Monty Hall Problem has struck again

[Gunny]

When the choice is three doors, you have a 1 in 3 chance of picking the right door or a 33.3% chance of being right. When the choice is then narrowed to two doors, it seems logical that you now have a 1 in 2 chance of picking the right door or a 50% chance of being right.

But then I guess I'm jaded because I am always aware that, until the door you picked is opened, the game managers can switch around the prizes any way they want to. So they actually have the power of deciding whether you will win or lose.

Heh ... now I CAN understand THAT theory.

 

[Larkinn]

Nah ... I don't get it. If I understand what you are saying correctly, you are saying that decreasing the choices does not change the odds. From my POV, if you decrease the choices from a 1 out of 3 chance to a 1 out of two chance, the odds HAVE to correspondingly change from 33 to 50%. It doesn't seem logical that the odds would remain at 33% with only two choices remaining.

Keep in mind that its not taking away one random box. Its specifically taking the box away with nothing in it (or a goat, or whatever bad thing you want to put in there). The odds are the same as when you originally guessed it.

Its not intuitive at all. It makes more sense if you do it out of 100 boxes. Think of that example. Me removing boxes 3-100 doesn't somehow mean that your original guess is more likely to be right.

 

[Paulie]

Is there a statistic that would adequately explain this scenario that's being discussed, that involves sticking with an original choice? You know, the whole "go with your original gut instinct" thing?

Are probabilities higher of being right when sticking with an original choice in a multiple choice situation (regardless of whether one choice is revealed to you or not)?

 

[Larkinn]

Is there a statistic that would adequately explain this scenario that's being discussed, that involves sticking with an original choice? You know, the whole "go with your original gut instinct" thing?

No. gut instinct isn't math.

Are probabilities higher of being right when sticking with an original choice in a multiple choice situation (regardless of whether one choice is revealed to you or not)?

No.

 

[Paulie]

No. gut instinct isn't math.

Well thanks for the brilliant education on that subject, even though I never said it was.

All I asked, is if there is a stat on first choices being right more than a changed choice, so you can take your cocky little holier than thou attitude and send it someone else's way. And you will, too, because that's your character on this board. You've been that way at least since I've been here, and that's about 9 months. You having problems getting laid?

 

[Larkinn]

Well thanks for the brilliant education on that subject, even though I never said it was.

Your welcome. Probability theory is math. Asking if statistics take into account an imaginary non-mathematical bullshit feeling like "gut instinct" doesn't take a long explanation to refute.

All I asked, is if there is a stat on first choices being right more than a changed choice, so you can take your cocky little holier than thou attitude and send it someone else's way. And you will, too, because that's your character on this board. You've been that way at least since I've been here, and that's about 9 months. You having problems getting laid?

You asked a question. I answered it with very little explanation. How that is holier than thou is beyond me. But you do seem to be off your rocker a bit.

 

[jillian]

Is there a statistic that would adequately explain this scenario that's being discussed, that involves sticking with an original choice? You know, the whole "go with your original gut instinct" thing?

It is counterintuitive, but it seems to work. And it's statistically consistent.

Are probabilities higher of being right when sticking with an original choice in a multiple choice situation (regardless of whether one choice is revealed to you or not)?

I think the whole Monty Hall thing is that they aren't.

BTW, I have to digress a moment and very proudly say that my 10 year old totally got it. ;o)

(That's not an insult, btw... I'm just being proud mom)

 

[Gunny]

Keep in mind that its not taking away one random box. Its specifically taking the box away with nothing in it (or a goat, or whatever bad thing you want to put in there). The odds are the same as when you originally guessed it.

Its not intuitive at all. It makes more sense if you do it out of 100 boxes. Think of that example. Me removing boxes 3-100 doesn't somehow mean that your original guess is more likely to be right.

If you eliminate 98 boxes, my chances of being correct have gone from 1% to 50%.

Now, given that there remains only two choices and one of them I have already chosen, obviously changing my choice is not a choice at all. There is is only one other box.

I can understand that removing the 98 boxes does not necessarily make my original choice more like to be correct, but are you saying that by changing my choice to the other only remaining unchosen box that I will actually INCREASE my chances of being right?

If so, what are the mechanics behind that?

 

[Larkinn]

If you eliminate 98 boxes, my chances of being correct have gone from 1% to 50%.

Nope...its still 1%. Try it 100 times. It should be intuitive that there is no way you will be correct 50% of the time.

Now, given that there remains only two choices and one of them I have already chosen, obviously changing my choice is not a choice at all. There is is only one other box.

What?

I can understand that removing the 98 boxes does not necessarily make my original choice more like to be correct, but are you saying that by changing my choice to the other only remaining unchosen box that I will actually INCREASE my chances of being right?

Yes.

This ONLY applies if the boxes being removed are known to be empty/the wrong ones .

The total probability MUST equal 100%. So if you had a 1% chance when you first picked the box, and it stays at 1% once you remove all of the others, well then all of the 99 other boxes get combined. At 1% each multiplied by 99, well there is now a 99% chance its in the second box.

If so, what are the mechanics behind that?

Read the wiki article...it explains it better than I can.

 

[midcan5]

LOL - this is funny as it demonstrates another aspect of our thinking. Could it be that the Monty Hall problem has allowed us to view the conservative mind and its inability to change. I was talking to my son yesterday, a magna cum laude graduate in math, (allow me to brag a little) and he remembered the argument and how even some of most brilliant people argued changing didn't make sense. Seems everyone can be wrong here. But this piece sums it up well and it was Marilyn vos Savant who originally opened Pandora's box.

http://www.cut-the-knot.org/hall.shtml