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re: Let's discuss the Monty Hall problem (probabilities, odds)

Posted on 8/12/17 at 9:11 am to
Posted by Nado Jenkins83
Land of the Free
Member since Nov 2012
59753 posts
Posted on 8/12/17 at 9:11 am to
Until you switch and lose and get a goat instead of Hyundai
Posted by SlapahoeTribe
Tiger Nation
Member since Jul 2012
12120 posts
Posted on 8/12/17 at 9:11 am to
quote:

Seems pretty easy to understand, not sure why people have such a hard time with it.
For my next thread I'll try to explain the probability of quantum tunneling.
Posted by PrimeTime Money
Houston, Texas, USA
Member since Nov 2012
27324 posts
Posted on 8/12/17 at 9:15 am to
quote:

I understand the theory. But it's still a theory.
It's been experimented. You can try it yourself.

Okay, last example to help you visualize. Imagine behind the doors are like this:

Door 1: Goat
Door 2: Car
Door 3: Goat


If you stay with your pick you have a 1/3 shot to win the car.

If you switch, there are 3 outcomes:

If you pick door 1, the host eliminates door 3 and you switch and win the car.

If you pick door 3, the host will eliminate door 1 and you switch and you win the car.

So 2 of the 3 scenarios so far when you switch wins you the car.

The only other option is you pick door 2, the host then eliminates either door 1 or 3 and you switch and lose.



So 2 of the 3 scenarios when you switch, you win. In only one scenario you lose. So you have a 2/3 chance of winning if you switch, and a 1/3 chance if you stay.
This post was edited on 8/12/17 at 9:17 am
Posted by Nado Jenkins83
Land of the Free
Member since Nov 2012
59753 posts
Posted on 8/12/17 at 9:20 am to
That is only if you switch.

I.see you edited. I understand it y'all can stop typing out novels. I understood it on page one. But I just don't buy it.

I would stick to my gut because I hate second guessing. Thats the psychological demon in it
This post was edited on 8/12/17 at 9:22 am
Posted by SlapahoeTribe
Tiger Nation
Member since Jul 2012
12120 posts
Posted on 8/12/17 at 9:21 am to
quote:

That is only if you switch.
Exactly. If you switch you get 2/3 odds.

If you don't switch then you only get a 1 in three chance of ever winning.
Posted by PrimeTime Money
Houston, Texas, USA
Member since Nov 2012
27324 posts
Posted on 8/12/17 at 9:32 am to
quote:

I understood it on page one. But I just don't buy it.
That doesn't even make sense. That's like saying I understand that 2 + 2 = 4 but I just don't buy it.

If you really understood it, you'd buy it. The only way you don't buy it is if you really don't understand it.
Posted by shel311
McKinney, Texas
Member since Aug 2004
111136 posts
Posted on 8/12/17 at 9:37 am to
quote:

At first you have a 1/3 chance. After host shows you the goat, wouldn't you now have a 1/2 chance? Door 3 no longer matters. You get a new pick between two doors. If the host knows, are we to assume he wants us to get the car?

The 2 easiest ways to try to explain it for me, assuming you originally choose door 1:

1. If I gave you the option to keep door 1 or without opening anything to switch and see what's behind BOTH doors 2 and 3, you know have a 2/3 chance of opening the door with the car, correct? It's the same thing, he's just opening 1 door for you beforehand.

2. Play through all 3 scenarios with the car behind door 1, 2, and 3. If you choose to switch, the ONLY way you lose is if the car was behind door #1, correct? And since you know you had a 1 in 3 chance of picking correctly with door #1, then you know you have a 2/3 chance of winning if you switch.
Posted by Nado Jenkins83
Land of the Free
Member since Nov 2012
59753 posts
Posted on 8/12/17 at 9:38 am to
I guess I should word that different.

I couldn't make the switch if something good was at stake. The chance of changing my choice and losing is more devastating to me.
This post was edited on 8/12/17 at 9:40 am
Posted by PrimeTime Money
Houston, Texas, USA
Member since Nov 2012
27324 posts
Posted on 8/12/17 at 9:41 am to
If you were thinking logically instead of with your emotions then you can live with your decision because you know you gave yourself the best possible chance to win.
This post was edited on 8/12/17 at 9:55 am
Posted by Nado Jenkins83
Land of the Free
Member since Nov 2012
59753 posts
Posted on 8/12/17 at 9:45 am to
Its still just an educated guess. It's not a guarantee
Posted by shel311
McKinney, Texas
Member since Aug 2004
111136 posts
Posted on 8/12/17 at 9:46 am to
quote:

I get that. But at this point, you're making a new choice between two doors. The other 998 are irrelevant.

3 options, you choose door 1 each time, you switch every time:

1. Car is behind door 1, you switch you lose

2. Car is behind door 2, you switch you win

3. Car is behind door 3, you switch you win


Switching wins 2 out of 3 times.
Posted by mdomingue
Lafayette, LA
Member since Nov 2010
30672 posts
Posted on 8/12/17 at 9:46 am to
I still think that the offer to switch is effectively a new paradigm in terms of the statistics. It's not really an offer to switch but a new choice of door 1 or door 2. The car is physically where it is, behind one of those two doors.


Another take on this: Warning, not a video but lots of word

But empirical data does seem to support the switch method over large sample sizes.

More words explaining the math and link to simulator

LINK to simulator

I think I finally agree you should switch.

Posted by SlowFlowPro
Simple Solutions to Complex Probs
Member since Jan 2004
423378 posts
Posted on 8/12/17 at 9:47 am to
there was a classic OT thread about this years ago
Posted by shel311
McKinney, Texas
Member since Aug 2004
111136 posts
Posted on 8/12/17 at 9:49 am to
quote:

I'm gonna side with the thousand of PhDs that disagree

Pssst, they don't disagree any more.

quote:

That one door out of the 999 doesn't hold the value of 999 doors. That's stupid

Wait, are you saying that out of 1000 choices, your odds wouldn't increase if you swapped after seeing 998?
Posted by SlowFlowPro
Simple Solutions to Complex Probs
Member since Jan 2004
423378 posts
Posted on 8/12/17 at 9:50 am to
quote:

Imagine there were 1,000 doors. 1 door had the prize and the 999 other doors had a goat.

Your odds of picking the right door off the bat are very low... 1 / 1,000. So you pick a door.

Now the host opens 998 doors which he knows contain goats. Now there are two doors left, the 1 door the host left and your door.

this is more like the scenario where the original big OT discussion occurred, as it came from the show "Deal or no Deal"

Posted by shel311
McKinney, Texas
Member since Aug 2004
111136 posts
Posted on 8/12/17 at 9:51 am to
quote:

I understand the theory. But it's still a theory.

Posted by SlowFlowPro
Simple Solutions to Complex Probs
Member since Jan 2004
423378 posts
Posted on 8/12/17 at 9:52 am to
this is why i make money playing poker (made my return last night after almost a month off)
Posted by shel311
McKinney, Texas
Member since Aug 2004
111136 posts
Posted on 8/12/17 at 9:53 am to
quote:

I understand it y'all can stop typing out novels. I understood it on page one. But I just don't buy it.
It's math, there's nothing to buy.

When you swap, the only way you lose is if you chose the car initially. Since the odds of choosing the car initially was 1 in 3, then the odds of winning on the swap is 2 in 3.
Posted by shel311
McKinney, Texas
Member since Aug 2004
111136 posts
Posted on 8/12/17 at 9:55 am to
quote:

Its still just an educated guess. It's not a guarantee
No one argued otherwise.

You're basically saying you rather stick with 33% chance of success instead of 67%. Well not basically, that's exactly what you're stating.
Posted by Nado Jenkins83
Land of the Free
Member since Nov 2012
59753 posts
Posted on 8/12/17 at 9:56 am to
I dont buy that the odds don't change
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