Do you know the correct answer?

[ShorelineJohn]

I wonder why the internet just can't answer "How many cars were given away on the original Let's make a deal"

[Jimmy W]

How did it not change that? Remember, after Monty reduces the options to 1 goat or 1 car, the punter is told to chose between the two doors.

Since Monty was left with two doors, there was a 100% chance that he had at least one goat. Showing you that he had a goat didn't change anything. He had to have it.

[Jim Bow]

All I know is that the name, “Marilynn vos Savant” always got a chuckle out of Tom and Ray Magliozzi.

[gypsie]

It's cognitive dissonance, not narcissism. Hence the ad hominem.
It's also a terrific example of how confirmation bias reveals itself in what otherwise looks like a logical problem.

I played this game here with my family using playing cards. Yep if you don't change you win about a third of the time. If you do change you win about two thirds.

Reflecting on my twist of the choice between reveal the goat and choose to change - or - don't reveal the goat and give the contestant the choice of both doors or the one they've picked: there is no practical difference between those choices.

Nicks insistence that the game has simply started again ignores that the first choice was probably wrong (it might have been right but only had a .33 chance of being so). This probability doesn't change because a door is opened.

[Peerie Maa]

OK, Nick, you don't have to re-read the thread.

Just posts no 880 and 882.

They elegantly provide the answer to the puzzle.

Have a look at this: https://ima.org.uk/4552/dont-switch-mathematicians-answer-monty-hall-problem-wrong/

‘Suppose you’re on a game show, and you’re given the choice of three doors: behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, ”Do you want to pick door No. 2?”’ Is it to your advantage to take the switch?’

Allow me to talk you through my argument

‘Suppose you’re on a game show, and you’re given the choice of three doors: behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the other doors,

This is key. If Monty did not know what was behind each door the odds would still be 1/3 for all doors.

opens another door, say No. 3, which has a goat.

If Monty did not reveal the goat the odds would be 1/3 for each door.

He then says to you, ”Do you want to pick door No. 2?”’ Is it to your advantage to take the switch?’

Having removed a goat from the initial conditions, Monty alters the ‘sample space’ of the problem so there are now only two equally probable elements.
I suggest that the people testing this are not setting up all of the initial conditions correctly as they play the game out.

[gypsie]

Once the goat is revealed the choice is not between two doors. It's between two scenarios. Each scenarios has three possible resolutions.
The sum of both scenarios is 50/50.
if you stick with the door you have a one in three chance of winning.
If you switch you have a two in three chance of winning.

The OP question is, if you switch does your chance improve. Yes it does.

stick; A is a goat. B is a car. C is a goat.
select A, C is revealed. You lose.
Select B, C is revealed. You win.
Select C, A is revealed. You lose.

Switch;
Select A, C is revealed, switch to B. You win.
Select B, C is revealed, switch to A. You lose.
Select C, A is revealed, switch to B. You win.

sum total of wins and losses is even, but if you switch, you win more.

[Paul Pless]

we're still doing this?

really?

[gypsie]

Just finished.

[Peerie Maa]

Just finished.

Good, you read the linky then!

[Tom Montgomery]

.
Think of it this way, Nick. There are three closed doors. Behind one is a car. You get to choose one door. I keep the other two doors. The odds that one of us has the car are 100%. The odds you selected the door with the car are 33.33%. The odds that the car sits behind ONE of the two doors in my possession are 66.66%. Those odds do not change REGARDLESS of what I may do or say to confuse the issue. I offer you the opportunity to trade your 33.33% odds for my 66.66% odds. Is it advantageous for you to accept the offer? Of course it is. Nothing prevents you from turning down the offer and keeping your 33.33% chance of possessing the door with the car. You may actually have the car. But if you play this game many times with the strategy of always keeping your first choice, do not bet money that you will win more than 33.33% of the time. If you do you will lose more often than you win. The number of times that you will lose will increasingly approach 66.66% the more times you play the game with that strategy.

[Ron Williamson]

The idea that the odds change when he reveals a goat is like the possiblity the the car moves from behind one door to behind the other door.
R

[Peerie Maa]

The idea that the odds change when he reveals a goat is like the possiblity the the car moves from behind one door to behind the other door.
R

Then odds change because on of the three possibities is revealed to be a goat and is removed from the game. That leaves two, car or goat. Go read the link that I provided, do.

[Tom Montgomery]

.
The odds never change. You had a 33.33% chance of winning from the start and no more.

[Peerie Maa]

.
The odds never change.

Have it your way. 1/3 it's a car, 1/3 it's a goat. That is all you are offered. Now chose between two equal odds.

[Tom Montgomery]

.
The argument presented in the link is incorrect. This is why a casino makes money. Unless it is owned and operated by Donald Trump, of course.

[Peerie Maa]

.
The argument presented in the link is incorrect. This is why a casino makes money. Unless it is owned and operated by Donald Trump, of course.

Explain why Clive Rix, University of Leicester is wrong, set out his mistake and justify your opinion.
I have set out where the odds change to evens, and explained why.

A casino makes money because they can "rig" all of the games.

[Tom Montgomery]

.
From the link:

Let us start by thinking about Monty’s objectives and motivations. As a game show host it is reasonable to assume that he has a number of things to worry about:

1. He has to manage the game; that is, he has to ensure that all the contestants have a reasonable hearing and that it finishes on time.

2. He has to entertain the audience; this is likely to mean, among other things, that the contestants win cars reasonably often.

3. He is not likely to want to give away too many cars because of the cost to his employers.

This should raise one's suspicions because they are all irrelevant.

The game is easy to duplicate at home with one's spouse or a friend standing in for Monty Hall. I challenge you to play it 100 times. Record the result of each play. Then explain the agregate result. If Mr. Rix had initially done so he would not have wasted his time writing the article. The facts of the matter would have stared him in the face.

[Tom Montgomery]

Explain why Clive Rix, University of Leicester is wrong, set out his mistake and justify your opinion.

Rix is saying the Monty Hall problem and the Three Prisoners problem are essentially the same. They are not. And I strongly doubt Martin Gardner would have claimed they were. The Three Prisoner's problem is a logic puzzle. The Monty Hall problem is not. The Monty Hall problem is a probability puzzle.

In the Three Prisoners problem, prisoner A convinces the warden to volunteer essential information.

In the Monty Hall problem Mr. Hall gives no essential information to the contestant. Monty Hall simply offers the contestant a 33.33% chance to win a car. And then, after a bit of irrelevant and deliberately misleading business, offers the contestant a 66.66% chance of winning the car instead. If you assume Hall would prefer not to give away a car, the game works in Monty Hall's favor because he knows human nature leads many (if not most) to misunderstand the odds and make the low-odds choice. It is essentialy a magician's trick.

[L.W. Baxter]

yes, hubris, (not narcissism). the blinding pride of someone very very very accustomed to being right.

so accustomed, so certain that his reason can't fail, he will resist even the easily accessible evidence of experiment.

just play the game for yourself, nick. the data will demonstrate the failure of your logic, even if you can't formulate it.

[Peerie Maa]

yes, hubris, (not narcissism). the blinding pride of someone very very very accustomed to being right.

so accustomed, so certain that his reason can't fail, he will resist even the easily accessible evidence of experiment.

just play the game for yourself, nick. the data will demonstrate the failure of your logic, even if you can't formulate it.

There is a lot of pot kettle here.
Several people who would rather snark than read and think about an alternative set of data and logic.

I dont believe that you can accurately replicate the game The person running the game has to know the identity of all three options, without revealing by any clue, which is which. As to how Monty ensures that the outcome is in the producers favour, Monty holds all of the cards, and may well be able to "force a card" on the punter just as a skilled magician does.

[L.W. Baxter]

There is a lot of pot kettle here.
Several people who would rather snark that read and think about an alternative set of data and logic.

I dont believe that you can accurately replicate the game. As to how Monty ensures that the outcome is in the producers favour, Monty holds all of the cards, and may well be able to "force a card" on the punter just as a skilled magician does.

"alternative set of data and logic"? can you hear yourself typing?

your refusal to replicate the game for your own edification is, to put it kindly, hubris.

[Peerie Maa]

Bluntness, not snark.

The difference is that those several people understood the correct answer last year, whereas your Hubris prevents you from summoning the courage to think.

It is like the opposite of an event horizon, rather than information not being able to escape, your Hubris prevents you from getting to the information.

Speaking for myself, I admit that I am like a moth to a flame, I can't help poking a stick at willfulness.

So, show me whare the linked source and my logic and argument alongside the link are wrong. Is that not new infoermation? I have bought new info to the table that NO ONE has really considered. Simply repeating last yers opinions does not adress yersterdays post.

[Peerie Maa]

Hubris.

So, you have got nothing.
Fairy nuff. PM me when you can address this

Having removed a goat from the initial conditions, Monty alters the ‘sample space’ of the problem so there are now only two equally probable elements.

Which is an edited C&P from the link.

[L.W. Baxter]

here's the logic:

at the outset, the player controls one of three doors. 1/3 probability of selecting the car at random.

at the outset, the dealer controls the remaining two doors. 2/3 probability of having the car behind one door.

by rule, the dealer must open a door with a goat.

that revelation does nothing to alter the original odds. the odds, and the game, work the same with transparent doors. the dealer still has a two thirds probability of having a car behind one of his doors.

you can demonstrate this experimentally with a deck of cards. deal three cards per round. face up or down, doesn't matter.

[L.W. Baxter]

well, i think it is fascinating to see a person of high iq willfully stumped and turned belligerant over a simple card trick.

[Tom Montgomery]

Lee Baxter is correct.

[Tom Montgomery]

I dont believe that you can accurately replicate the game The person running the game has to know the identity of all three options, without revealing by any clue, which is which.

It is actually very simple to duplicate with three paper cups and a paper clip at the pub. The person running the game needs not know the identity of all three to begin. He merely has to cover the paper clip with one cup, mix them around a bit, and have you select one. Then while you look away for a moment he looks under the two cups in his possession and takes away one without the paper clip. He asks, "Do you want to switch yours for my remaining cup?" Reveal the location of the paper clip and record who has it. Rinse and repeat. It goes very quickly. Over many plays you will find that when you stay with your original choice of cup you will have the paper clip around 33.33% of the time. And when you accept the offer to switch you will have the paper clip around 66.66%of the time.

Play with a significant other if you wish to eliminate the chance being cheated. Play with two others if if it would make you feel better. While two of you look away the third can place the paper clip under a cup and mix them around. Then proceed with just you and the second person who has no idea where the paper clip is to begin.

[L.W. Baxter]

it is fascinating.

here is a relevant article from scientific american.

the "motion with a purpose", in this case, is the opening of a door, one of three closed doors. the motion creates an illusion of something happening. but nothing has changed.

the game would work the same if there were no doors at all. but there would be no trick.

[L.W. Baxter]

if the game is played face up, meaning that the prizes are dealt without doors obscuring them, the player would see that two times in three, the dealer has the car. and two times in three, it would behoove the player to trade their one prize for the dealer's two.

the face down deal, and the door opening with a flourish, are a magician's trick. and we have seen how powerful a trick it is, in fooling some people of very high intelligence for far longer than expected, causing them to try to think their way to having their first intuition be correct.

[George Jung]

You people. Gosh.

There is a movie out, Kevin Spacey, I believe - a professor with a class of 'genius's'. Didn't watch, but in the trailer, he poses this same problem - and the obnoxious student 'got' the answer, immediately.

FYI - he's not posting to this thread.

[Jimmy W]

.
Suppose you're a contestant on the game show Let's Make A Deal. You are given the choice of three doors: behind one door is a car; behind the other two, goats.

You pick a door, say #1, and the host (who knows what's behind all the doors) opens another door, say #3, revealing a goat. Then he says, "Before I open the door with the car... you may stick with your first choice of door #1 or you may now switch your choice to door #2. "

Is it to your advantage to switch to door #2?

No fair searching the internet for the answer. Give your reasoning. Enjoy.
.

The host is going to reveal a goat. He is not opening a random door that might contain a goat. After that the possibility of any one door containing the car changes, it doesn't stay at 1/3.

[George Jung]

I know that - and obviously, YOU know that...


but how 'bout all these other deluded fools?

[Tom Montgomery]

I know that - and obviously, YOU know that...


but how 'bout all these other deluded fools?

I only wish I could make cash wagers with them on each outcome over 100 plays.

[George Jung]

Yeah.... could pay off my school loans....

But honestly - *you would think* those so convinced this doesn't work, that they would pony up some $$$ and prove you wrong.

[L.W. Baxter]

The host is going to reveal a goat. He is not opening a random door that might contain a goat. After that the possibility of any one door containing the car changes, it doesn't stay at 1/3.

that's not quite right, i don't think. the probability stays the same, start to finish. the probabilities have nothing to do with doors being closed, or one door being opened.

the closed doors, and the "motion with a purpose" of opening one door, are designed to confuse. it works a trick.