Do you know the correct answer?

[bluedog225]

Must keep the thread alive….just a bit longer….

[SchoonerRat]

This question has gotten under my skin. I woke yesterday thinking about it and that's not good.

I can finally see the other side's view of this. I can't prove that it's wrong and I don't agree that it's right.

I now see my own view in the same light. I can't add or detract to what's been said.

This is going to hound me for a long time until I work it out.

Pardon me for asking a stupid question.......................................... .................but what is your view?

[twodot]

Must keep the thread alive….just a bit longer….

It's not looking good to hit 1000 posts.

[twodot]

This question has gotten under my skin. I woke yesterday thinking about it and that's not good.

I can finally see the other side's view of this. I can't prove that it's wrong and I don't agree that it's right.

I now see my own view in the same light. I can't add or detract to what's been said.

This is going to hound me for a long time until I work it out.

Maybe there is some contrition on the horizon?

You can say it as many times as you want, you do not understand basic probability theory. Yes, all you are doing is restating the same belief without a logical argument. You do not understand what you are talking about. That is the most polite way I can say it.

[bluedog225]

6680429[/URL]]It's not looking good to hit 1000 posts.

No stopping it once we past 850. Stubborn crew.

[David G]

Hang in there CW... cipher it out. I bet you can. If you can't, you might have to come to terms with the possibility that your powers of synaptogenesis are fading, resulting in a habitual too-quick reversion to Type1 (fast/intuitive) thinking.

[Tom Wilkinson]

This question has gotten under my skin. I woke yesterday thinking about it and that's not good.

I can finally see the other side's view of this. I can't prove that it's wrong and I don't agree that it's right.

I now see my own view in the same light. I can't add or detract to what's been said.

This is going to hound me for a long time until I work it out.

Consider the game with 100 doors. Or 1000 doors. The Harvard prof addresses it that way towards the end of his talk. It becomes much more clear that it cannot be 50/50 odds.


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[Dave Wright]

Hang in there CW... cipher it out. I bet you can. If you can't, you might have to come to terms with the possibility that your powers of synaptogenesis are fading, resulting in a habitual too-quick reversion to Type1 (fast/intuitive) thinking.

He'll work it out I'm sure, but for that other old codger synaptic plasticity comes down to elephant, umbrella, orange, bicycle.

[CWSmith]

Pardon me for asking a stupid question.......................................... .................but what is your view?

50:50

[CWSmith]

Maybe there is some contrition on the horizon?

Not likely. Right or wrong, I stand behind my remark that many people have just been repeating what they read without adding understanding.

[twodot]

Not likely. Right or wrong, I stand behind my remark that many people have just been repeating what they read without adding understanding.

Heh, you might also consider that everyone here understood what they were repeating.

[Dave Wright]

Not likely. Right or wrong, I stand behind my remark that many people have just been repeating what they read without adding understanding.

The young child quickly learns that if he can turn over two of the three inverted cups, that he has a better chance of getting the coin, than if he can just turn over one cup.

Two tries are better than one.

If you played this game with Monte, in reality you get two tries. After you pick one cup he sets the other two cups aside. He picks one, and he always picks the cup he knows has no coin under it, and he shows you that it doesn't. Monte's pick is actually one of your picks, and if you switch from your first choice, you pick the remaining cup. This is equivalent to a second pick for you

[Chris Woodward]

1/3 +0 + X = 1
solve for X
9th grade algebra.

[Paul Pless]

You folks are messing up my nice graph showing a bell curve.

uhhhh. . .

[twodot]

uhhhh. . .

It's a bell curve, dammit!

[Keith Wilson]

1/3 +0 + X = 1
solve for X
9th grade algebra.

Best yet.

[CWSmith]

1/3 +0 + X = 1
solve for X
9th grade algebra.

Like I said, nothing new. This is just post #1.

9th grade algebra isn't always the solution.

[CWSmith]

I really do regret admitting that I was having second thoughts about this problem.

It brought all the little people out to feel important.

[twodot]

Like I said, nothing new.

We don't need new. The answer to post no. 1 was well presented within the first two pages of the thread, as well as innumerable times in the following 24 pages. One presentation was less than 20 words.

[twodot]

It brought all the little people out to feel important.

You need a break from the forum.

As for myself, this is my last post on the forum until September 1st. I will not open the forum until September 1st.

[Paul Pless]

As for myself, this is my last post on the forum until September 1st. I will not open the forum until September 1st.

do you need internet access money?

i have a hotspot i can loan you. . .

[Breakaway]

You need a break from the forum.

As for myself, this is my last post on the forum until September 1st. I will not open the forum until September 1st.

Enjoy your summer!


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[Chris Woodward]

Like I said, nothing new. This is just post #1.

9th grade algebra isn't always the solution.

Please show your equation.

[ron ll]

In post #6, Tom, he who posed the problem, said I was correct in post #4. (Never mind that I had no reason).

[CWSmith]

Please show your equation.

I showed my thinking on post #24. There have been some interesting comments about it and some not so interesting.

This is not a matter of simple algebra. It is about the logic behind it.

It was stated in one of the posts that this problem has brought PhDs out of the woodwork to complain that the original solution is wrong. This should tell you that there are interesting questions here. I'm finding it far more interesting that I first imagined.

And I will end with this - They do still play this game on the show and the rabid fans do not always switch. I would think that after watching the show so many times, they would know to switch if that is the right answer.

[Mcjim]

The chart in post 24 shows the contestant originally selecting the correct door six times out of twelve.
I am quite certain there is a fundamental error right there.

[CWSmith]

The chart in post 24 shows the contestant originally selecting the correct door six times out of twelve.
I am quite certain there is a fundamental error right there.

You're right! And that is a very interesting observation. I had not looked at it that way. Thank you.

[Dave Wright]

It brought all the little people out to feel important.

"THE LITTLE PEOPLE" hahaha

[Keith Wilson]

Like I said, nothing new. This is just post #1.
9th grade algebra isn't always the solution.

It is in this case. Of course it's nothing new, the correct answer has already been explained hundreds of times in myriads of different ways. This one was particularly clear and succinct.

[Chris Woodward]

Okay, Nick, I'll see if this old dog can learn a new trick:

Contestant Picks this Door	Prize is Behind This Door	Monty Shows This Door	Stays	Switches
1	1	2	Win	Lose
1	1	3	Win	Lose
1	2	3	Lose	Win
1	3	2	Lose	Win
2	1	3	Lose	Win
2	2	1	Win	Lose
2	2	3	Win	Lose
2	3	1	Lose	Win
3	1	2	Lose	Win
3	2	1	Lose	Win
3	3	1	Win	Lose
3	3	2	Win	Lose
		Win %	0.5	0.5

Okay, Tom, I told you what I thought was wrong with your chart. Now I'd like you to tell me what is wrong with mine.

Edit - Sorry. I had a typo that I corrected.

It appears that you have accounted for the same choice twice. If your first choice is correct, it make no difference which door the host opens. You win either way by not switching. But your graph shows that as two separate probabilities when it is really only one. The prize is behind Door 1,2,or3. But you have laid it out as Door 1,1,2,or 3.
This following graph is correct.

^
ron ll is correct. The answer is indeed counter-intuitive which makes it an interesting puzzle.

Intuition says that when it was revealed that an unchosen door did not contain the prize the odds changed to 50-50 and so switching the choice of doors is not advantageous.

But the fact is that the odds never change. Given a choice of three doors, there is a 2/3 chance the prize is behind one of the other two. That does not change when it is revealed that one of the unchosen two doors does not have the prize. The odds remain only 1 in three that the prize is behind your chosen door. And the odds also remain 2 in 3 that the prize is behind one of the other two doors.

[WszystekPoTrochu]

Only 103 more to go

[Breakaway]

102, actually!



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[bluedog225]

Bump

[CWSmith]

It appears that you have accounted for the same choice twice. If your first choice is correct, it make no difference which door the host opens. You win either way by not switching. But your graph shows that as two separate probabilities when it is really only one. The prize is behind Door 1,2,or3. But you have laid it out as Door 1,1,2,or 3.
This following graph is correct.

No, what I've done is to recognize that the two cards held by the host are distinct. As such, they represent two choices.

I'm counting unique choices.

It's like saying you have two daughters. Are they interchangeable, or is each unique?

That's the real question in this problem: are the two choices unique when counting possible realizations?

I am beginning to think I'm wrong, but this argument really does not explain it.

[Chris Woodward]

The more important choice is not the one door that you chose. Rather it is the two doors that the host holds. This is the whole of the game.
If he holds two goats, then either one is zero. It matters not which one you switch to, you lose. In reality this constitutes only one choice.
Otherwise, he holds two winning choices if you switch.
Car vs Goat,Goat. Switch and you lose. Regardless which goat he exposes.
Goat vs Goat,Car. Switch and you win.
Goat vs Car,Goat. Switch and you win.