A logic problem

[Sgt.Squarehead]

Still reading.....I'm into the references now. 

Edited January 23, 2022 by Sgt.Squarehead

[Bulletpoint]

Another way to explain this is to imagine there are not only three doors, but one thousand doors. You pick one, then the host opeens 998 doors and they are all empty. Would you then switch?

Edited January 24, 2022 by Bulletpoint

[BornGinger]

This is the funniest thread so far. Keep them posts coming.

[Amedeo]

Another way - I mean, without doing the math - to understand that the counterintuitive answer to the Monty Hall problem is true is with an empirical test. You only need a collaborating partner and three game cards, one of which is, say, an ace. Then just play the game "guess where's the ace" a hundred times, twice. The first time without changing your original choice, the second time always switching cards and record the relative frequencies both times. You will see that the frequencies will approximate the probabilities given above.

23 hours ago, Suchy said:

@Sgt.Squarehead

 

This is a well-known mathematical problem. The solution is also perfectly known. civdiv is right although intuition suggests otherwise. But strict probability calculus is absolute. Don't forget that the knowledge of the person opening the curtains and knowing from the beginning what is behind each curtain also comes into play. This person opens one of them because he knows beforehand that it is empty.

This.

Classical probability is a measure of our ignorance, not a measure of an objective property of a system. If our knowledge changes, so does probability. This is in contrast to what happens in quantum mechanics where probability seems to be ontological rather than epistemic (actually it depends on the interpretation but... well, let's not start another OT in what already is an OT ).

[ratdeath]

My problem is that behind every door is a CM family I want to play but can't really choose one at the moment. Almost tempted to take the backdoor to yesterday and install CMBB!

[herr_oberst]

20 hours ago, ratdeath said:

My problem is that behind every door is a CM family I want to play but can't really choose one at the moment. Almost tempted to take the backdoor to yesterday and install CMBB!

Oh the good ol' days... and quite possibly the gamiest move ever conceived by man...

In CMAK, on a dry desert map, buy 2 or 3 of the fastest tracked vehicles your side allows.  In front of your advancing forces, run those vehicles back and forth to create a dust cloud the width of the map...

Your opponent has no idea how much of what you have advancing.  Sheer genius!!!

 

Quantum that!  

Edited January 26, 2022 by herr_oberst

[A Canadian Cat]

On 1/23/2022 at 1:43 PM, civdiv said:

The simplest way I can explain it is that with your first choice you have a 33% of picking the right curtain, so the chance is 67% you are wrong. Since your choice is now binary, changing your choice flips the odds. So you aren’t flipping 50/50, you are flipping 33/67.

Yep, this. Although I also like the 1000 doors example. The host is giving you more information by opening a door - they always open the door that does not have the prise.

My only nit pic is this is not a logic problem its a math problem - probabilities to be specific. But that's just being pedantic.

[Sgt.Squarehead]

I'm amazed at how easily I missed the obvious in this problem, ie: that the only chance of Monty offering you an empty box as an exchange would be the 33.3% chance that you picked the correct box in the first instance. 

Damn it's so obvious to me now, it's embarrassing!