Quiz Time

[yord]

Mar 10, 2022 7:06:36 GMT happyhammerhead said:

.....

Funny thing is, when this was first posited, many prominent mathematicians utterly refused to believe it.

And,, they were correct, unless you have the ability to think outside the syntax of language, possess a very small but powerful magnet to stick over a box, or have plucked the infinite green cube of luck. The odds are an even 50 / 50

[happyhammerhead]

And you wonder why you haven't got a yacht...

[yord]

I did have one once, a very long time ago, along with a cherry red Fairthorpe sports car that quickly glanced at looked if it was capable of breaking land speed records, but was next to impossible exceed 40 mph without choking on the oil fumes seeping through the dashboard. OOhhh such is the spinning wheel of fate.

[ootlg]

To get the rules correct: 1) Is it the host's job to ensure the contestant loses? 2) Can the contestant choose to switch autonomously? 3) Is it at the whim of the host only, or 4) either? Because if the host doesn't offer the switch it's clear that you've picked the goat, whereas if he does offer the switch it's clear you've picked the car. Finally, if it's an autonomous decision the odds are 50/50 on the remaining two doors.

[flatandy]

The host only reveals one of the two remaining - goat filled - doors. He always offers the switch to the remaining closed door. He has no control over whether he offers or not.

The host's job is to get people to watch the show. The cost of the car is trivial to the cost of hosting and broadcasting the show and therefore keeping or losing the car doesn't matter to the host.

The contestant does choose autonomously.

Your odds are much better if you switch, because the host didn't eliminate a door randomly (otherwise sometimes he'd eliminate the car).

[mids]

That's a very good point- he only ever eliminates a goat door. Thinking about that, how could he manipulate it to be 50/50 after one door has gone? Switch from car to goat on each elimination?

[mids]

In subsequent games, that is.

[flatandy]

The host can't manipulate it to be 50:50

It's always 66:33

[ootlg]

The contestant chooses one door out of three. The host eliminates 1 goat door. That leaves 1 car door and 1 goat door. The contestant can choose to remain with the door he's chosen or not. Is that it?

[flatandy]

That is correct.

[mids]

But if it is the case that the host only ever eliminates a goat door, he could manipulate the results by only ever eliminating the car door.

[mids]

That's if thee contestant doesn't pick the car first.

[ootlg]

When the contestant started he had a 33% chance of winning the car. When the host removed a goat door the contestant then had a 50% chance of winning the car. I really don't see the problem here.

[Marshall]

Marilyn vos Savant was deemed the world's smartest woman. She had a column in the paper where people would ask her tough puzzles or questions and she'd reply.

This "Monty Hall" problem was put to her and she got a lot of flack for her answer (your odds are better to switch), even from math professors but was proven correct.

Here's a longer explanation of the answer:
priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/

[mids]

"the world's smartest woman"

Hehehe. Lucky you didn't post that yesterday.

[happyhammerhead]

Mar 10, 2022 17:25:25 GMT mids said:

But if it is the case that the host only ever eliminates a goat door, he could manipulate the results by only ever eliminating the car door.

Oh ffs... What's behind each door is set before the 'game' starts.

The contestant picks one, the host opens another (which always contains a goat), then asks the contestant whether they wish to switch from their initial choice, before that door is opened.

It's in your favour to switch. I know this from statistical analysis - there is a mathematical expression confirming it but pure maths... I admit to being a bit rubbish there.

[mids]

Ah, right got it. The host opens the door. I think I did know that initially.

[ootlg]

Mar 10, 2022 17:41:13 GMT Marshall said:

Marilyn vos Savant was deemed the world's smartest woman. She had a column in the paper where people would ask her tough puzzles or questions and she'd reply.

This "Monty Hall" problem was put to her and she got a lot of flack for her answer (your odds are better to switch), even from math professors but was proven correct.

Here's a longer explanation of the answer:
priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/

But the host doesn't open the door with the auto behind it, so all the examples given are unsound. The probability theory doesn't work if one of the three doors cannot be opened, ie., the host only opens a goat door.

QED

[Marshall]

I'll admit, I'm still missing something in the explanation. I don't see why your initial door stays at 33% chance while the other unopened one increases to 66%.

[flatandy]

Your choices are effectively:

(one door) (two doors)

That's really what it boils down to. You're effectively choosing both of the (two doors) by making the switch. Your host has made sure that if the car is behind either of the (two doors) it's behind the one left shut.