oh no you didn't....

[Jeeebus]

It took me a day, but I'm actually starting to process this. My mind is blown.

I refuse to look at the remaining problems.

 

[_Rick_]

That's why I used the limit case n-> infinity.
You are guaranteed to pick a loser, despite one winner being in there.
All losers, except the one you picked, and the winning ticket are now removed from the pool. Knowing that you have a loser (because P(pick a winner)=0) you now take the only other non-eliminated lot. It is the winner.

Or in the 3-door case:
You have a 1 in 3 chance of picking the right door, and a 2 in 3 chance of determining which losing door is going to be opened. This is where the magic happens, that renders it non 1:1 odds. By determining which door is opened, you influence the probabilities of the remaining lots. Which is why the remaining odds are not independent of the choice of the first door.

Look up conditional probability theory.
Also, the order of operations is important.
First you make a choice.
Then everything except your choice and the wining lot (except in the case you picked the winning lot at the start) is eliminated.
From the remaining two, one is marked "your choice" and one is marked "not eliminated".
The tickets are only voided that way because you made a choice.

Seriously, take a step back, and re-examine the problem. Make sure you understand the order of execution of the elimination algorithm.

 

[TheVrolok]

I think the picture that shows the three possible outcomes should be sufficient.

The problem with the visual representation is that the (incorrect) viewer looks at the picture, draws a big red X over the first door and then sees two remaining doors and goes "50/50! See!"

 

[TheVrolok]

And so on until you're left with two tickets. You aren't at one in a million if all other other tickets have been voided.

The problem is, as already explained, that you're looking at it as if the "voided" possibilities never existed, but they did, and it matters.

 

[Pheran]

I refuse to look at the remaining problems.

But then you won't find out that your friends are more popular than you.

 

[sunzt]

It took me a day, but I'm actually starting to process this. My mind is blown.

I refuse to look at the remaining problems.

Are you going to punch yourself in the prostate?

Did you try the simulator?

 

[blackdogdeek]

Are you going to punch yourself in the prostate?

Did you try the simulator?

There's a prostate punching simulator?

 

[Jeeebus]

Are you going to punch yourself in the prostate?

Did you try the simulator?

I already stubbed my toe to a newly discovered shade of purple yesterday. I've suffered enough.

 

[Red Storm]

Wow I didn't know the Monty Hall problem was controversial. I also didn't know it was called the Monty Hall problem.

It makes perfect sense.

 

[sunzt]

There's a prostate punching simulator?

Hmmm i wonder if there's a market for this...

I remember those vests they made in the 90's for video games that simulated the punches and kicks......

 

[Schfifty Five]

For the monty hall problem, think about it like this. We'll use the 50 door example.

So you pick 1 door, 49 remain. Instead of Monty opening up 48 wrong doors, he just goes, "look, I'll trade you my 49 doors for your 1 door. If the car is in any of the 49 doors, you get to keep it." Would you accept his offer? Of course right? Because 49/50 is better than 1/50.

Well that is essentially what is going on even if Monty opens up the doors.

What it boils down to is that you are essentially TRADING your 1 door for his 49 doors (or 2 doors in the original problem).

 

[Schfifty Five]

Wow I didn't know the Monty Hall problem was controversial. I also didn't know it was called the Monty Hall problem.

It makes perfect sense.

It is. It is. It does (for some).

 

[Schfifty Five]

I already stubbed my toe to a newly discovered shade of purple yesterday. I've suffered enough.

Oh not enough. Punch your prostate.

 

[Ichinisan]

I don't get fact # 6 at all. The plumber is an accountant simply because he accepts money as payment for parts used and services rendered?

 

[Cerpin Taxt]

Ok, but what if instead of a car and a goat, behind 1 of the doors there is Schroedinger's cat, and a behind 0.999... of the doors there is a plane on a treadmill? If you switch doors, does the dead cat take off?

 

[zinfamous]

^Idiots who think they're right.

again, you can test this out yourself and see that we are, in fact, correct.


Or you can continually pound out your hilariously wrong rants on the internet and dig a deeper hole for yourself.

It's funny really. I have no idea where this condition stems from: the unmitigated need to be write, in the clear face of being wrong, when there is a simple and easy enough solution for one to see just how wrong they are.


fascinating, really.

 

[Cerpin Taxt]

I don't get fact # 6 at all. The plumber is an accountant simply because he accepts money as payment for parts used and services rendered?

I didn't read the explanation thoroughly, but just from glancing at the Venn diagrams, it seems the key lies in the fact that the only two choices are "Accountant" or "Accountant and Plumber" rather than "Accountant" or "Plumber." Something about the the set of "Accountant and Plumber" being smaller than the set of "Accountant" because it is a subset.

This seems kinda dumb because it deals with the problem strictly mathematically, and doesn't deal with the (highly relevant, IMO) real-world context.

 

[zinfamous]

I'm pretty sure it has to be trolling. I have seen grown adults unable to understand this problem though.

To me the issue with the original version of the problem has always been one of psychology. There's actually a fairly large chance that you picked the right door (1/3) and you're going to feel 'dumb' if you switch and lose, even though it was the correct way to play.

Most of us don't get repeated chances to play dominant strategy games like this for high stakes. You don't get two-thirds of a new car for playing properly. You either get the car, or you don't.

there's actually a funny history to the Monty Hall problem

I forget the paper, but this was presented and replied to by a somewhat well-regarded "math hobbiest" in some paper--it might have been the NY Times?--appropriately.

The reader submitted the question, and the columnist, despite her own assumptions that the odds are always the same, calculated and tested the problem, and responded in the right: the odds always favor switching.

Her response created a mini uproar in the academic mathematics community. There were several letters from professors and qualified "math geniuses" published in the paper, by the end of the week, admonishing her for her error. Many of them had the same type of reaction that the deniers do, in here. Refusal to perform the very simple testing required; yet outright assurance that they are correct and failure to understand the core problem.

 

[Pheran]

I didn't read the explanation thoroughly, but just from glancing at the Venn diagrams, it seems the key lies in the fact that the only two choices are "Accountant" or "Accountant and Plumber" rather than "Accountant" or "Plumber." Something about the the set of "Accountant and Plumber" being smaller than the set of "Accountant" because it is a subset.

This seems kinda dumb because it deals with the problem strictly mathematically, and doesn't deal with the (highly relevant, IMO) real-world context.

Yeah, that one is kind of stupid. I mean, it's right, but in the real world chances are the guy is just a plumber - but that's not one of the options they offer. Stripping it down to bare math, the chance of X will always be greater than the chance of X AND Y.

 

[zinfamous]

Same concept applies. Even though your odds were one in a million, you know that was a farce.

You know for a fact that:
John Smith on Cherry street didn't win. That makes your odds go up.
Your lotto pool at the office didn't win. That makes your odds go up even more.
Jenny who prayed to Jesus for the winning numbers didn't win. That makes your odds go up.

And so on until you're left with two tickets. You aren't at one in a million if all other other tickets have been voided.

your ticket wasn't part of the voided pool. I don't see how you think that your one ticket with 1/175mill odds has the same chance of winning as another one that survived the culling--which is a more or less guaranteed chance of winning.

think about it this way: before the tickets are removed from the other pot, you switch your picked ticket with one in the pot, then all the losers are removed from that pot, save the one potential winning ticket.

Now, you can choose the ticket that you switched before, or switch to the surviving ticket.

do you still think that magically, somehow, your ticket with 1/175mill odds has traveled through a wormhole into a dimension that rejects all math and probability, and has suddenly become 1:2 odds? Do you still stand by this argument?

 

[Rakehellion]

I don't get fact # 6 at all. The plumber is an accountant simply because he accepts money as payment for parts used and services rendered?

Well, he necessarily has to be a plumber by definition since he works on plumbing fixtures.

 

[kranky]

think about it this way: before the tickets are removed from the other pot, you switch your picked ticket with one in the pot, then all the losers are removed from that pot, save the one potential winning ticket.

It's critical to remember the person removing the losers KNOWS which ones are losers, and both the player and the host know there are that many losers in the pile. So removing the losers does not change the odds of the INITIAL choice. The host knows which one is the winner - this is key. The ones that were removed are not chosen at random!

 

[Puppies04]

A site that requires the reader to stare at an ad for 15 secs before moving to content? Forget that.

A person who doesn't know what adblocker is? Forget that.

 

[zinfamous]

It's critical to remember the person removing the losers KNOWS which ones are losers, and both the player and the host know there are that many losers in the pile. So removing the losers does not change the odds of the INITIAL choice. The host knows which one is the winner - this is key. The ones that were removed are not chosen at random!

I know. I was hoping that this would sink through--that, after the tickets are culled, the OP realizes that there are two completely separate odds. the host knows the outcome of your ticket, and those in the pot.

that is the point--yet the deniers seem to want to remove this detail from the problem.

Even in my example--allowing you to switch your initial ticket choice with another from the pot, then the losing tickets are removed, should make one realize that the odds of your pick are vastly different from the one ticket remaining in that pot, and that your 1:175mill chance remains as it was.

Again--the host's knowledge is the crux of the problem.

 

[Cheesetogo]

I don't get fact # 6 at all. The plumber is an accountant simply because he accepts money as payment for parts used and services rendered?

Six is merely saying that if your only two options are that a person is an

Accountant
Accountant AND a Plumber

that the first option is more likely. The first option includes ALL accountants, the second includes ONLY accountants that are also plumbers.