Comment by lijogdfljk | Hacker News Reader

Comment by lijogdfljk | Hacker News Reader

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Funny, i think (but am not arguing i'm correct) it does change probability when the doors change. As i explained[1] in the sister post.

Perhaps this is some mathematical concept? To me i'm viewing every choice as a dice roll. I have no question that the first dice roll was worse than the 2nd. However to me the 2nd is a die with two faces. Two choices, of which both are equally possible.

To look at it differently. The doors changing probability to me sounds like.. imagine two people, the PersonA has this primary scenario. They had 100 doors, chose one, and are then asked if they'd like to switch. PersonB then is asked the second question, of the 2 doors, which do they want? PersonA and B are standing next to each other. The doors are the same for both of them. Why would PersonA have different odds than PersonB? And how could PersonB's odds be any different than 50/50 with no prior history of the doors?

Is there some fundamental difference between the grand idea of probability and "reality" as i'm trying to describe it here?

[1]: https://news.ycombinator.com/item?id=31535557

> Funny, i think (but am not arguing i'm correct) it does change probability when the doors change. As i explained[1] in the sister post.

The probability that you have the winning door does not change when the 98 doors are opened. The simple reason for this is that it is always possible to open 98 doors without the prize regardless of which door you initially chose.

So it provides no extra information about your chosen door. But it does provide information about the single remaining door because in most situations, that specific door would need to have been opened.

> To look at it differently. The doors changing probability to me sounds like.. imagine two people, the PersonA has this primary scenario. They had 100 doors, chose one, and are then asked if they'd like to switch. PersonB then is asked the second question, of the 2 doors, which do they want? PersonA and B are standing next to each other. The doors are the same for both of them. Why would PersonA have different odds than PersonB? And how could PersonB's odds be any different than 50/50 with no prior history of the doors?

If PersonB saw everything happen, they have all the information PersonA has and therefore can make the same choice (99% correctly).

If PersonB came in after the door was chosen and the 98 doors were opened, (assuming they can't tell which door PersonA chose) their chance of picking the winning door is indeed 50%.

When thinking about probabilities, it is very important to think about the information that each person knows. The game master knows everything, so if they were playing their own game, they could win 100% of the time. PersonA can only win 99%. And PersonB can only win 50%. It all depends on what information you are given.

You pick a room 1/3 = %33

The other two rooms = %66

After host opens one of the rooms

The odds are still 33% vs 66%

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