A brain teasing probability puzzle

Erronius

Erronius

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Itlan

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Although these issues are mathematically significant, even when controlling for these factors nearly all people still think each of the two unopened doors has an equal probability and conclude switching does not matter (Mueser and Granberg, 1999). This "equal probability" assumption is a deeply rooted intuition (Falk 1992:202). People strongly tend to think probability is evenly distributed across as many unknowns as are present, whether it is or not (Fox and Levav, 2004:637). Indeed, if a player believes that sticking and switching are equally successful and therefore equally often decides to switch as to stay, they will win 50% of the time, reinforcing their original belief. Missing the unequal chances of those two doors, and in not considering that (1/3+2/3) / 2 gives a chance of 50%, similar to "the little green woman" example (Marc C. Steinbach, 2000).

The problem continues to attract the attention of cognitive psychologists. The typical behaviour of the majority, i.e., not switching, may be explained by phenomena known in the psychological literature as: 1) the endowment effect (Kahneman et al., 1991); people tend to overvalue the winning probability of the already chosen ? already "owned" ? door; 2) the status quo bias (Samuelson and Zeckhauser, 1988); people prefer to stick with the choice of door they have already made. Experimental evidence confirms that these are plausible explanations which do not depend on probability intuition (Morone and Fiore, 2007).
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poop
 
Tuco

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Kaines_sl said:
The math works for any number of boxes above 2. Be it 3, 4, 5, 10, 20, 100, or infinite. The math is the same every time. The odds your first choice is wrong is (n-1)/n. Vegas would take those odds, and your money, any day.
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awww shiiit, makin' them aggies proud with that p(n-1) stuff
 
Siddar

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Kaines_sl said:
Given the way the problem is laid out, the first choice is a false choice. The game ends up the same whether you beat the odds the first time and chose the winning box or not. In the end you have the choice of TWO boxes. The one you initially picked and the box the host didn't open. One is ALWAYS the winning box and one is ALWAYS a loser. The odds for the second choice are exactly same after the first choice no matter how many boxes you started with.... 50/50.
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The host had two box to your one box in the first round that fact carries over.

Why is this tread still going?
 
Xequecal

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Araysar_sl said:
I think the real stumbling block is assuming that some sort of arbitrarily decided sequence of events has an effect on the final outcome.

In my example, the 1,000,000th flip is still 50/50 regardless of the fact that the previous 999,999 flips have been tails.
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The real stumbling block on the Monty hall problem is the fact that it's never made clear that Monty is predestined to reveal one of the booby prizes. The OP did not say this. That leaves open the possibility that Monty could sometimes not reveal a booby prize, and since you don't know whether he always reveals one regardless of your choice or only does so if you originally picked the million, the opened door does not give you any information. Switching is only better if Monty is predestined to show a booby prize to all contestant and you know this ahead of time.

The exact same problem plagues the "airplane on a conveyor belt" problem, the setup is ambiguous and leads to confusion.
 
T

The Master

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Has been gone over in the thread. We just assumed the OP was talking about the actual Monty Hall Problem (where that is in fact clear) and not, as it is known, The Ignorant Monty Hall or Monty Fall Problem.
 
Szlia

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Araysar_sl said:
I think the real stumbling block is assuming that some sort of arbitrarily decided sequence of events has an effect on the final outcome.
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Since writing a song about it was not enough, let me use your own argument against yourself: Why would you assume that some sort of arbitrarily decided sequence of events has an effect on your initial pick? Because that's what you are saying: you pick a door with a one chance of three to win a car, some things happen, and suddenly the pick you made is retroactively boosted from 1/3 odds to 1/2 odds.
 
Tuco

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Araysar, if you were in a job interview and were asked this question would you answer it the way that the mathematical community has decided was right or would you argue your ignorant beliefs?
 
T

The Ancient_sl

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Xequecal_sl said:
The real stumbling block on the Monty hall problem is the fact that it's never made clear that Monty is predestined to reveal one of the booby prizes. The OP did not say this. That leaves open the possibility that Monty could sometimes not reveal a booby prize, and since you don't know whether he always reveals one regardless of your choice or only does so if you originally picked the million, the opened door does not give you any information. Switching is only better if Monty is predestined to show a booby prize to all contestant and you know this ahead of time.
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No, dummy, if Monty doesn't show a booby prize that means he shows the real prize and it doesn't matter if you switch or not. You've already lost. It also makes no possible sense frame the question like this because it's completely pointless.
 
Araysar

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Tuco_sl said:
Araysar, if you were in a job interview and were asked this question would you answer it the way that the mathematical community has decided was right or would you argue your ignorant beliefs?
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I'd convince them that I was right through my superior math skills, charming personality and rapier wit.
 
Araysar

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Szlia_sl said:
Since writing a song about it was not enough, let me use your own argument against yourself: Why would you assume that some sort of arbitrarily decided sequence of events has an effect on your initial pick? Because that's what you are saying: you pick a door with a one chance of three to win a car, some things happen, and suddenly the pick you made is retroactively boosted from 1/3 odds to 1/2 odds.
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It doesnt have an effect, that's what I am saying. The second 1/2 pick happens in a vacuum. Just like every probability pick in human existence.
 
Eomer

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Araysar_sl said:
It doesnt have an effect, that's what I am saying. The second 1/2 pick happens in a vacuum. Just like every probability pick in human existence.
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Except that the parameters of the game show problem clearly do have an effect on the second pick, since a booby prize is always removed. Let's go back to the OP:

Neki_sl said:
Imagine you are on a game show with only three sealed red boxes.

The three cash prizes are $1, $1 and $100,000. You pick a box, let's say box two.

The host,who knows what's inside the boxes, opens another box, say box three and then tempts you with an offer. Box three is opened in front of you revealing a $1 prize, and he offers you the chance to change your mind to choose box one. Does switching improve your chances of winning the $100,000?
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The host's knowledge of what's in each box and their always selecting one with a booby prize clearly have an effect on the probabilities. The two picks are not independent events, as they are linked by the removal of one booby prize between them. It's not as simple as coin tosses, which you keep coming back to.
 
Araysar

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Eomer_sl said:
Except that the parameters of the game show problem clearly do have an effect on the second pick, since a booby prize is always removed. Let's go back to the OP:



The host's knowledge of what's in each box and their always selecting one with a booby prize clearly have an effect on the probabilities. The two picks are not independent events, as they are linked by the removal of one booby prize between them. It's not as simple as coin tosses, which you keep coming back to.
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Bro, if I didnt agree with the dozen other clowns who trotted this out, what makes you think I'll agree with you and the moose you rode in on?
 
Szlia

Szlia

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Araysar_sl said:
It doesnt have an effect, that's what I am saying. The second 1/2 pick happens in a vacuum. Just like every probability pick in human existence.
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Maybe it's a cultural thing... when playing Russian roulette with one bullet for six chambers and a single initial shuffle, do you believe you have five chances out of six to survive the third shot?
 
Araysar

Loser Araysar

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Szlia_sl said:
Maybe it's a cultural thing... when playing Russian roulette with one bullet for six chambers and a single initial shuffle, do you believe you have five chances out of six to survive the third shot?
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Yep.

Because every player respins the cylinder for their turn. Learn the rules of the game, bitch.
 
Hoss

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Do you always change the rules, or does that only happen when you're confused?
 
Xequecal

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The Ancient_sl said:
No, dummy, if Monty doesn't show a booby prize that means he shows the real prize and it doesn't matter if you switch or not. You've already lost. It also makes no possible sense frame the question like this because it's completely pointless.
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No, the host could just not offer you the option to switch at all. This happened on the actual show, and the OP does not say anything about how the host always opens a door, just that he did in this instance. Switching only benefits you if the host is forced to always reveal an unchosen booby prize regardless of what door you picked, and this is not made clear.
 
Erronius

Erronius

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God damnit, some sadistic MMO Dev needs to sit down and find a way to structure loot distribution like this. I cannot even imagine the debates there would be in guildchat over this.
 
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