This has nothing to do with Classical vs. Bayesian. This is about treating X as an unknown, even after you see the contents of the first envelope. If you trust the algebra it leads you to a model that correctly reflects a real world case. The fallacy is an algebraic one.

Besides you shouldn't be a Bayesian or Frequentist, you should do both.

So your example of knowing the contents of both envelopes isn't at all analogous the example of only knowing what's in the one we have. — Michael

What you are overlooking with the real world example is that my algebraic model reflected it exactly and all from the same information you confined your model to. The real world example showed that my algebra and probability model correctly predicted what would be actual. However, your approach created a model that does not reflect reality at all. The goal of probability is to accurately model reality. We test our probability models by either simulating a real situation or actually using them. In this test my model passed while your model failed.

Also, calling Obama an idiot does not bother me one bit. It never has, and that is because it is not true. Say what you will about Obama, but the man clearly is moderately intelligent. He is not super intelligent, but he a bit above average.

Which makes me wonder if calling Trump a clueless idiot causes such discord because it rings too close to home for some people. Perhaps they don't want to face the truth that the current President of the most powerful army on the planet is a moron.

I am starting to wonder if people are really offended by the crudeness of the word idiot, or the fact that it is targeted at Trump.

It bodes well for the American Dream if a clueless idiot can become a multi billionaire and president. — FreeEmotion

That has to be one of the most thoughtless sentences I have ever heard expressed.

If you don't want to read my post then don't; but reading them then complaining about them kind of seems like you enjoy the engagement on some level.

I have always found that odd, as much as people complain about trolls they are attracted to them like flies on shit. They also think about what the troll has said much more fully than what Mr. Agree-to-disagree said. I mean here you are, already written me off as a troll, yet you keep engaging me.

One can only explain things so many different ways. I could keep rephrasing the same thing over and over, but as much fun as that it is, it gets tiring.

Your math and code is wrong, and it has been shown as wrong several time. Pointing to your incorrect math does not prove you right.

The algebra already showed that you are wrong in more ways than one and so does a real world example. You are not averaging your expected returns over the two possible cases.

What we have to do is average the expected returns between the two cases.

1/2(5) + 1/2(10) = 7.50 the mid point between 5 and 10. Therefore there is no difference in switching.

You are saying if you switch then you have 50% chance for 1/2X and a 50% for 2X and your argument is centered around expected gain. Which you claim is in favor of switching.

Algebraically your expected value can be expressed as such:

1/2(x/2)+1/2(2x) = (5x)/4

Now let's try thinking about this when we know the contents of both envelopes and we are just flipping a fair coin to determine the envelope selection.

Let's say envelope A contains 5 bucks and envelope B contains 10 bucks.

Under your claim if we get A initially then the other envelope either has 2.50$ or 10$.

Under your claim if we get B initially then the other envelope has 5$ or 20$.

See how that can't work, as 2.50$ and 20$ are not even possible outcomes.

I don't know R, but from what I can gather that's just selecting an outcome at random and showing that the number of times you win is equal to the number of times you lose?. — Michael

That is because mine is set up correctly while yours is set up incorrectly. You are adding up sums of known numbers. Where mine is adding up an unknown, because X is an unknown.

We've established that where X is gained, X = 10 and where X is lost, X = 5. — Michael

You are letting your examples confuse you once more. What we have establish is that -X and X are equally likely to occur. If X = 5 then that is -5 or 5. If X = 10 then that is -10 or 10. If X = 15456783134.1346854654 then that is -15456783134.1346854654 or 15456783134.1346854654. That is what it means to be an unknown variable. What you are suggesting is that for each X there are two possible outcomes, and well that does not fit the definition of a function. You are not considering that L and K are independent events and that -X and X are conditional events.

|-X| = |X|, which means -X cannot equal -5 while at the same time X is equal to 10, as |-5| does not equal |10|. If X = 10 then -X=-10 and if X= 5 then -X=-5.

I really don't know many more different ways I can say this.

At any rate I think the probability of me going to get something to eat is very high at this time.

X is an unknown, so you can't treat it as a known.

You are forgetting that X is a variable.

Recall that event L is when you start with 2X and event K is when you start with X

Since we don't know which it is upon seeing the money we will consider this an uninformative prior and give each a fair 50% likelihood. Then our sample space is [K,L]

In the event of L our expected gain loss sample space is [-X, 0]

In the event of K our expected gain loss sample space is [X,0]

That is the same even if you go the 1/2 route.

Let's try running a simulation on that structure.


The Result are:

x: 2528
-x: 2510
0: 4962
```

I don't think that is quite the right way to look at this.

Let's try mapping this out and go back to our cases which I hope we are on the same page now.

Case one X = 5

If you have 2X and switch then you are left with 5 bucks. You had 10 and now you have 5. You got a -X.

Case two X = 10

If you have X and switch then you are left with 20 bucks. You had 10 and now you have 20. You got a +X. — Jeremiah

Let's call case one L and case two K. Where L is the event you start with 2X and K is the event you start with X. These are two different events.

You open it up and see you have 10 bucks:

In the event of L if you switch then you gain -X, which in this case is a loss of 5 bucks. If you don't switch then you gain 0.

In the event of K if you switch then you gain +X, which is gain of 10. If you don't switch then you gain 0.

These are two different events.

Now let's do it in the 1/2 terms.

In the event of L you get -1/2X, which would be a loss of 5 bucks. If you don't switch then you gain 0.

In the event of K if you switch you get 2X, which would be a gain of 10 bucks. If you don't switch then you gain 0.

Ya, I am moving that way, I am working on it now.

Only if you have X.

The fact that X is a variable is what makes this different, as even if you know the amount in one envelope you still don't know if that amount it is X or 2X. So I guess the question is: Does the new information of an amount shift the odds at all, given that you still don't know if it is X or 2X?

My reasoning is:

I have £10. If X is 5 then I lose £5 by switching. If X is 10 then I gain £10 by switching.

So it's either -5 or +10. This is not the same. — Michael

Look here:

Case one X = 5

If you have 2X and switch then you are left with 5 bucks. You had 10 and now you have 5. You got a -X.

Case two X = 10

If you have X and switch then you are left with 20 bucks. You had 10 and now you have 20. You got a +X.

Exactly what I said before. — Jeremiah

Case one X = 5. You lose 5 bucks.

You had 10 and now you have 5. Means you lost 5 and in that case X = 5. Therefore you got a -X.

Case two X = 10. You gain 10 bucks.

You had 10 and now you have 20. Means you gained 10 and in that case X=10. Therefore you got a +X

The same outcome as you.

You have to understand that X is a variable.

I'm saying that if I have £10 then I either lose £5 by switching or gain £10. — Michael

There are two possibilities in this case either X = 5 or X = 10

Case one X = 5

If you have 2X and switch then you are left with 5 bucks. You had 10 and now you have 5. You got a -X.

Case two X = 10

If you have X and switch then you are left with 20 bucks. You had 10 and now you have 20. You got a +X.

Exactly what I said before.

It's not. Mine is closer to how one would understand it were we to look in the envelope before deciding. — Michael

It is the same thing, the math comes out exactly the same.

Your expected gain and loss is tied to the uncertainty of what you start with.

You just said the same exact thing I did, as it can only be half X if you start with 2X. Which still results with a -1 X.

I am not sure that is quite right, as you have added information that was not in the OP. In your example you have a starting amount that is known, but in our case you don't know your starting amount.

You could have X or 2X. If you have X and you switch then you get 2X but lose X so you gain X; so you get a +1 X. However, if you have 2X and switch then you gain X and lose 2X; so you get a -1 X.

Yes.

I could have one with you, though. — frank

I really doubt you have the grit for it.

I am sure that is your typical approach to the world, but I have made several reasoned arguments filled with relative content.

Not at all what I asked.

that name-calling has no place in reasoned discourse wherever one may happen to break out [...] you have resigned from serious discussion. — frank

Do you apply that same standard to Trump?

Modern "philosophy" is far too subjective and it seems some people are in the habit of using the word as a slap on sticker label to superficially elevate their arguments.

not really a hallmark of reasoned philosophical discourse, — FreeEmotion

One does not have to be nice to be right. Trump has done and said many things which demonstrates he is on the lower end of the intelligence scale and his lack of experience is well known; as such, he is a clueless idiot. It is a fitting description and the fact that you find it crude has less to do with "philosophy" and more to do with you personally. Philosophy is the love for the pursuit of truth, that and only that, and all this conceptual decor you subjectively find pleasing is extra baggage you decided to drag along. This is exactly why I turned from philosophy and literature to science and math. I am not interested in who can be the most agreeable, I am interested in the truth.

A judge tries to end child separation and she/he is pissed over it. I thought the Left was the supposed emotional side.

I never claimed to have all the answers, my position was and still is that child separation is wrong. One does not have to be all knowing to know that.

Whew! I am glad we agree on something!
Now, where would you like to house the 10K unaccompanied minors?
They are not nonsense, they are kids without parents.
Now what? — ArguingWAristotleTiff

Not sure what this has to do with the accompanied minors that were removed from their parents who were accompanying them. Why you would think that somehow justifies child separation I have no clue and you are very obviously engaging in a straw man. Do you understand that? Do you know what a straw man is? Do you understand that the presence of unaccompanied minors is not an excuse to make more unaccompanied minors?

Now what? — ArguingWAristotleTiff

How about the lazy Republican congress doesn't take a break, and they don't take a recess until the job is done? Could we start there maybe?

You were right,I was wrong. — ArguingWAristotleTiff

That is what I kept trying to tell you. The rest of your post is of course hyperbolic nonsense.

Interesting how you also display a lack of empathy here.

Sounds like a stereotype of people you decide to label "bully".

A federal judge in California has issued a nation wide injunction to bar the practice of child separation and ordered the parents be reunited. 17 US states have also challenged the legality of these practices.

I guess it was not as in line with our laws as some here argued.

The judge noted this:

“The government readily keeps track of personal property of detainees in criminal and immigration proceedings. Money, important documents, and automobiles, to name a few, are routinely catalogued, stored, tracked and produced upon a detainees’ release, at all levels—state and federal, citizen and alien. Yet, the government has no system in place to keep track of, provide effective communication with, and promptly produce alien children. The unfortunate reality is that under the present system migrant children are not accounted for with the same efficiency and accuracy as property.”