Random Thoughts IV: the Abyss Gazes Back

[Timsup2nothin]

Four possible outcomes is being done in a way to destroy the true nature of the problem. It doesn't even properly represent it. Proper analysis is done with mathematics.

That is mathematics. There are four outcomes, two good and two bad. That's also the "true nature of the problem." The ruse is that the first choice has any relevance at all.

 

[cardgame]

That there are four outcomes split equally between good and bad does not mean their likelihood of occurring is equal.

 

[Timsup2nothin]

That there are four outcomes split equally between good and bad does not mean their likelihood of occurring is equal.

Yeah, except they are equally likely.

 

[cardgame]

tell it to wikipedia

 

[Timsup2nothin]

tell it to wikipedia

As I said already, they are in a different business. Creating a paradoxical outcome gets far more hits than creating a useful outcome does.

 

[cardgame]

Ah, but the reason it's even a thing is because it is useful.

 

[Takhisis]

tell it to wikipedia

It's only as good as its contributors.

 

[cardgame]

I was wrong and I apologize. I conceded an argument I had no business conceding.

There are not four scenarios. That was an artificial and merely partial construct of the situation, devoid of context. There are only three scenarios. All three of these scenarios are equally likely.

The prize is behind door #1:

[x] [-] [-] = Host opens door #2. If you switch from door #1, you get nothing.

The prize is behind door #2:

[-] [x] [-] = Host opens door #3. If you switch from door #1, you get the prize.

The prize is behind door #3:

[-] [-] [x] = Host opens door # 2. If you switch from door #1, you get the prize.

 

[Timsup2nothin]

I was wrong and I apologize. I conceded an argument I had no business conceding.

There are not four scenarios. That was an artificial and merely partial construct of the situation, devoid of context. There are only three scenarios. All three of these scenarios are equally likely.

The prize is behind door #1:

[x] [-] [-] = Host opens door #2. If you switch from door #1, you get nothing.

The prize is behind door #2:

[-] [x] [-] = Host opens door #3. If you switch from door #1, you get the prize.

The prize is behind door #3:

[-] [-] [x] = Host opens door # 2. If you switch from door #1, you get the prize.

You are indeed wrong, but apology accepted. You left out prize is behind door number one, host opens door number three, you switch to door number two and get nothing. No matter how you slice it, your initial choice makes no difference and after one of the goat doors is open you have a fifty fifty chance.

 

[Traitorfish]

A-are we really doing the Monty Hall argument? In this, the year of Our Lord two thousand and eighteen?

 

[Ryika]

You are indeed wrong, but apology accepted. You left out prize is behind door number one, host opens door number three, you switch to door number two and get nothing. No matter how you slice it, your initial choice makes no difference and after one of the goat doors is open you have a fifty fifty chance.

This is incorrect. It's true that there are 4 possible outcomes, but they don't share the same probability.

You choose the door with goat a (1 in 3) -> Host must show goat b (because the third door holds the price) -> 1 in 3 chance to occur.

You choose the door with goat b (1 in 3) -> Host must show goat a (because the third door holds the price) -> 1 in 3 chance to occur.

You choose the door with the price (1 in 3) -> The host has a 1 in 2 chance to show you goat a -> 1 in 6 chance to occur.
You choose the door with the price (1 in 3) -> The host has a 1 in 2 chance to show you goat b -> 1 in 6 chance to occur.

Basic probability math. It's only a 50/50 if you start with one door being opened and only then have the ability to make your first choice.



The solution that helped me make sense of the paradox is actually pretty... weird, but it does make sense:

Because there's a 1-in-3 chance that the car is behind each door, the chance that the price is behind your door, is always 33%. Each door is twice as likely to loose than it is to win, that's the initial chance for each door.

When one of the other doors is being opened, we gain no new information about our own door, because we already knew that one of the other doors is a goat, and the host is bound to show us a goat in ALL cases. So that opening of the door changed nothing at all about the probability of the goat being behind our door.

Because we have no new information on our own door, we now actually have new information on the other door - namely that because our door still has a chance of 33% to hold the price, and that because there is now one less door, the door now must have a chance of 67% to hold the price.

And that's correct - if you don't believe it, simulate it.

 

[Timsup2nothin]

This is incorrect. It's true that there are 4 possible outcomes, but they don't share the same probability.

You choose the door with goat a (1 in 3) -> Host must show goat b (because the third door holds the price) -> 1 in 3 chance to occur.

You choose the door with goat b (1 in 3) -> Host must show goat a (because the third door holds the price) -> 1 in 3 chance to occur.

You choose the door with the price (1 in 3) -> The host has a 1 in 2 chance to show you goat a -> 1 in 6 chance to occur.
You choose the door with the price (1 in 3) -> The host has a 1 in 2 chance to show you goat b -> 1 in 6 chance to occur.

Basic probability math. It's only a 50/50 if you start with one door being opened and only then have the ability to make your first choice.



The solution that helped me make sense of the paradox is actually pretty... weird, but it does make sense:

Because there's a 1-in-3 chance that the car is behind each door, the chance that the price is behind your door, is always 33%. Each door is twice as likely to loose than it is to win, that's the initial chance for each door.

When one of the other doors is being opened, we gain no new information about our own door, because we already knew that one of the other doors is a goat, and the host is bound to show us a goat in ALL cases. So that opening of the door changed nothing at all about the probability of the goat being behind our door.

Because we have no new information on our own door, we now actually have new information on the other door - namely that because our door still has a chance of 33% to hold the price, and that because there is now one less door, the door now must have a chance of 67% to hold the price.

And that's correct - if you don't believe it, simulate it.

Or accept the reality that as I have now said TWICE the first "choice" is a sham. You are being led down the path by a paradox creator. Saying "if you look at it this way, through the lens of this false choice, OH BOY what an astonishing paradox...you can even simulate it" doesn't make it any more valid. You did gain new information about your door. The updated information is that it is in a two door set, not a three door set. Again, the "got no new information about our door" is a misrepresentation used to create the false paradox.

 

[Ryika]

But it's not a sham. Tbh, I don't even understand what you mean by that, or what exactly your position is, or why you call it a false paradox.

If you play it right, the chance of you winning the game is 67%. Do you disagree with this?

 

[Timsup2nothin]

But it's not a sham. Tbh, I don't even understand what you mean by that, or what exactly your position is.

If you play it right, the chance of you winning the game is 67%. Do you disagree with this?

Yes, because it isn't true. Ultimately, you face a choice of two doors, and your chance of winning is fifty fifty. The sham is "you are given a choice of three doors," because you aren't. You are participating in a meaningless diversion, then you are given a choice of two doors. That's that.

 

[Ryika]

Yes, because it isn't true. Ultimately, you face a choice of two doors, and your chance of winning is fifty fifty. The sham is "you are given a choice of three doors," because you aren't. You are participating in a meaningless diversion, then you are given a choice of two doors. That's that.

Alright, then let me summarize this whole discussion:
You have no idea what you're talking about and should look into what people have written about the Paradox instead of constructing wikipedia conspiracy theories.

You WILL win the game 67% of the time if you switch the door, not 50% as you claim.

 

[cardgame]

Yes, because it isn't true. Ultimately, you face a choice of two doors, and your chance of winning is fifty fifty. The sham is "you are given a choice of three doors," because you aren't. You are participating in a meaningless diversion, then you are given a choice of two doors. That's that.

There are 100 doors. You pick door #1. The host opens 98 doors to reveal goats. There are two doors left, your door and one other door. IT'S A 50% CHANCE!!!

 

[Timsup2nothin]

Alright, then let me summarize this whole discussion:
You have no idea what you're talking about and should look into what people have written about the Paradox instead of constructing wikipedia conspiracy theories.

You WILL win the game 67% of the time if you switch the door, not 50% as you claim.

Or, I can summarize it that YOU have no idea what you are talking about. "What people have written about the paradox" is a great bit of fun, because what they are doing is demonstrating how a seeming paradox can be created using a sleight of hand analysis. Taking it as some sort of "lesson in probability" is hilarious.

 

[Timsup2nothin]

There are 100 doors. You pick door #1. The host opens 98 doors to reveal goats. There are two doors left, your door and one other door. IT'S A 50% CHANCE!!!

Indeed, because the first choice was a sham. You are assuming that the door you picked was wrong, and when you made the choice that was a high probability assumption. But every time they open a door the odds that your assumption is correct decline. When they have opened 98 doors the odds that your assumption is correct have reached 50/50. The actual math is a huge series of probabilities in a summation that does come to 50%. The "oh look a paradox" math is a very simple "calculation" based on a false premise....for entertainment.

 

[cardgame]

oh dear. you never took a statistics class?

 

[Ryika]

Indeed, because the first choice was a sham. You are assuming that the door you picked was wrong, and when you made the choice that was a high probability assumption. But every time they open a door the odds that your assumption is correct decline. When they have opened 98 doors the odds that your assumption is correct have reached 50/50. The actual math is a huge series of probabilities in a summation that does come to 50%. The "oh look a paradox" math is a very simple "calculation" based on a false premise....for entertainment.

But that's exactly NOT what happens. That WOULD be what happens if doors were opened at random, but they're not - the host only ever opens doors with goats, which is what makes it so our actual chance to win the game is higher than the chance we would intuitively ascribe to it.

That's true, and you should look into it, because right now you're just making yourself look silly because you don't even understand the problem that you're trying to address.