P.I. and Monty Hall problem

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Romain672
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P.I. and Monty Hall problem

Post by Romain672 » 21 August 2020, 10:55

https://en.wikipedia.org/wiki/Monty_Hall_problem

Hi,

For those who doesn't know Month Hall problem, check my link, or read a variant below.
You have 100 doors in front of you, one of them is full of gold, 99 are empty. You choose one. It's the number 57.
Then, me, the presentator, open 98 empty room. I open all except 57 and 73.
Then, you have the choice between stick with your 57 door choice, or change it and goes to the 73 one.
The best choice is to change.


On P.I., I feel like sometimes we have the same problem.
But I got a lot of troubles for seeing it.
Am I wrong? Am I right?

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nmego
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Re: P.I. and Monty Hall problem

Post by nmego » 21 August 2020, 11:18

Can you provide an example, when does P.I. turn into a monty hall problem?

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RicardoRix
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Re: P.I. and Monty Hall problem

Post by RicardoRix » 21 August 2020, 11:19

You'll have to present the exact scenario in PI.

Occasionally you can get an equal choice, but yet one them has a cube of my opponent, and you think - did they choose that card to stop me picking it...?
I'd say there is a slight favour bias to that but definitely not all the time. In fact the last time it happened, it wasn't my character, so I goofed.

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Romain672
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Re: P.I. and Monty Hall problem

Post by Romain672 » 23 August 2020, 14:09

nmego wrote:
21 August 2020, 11:18
Can you provide an example, when does P.I. turn into a monty hall problem?
That's the problem. I initially though they were linked, but I got lots of difficulty to find an example, so it make me think it could be false.

Sometimes, you can have possibilities like AX, AY, AZ, BX, BY, BZ, CX, CY, CZ, DX, DY, DZ and EW.
And you can get informations which came from more than one detective, from lots of elimination, or from others players results which can change drastiquely the probability of that EW, which started to be unlikely.

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RicardoRix
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Re: P.I. and Monty Hall problem

Post by RicardoRix » 24 August 2020, 14:22

Well the thing is you're not choosing something to start with and then later finding out information to then change your mind.
So I don't think the Monty Hall problem is relevant.

Take the extreme - if it was A or B and you had a million pieces of evidence to say it might be A, but only 1 piece of evidence to say it might be B.
It just sounds like you've been spending too much time studying A and not B. Doesn't sound like the probability should change.

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Romain672
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Re: P.I. and Monty Hall problem

Post by Romain672 » 25 August 2020, 11:43

So that mean whatever results of detective and cards, all the possibilities for your investigation has equal probabilities?

This mean if you have possibilities AX, AY, AZ, and EW, there is 75% chance it's A, and 25% it's E?

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Romain672
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Re: P.I. and Monty Hall problem

Post by Romain672 » 25 August 2020, 11:59

Like, on my example, you have two differents main possibilities, the blue one, or the red one.

Red has 11 possibilities. Blue has 16 possibilities.
So all these probabilities are equal to 1/27? The blue one isn't more likely (than 16/27)?
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RicardoRix
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Re: P.I. and Monty Hall problem

Post by RicardoRix » 25 August 2020, 12:17

Almost completely lost.
This is definitely not related to the Monty Hall problem. It is a very interesting logic/probability question.
I don't know where you're getting your probabilities, Red has 11 possibilities for what?
And what does AX, AY, AZ, EZ mean?

Are you ignoring no crime/no suspect tiles?

Also why can't the 2 yellow investigators on the right both be pointing to Rusty say... or the top 2 for Knuckles, etc.

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diamant
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Re: P.I. and Monty Hall problem

Post by diamant » 25 August 2020, 21:02

At the beginning of a mini-game, your case is determined by the draw of 3 elements chosen respectively from 14, 12, 10 different elements. Which leads to 1,680 different cases.
However, you know the case of an adversary; also for the elements of your case, there remain only 13, 11, 9 possibilities. That’s 1,287 possible cases. If you try to solve your case at this time, without further information, you have only one chance in 1287 to guess its 3 elements.

The clues you get during the mini-game allow you to eliminate certain possibilities, but if the number of possible cases decreases, they remain equiprobable, even if this is not true for the elements that compose them, taken individually.

With the Month Hall problem, someone eliminates losing cases except for two cases, one of which you had previously chosen. Such a situation does not occur in this game.

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Romain672
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Re: P.I. and Monty Hall problem

Post by Romain672 » 27 August 2020, 15:47

RicardoRix wrote:
25 August 2020, 12:17
Are you ignoring no crime/no suspect tiles?
Nope.
RicardoRix wrote:
25 August 2020, 12:17
Also why can't the 2 yellow investigators on the right both be pointing to Rusty say... or the top 2 for Knuckles, etc.
Yeah I forgot those, mb :(
diamant wrote:
25 August 2020, 21:02
The clues you get during the mini-game allow you to eliminate certain possibilities, but if the number of possible cases decreases, they remain equiprobable, even if this is not true for the elements that compose them, taken individually.

With the Month Hall problem, someone eliminates losing cases except for two cases, one of which you had previously chosen. Such a situation does not occur in this game.
Thanks, that was exactly what I wanted.
That still seem so weird for me, I will have some difficulty to fully trust that but I will try :P

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