Part IV
« Reply #235 on: August 15, 2018, 10:10:44 am »
0

I once had an internship at this tech company, and the IT guy was trying to convince me that since it could either rain or not rain (two outcomes), the chance of rain was always 50% and weather reports were nonsense.
You can extend that kind of reasoning to prove that there is life outside our galaxy.
Chance of Cows outside our galaxy? Don't really know, two options, call it 50%.
Chance of Pigs? 50%
Chance of Trees? 50%
...
Chance of lifeform n? 50%

Chance of none of them? Well that would be (0.5)^n, which tends to 0 as n increases.
Therefore it's pretty much certain there's at least one lifeform existing outside our galaxy... what do you mean 'they're not independent'?!

No, you see, because our two options are whether there is life or not, it's just 50%!
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Kuildeous

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Re: Random Stuff Part IV
« Reply #236 on: August 15, 2018, 10:12:39 am »
+1

Is it wrong of me to want to change every reference of Chester A Arthur to Chester an Arthur?
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sudgy

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Re: Random Stuff Part IV
« Reply #237 on: August 15, 2018, 07:03:56 pm »
0

Does anybody have suggestions on things like Skype that are entirely browser based?  When I google I just get things like chat roulettes.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Awaclus

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Re: Random Stuff Part IV
« Reply #238 on: August 15, 2018, 07:53:25 pm »
0

Does anybody have suggestions on things like Skype that are entirely browser based?  When I google I just get things like chat roulettes.

You can use IRC with a web client.
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sudgy

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Re: Random Stuff Part IV
« Reply #239 on: August 15, 2018, 08:58:09 pm »
0

Does anybody have suggestions on things like Skype that are entirely browser based?  When I google I just get things like chat roulettes.

You can use IRC with a web client.

IRC has video chat?
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Mic Qsenoch

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Re: Random Stuff Part IV
« Reply #240 on: August 15, 2018, 10:33:26 pm »
0

Does anybody have suggestions on things like Skype that are entirely browser based?  When I google I just get things like chat roulettes.

Well there's web.skype.com, or Google Hangouts.
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Re: Random Stuff Part IV
« Reply #241 on: August 16, 2018, 08:05:13 am »
0

You can use discord entirely in browser. (That's what I do)
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GendoIkari

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Re: Random Stuff Part IV
« Reply #242 on: August 16, 2018, 10:26:42 am »
0

The funny thing is that, if the door that is revealed to have a goat was chosen randomly, then it doesn’t make any difference whether you swap doors or not, you have a 50% chance either way. It’s only because the host guarantees that he will open a door with a goat behind it that the odds are skewed in favour of swapping doors.

Right, this is the premise behind Deal or No Deal. Because each chest is opened randomly, you actually do gain new information with each opened chest, and the expected worth of your chest changes each time.
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Kuildeous

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Re: Random Stuff Part IV
« Reply #243 on: August 16, 2018, 11:36:00 am »
0

Right, this is the premise behind Deal or No Deal. Because each chest is opened randomly, you actually do gain new information with each opened chest, and the expected worth of your chest changes each time.

And the mathiness of Deal or No Deal is pretty neat too. Not as controversial as Let's Make a Deal obviously.

Fun fact: I happened across the show while flipping channels and got sucked in by mistake. The contestant was deciding which box to open, and her family was behind her encouraging her to take her time in making such an important decision. So much math rage that day.
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GendoIkari

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Re: Random Stuff Part IV
« Reply #244 on: August 16, 2018, 11:42:45 am »
0

Right, this is the premise behind Deal or No Deal. Because each chest is opened randomly, you actually do gain new information with each opened chest, and the expected worth of your chest changes each time.

And the mathiness of Deal or No Deal is pretty neat too. Not as controversial as Let's Make a Deal obviously.

Fun fact: I happened across the show while flipping channels and got sucked in by mistake. The contestant was deciding which box to open, and her family was behind her encouraging her to take her time in making such an important decision. So much math rage that day.

I think those types of things are more people being bad with superstition than people being bad with math. They feel like a certain number is a lucky winner (or loser); not that a certain number actually has a mathematically better chance.
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Re: Random Stuff Part IV
« Reply #245 on: August 16, 2018, 02:25:24 pm »
+3

Hi, I am using this thread to unlock my full potential as a forum user.

To distract you from my true purpose I will distract you with a depressing thought:

The average person spends 6 months of their lifetime waiting on a red light to turn green.

Now I will back myself out of this conversation...
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Awaclus

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Re: Random Stuff Part IV
« Reply #246 on: August 16, 2018, 03:01:28 pm »
+2

Hi, I am using this thread to unlock my full potential as a forum user.

To distract you from my true purpose I will distract you with a depressing thought:

The average person spends 6 months of their lifetime waiting on a red light to turn green.

Now I will back myself out of this conversation...

I've already spent 9½ months of my lifetime shitposting on f.ds, it's not that depressing in comparison.
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fisherman

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Re: Random Stuff Part IV
« Reply #247 on: August 16, 2018, 03:16:35 pm »
+3


The average person spends 6 months of their lifetime waiting on a red light to turn green.



Once we waited for a stop sign to turn green...
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silverspawn

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Re: Random Stuff Part IV
« Reply #248 on: August 16, 2018, 03:22:52 pm »
+1

That's almost certainly untrue when taken literally. The median person doesn't own a car. It might be true when we restrict it to just a few regions.

Awaclus

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Re: Random Stuff Part IV
« Reply #249 on: August 16, 2018, 03:28:35 pm »
+4

That's almost certainly untrue when taken literally. The median person doesn't own a car. It might be true when we restrict it to just a few regions.

Pedestrians also wait for red lights to turn green.
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