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The two envelopes problem
Posted: 04 November 2012 10:04 PM   [ Ignore ]   [ # 1546 ]
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StephenLawrence - 31 October 2012 12:58 AM

This is impossible. One person’s gain is the others loss in this set up.

From the respective perspectives of both players, there is potential gain/loss.

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Posted: 04 November 2012 10:08 PM   [ Ignore ]   [ # 1547 ]
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StephenLawrence - 31 October 2012 01:02 AM

The formula does recommend switching a second time, if you get the chance.

So the problem is it does and it doesn’t.

However, we know switching twice or any even number of times is equivalent to not switching at all. So, we switch once or any odd number of times.

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Posted: 04 November 2012 10:43 PM   [ Ignore ]   [ # 1548 ]
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StephenLawrence - 31 October 2012 01:10 AM

What we can do is stick with a pair of numbers.

We don’t have to consider more than 1 pair of numbers.

You have no reasonable objection to doing that.

If you do that, it is a simplification and/or an incomplete description of the TEP because for any finite value of X, either (X, 2X) or (X, 1/2X) are in the two envelopes.

For example, if we consider the pair (10, 20), it is also possible (5, 10) are in the two envelopes.

So, both (10, 20) and (5, 10) must be considered in a complete description of the TEP.

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Posted: 04 November 2012 11:05 PM   [ Ignore ]   [ # 1549 ]
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kkwan - 04 November 2012 10:04 PM
StephenLawrence - 31 October 2012 12:58 AM

This is impossible. One person’s gain is the others loss in this set up.

From the respective perspectives of both players, there is potential gain/loss.

And they must cancel each other out.

Stephen

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Posted: 04 November 2012 11:08 PM   [ Ignore ]   [ # 1550 ]
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kkwan - 04 November 2012 10:08 PM
StephenLawrence - 31 October 2012 01:02 AM

The formula does recommend switching a second time, if you get the chance.

So the problem is it does and it doesn’t.

However, we know switching twice or any even number of times is equivalent to not switching at all. So, we switch once or any odd number of times.

Kkwan the contradiction is there you can’t remove it as you are trying to do.

The reason is we also know that on the second go if you are asked if you want to switch the formula says you should switch too.

The same formula is saying you should and you shouldn’t

Stephen

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Posted: 04 November 2012 11:18 PM   [ Ignore ]   [ # 1551 ]
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kkwan - 04 November 2012 10:43 PM

For example, if we consider the pair (10, 20), it is also possible (5, 10) are in the two envelopes.

So, both (10, 20) and (5, 10) must be considered in a complete description of the TEP.

What we know is we either have $10 and $20 or $5 and $10, or another pair of numbers.

Because whatever two numbers we have makes no difference we can simply imagine any pair we like and work with that.

We don’t have to compare two different situations that we might be in at all.

I’m sure the only interesting bit is what goes wrong when we do the T.E.P that way and how should we work out what to do when we open our envelope.

Stephen

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Posted: 04 November 2012 11:39 PM   [ Ignore ]   [ # 1552 ]
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kkwan,

Choosing different descriptions for two unknown but fixed amounts is of no relevance for any calculation. But you do as if it makes a difference.

kkwan - 04 November 2012 09:57 PM

Your argument is flawed because it is based on the premise that the total amount has changed which is not so.

<snip>

Hence, either 3X or 3/X are the total amounts in the two envelopes.

This is a contradiction kkwan: you use 3X when you choose the envelope with smallest amount first, and you use (3/2)X when you pick the envelope with the biggest amount first. For the same X these are different amounts.

Again: show me where you use that the total amount does not change. You haven’t done that yet.

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Posted: 04 November 2012 11:42 PM   [ Ignore ]   [ # 1553 ]
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GdB - 04 November 2012 11:39 PM

kkwan,

Choosing different descriptions for two unknown but fixed amounts is of no relevance for any calculation. But you do as if it makes a difference.

kkwan - 04 November 2012 09:57 PM

Your argument is flawed because it is based on the premise that the total amount has changed which is not so.

<snip>

Hence, either 3X or 3/X are the total amounts in the two envelopes.

This is a contradiction kkwan: you use 3X when you choose the envelope with smallest amount first, and you use (3/2)X when you pick the envelope with the biggest amount first. For the same X these are different amounts.

Again: show me where you use that the total amount does not change. You haven’t done that yet.

Kkwan only needs to say that he is comparing two different situations that he might be in, which he has agreed to many times.

So the total amount does not change.

Stephen

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Posted: 05 November 2012 12:02 AM   [ Ignore ]   [ # 1554 ]
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We are in only one situation, not two.

I dealt with that here.

In reality, of course the ‘two situations’ are just one, only with different descriptions.

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Posted: 05 November 2012 12:26 AM   [ Ignore ]   [ # 1555 ]
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GdB - 05 November 2012 12:02 AM

We are in only one situation, not two.

Which is banal.

In reality, of course the ‘two situations’ are just one, only with different descriptions.

In reality Kkwan is comparing two different situations. $5 and $10, $10 and $20, for instance.

He insists there is a need to do that and we agree there is no need .

But he can do that and the amounts don’t change half way through when he does it because he’s comparing what would be the case if he were in the two different situations in the first place.

Stephen

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Posted: 05 November 2012 01:13 AM   [ Ignore ]   [ # 1556 ]
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StephenLawrence - 05 November 2012 12:26 AM

In reality Kkwan is comparing two different situations. $5 and $10, $10 and $20, for instance.

He insists there is a need to do that and we agree there is no need .

There is not ‘no need’, it is just wrong.

Imagine we have two amounts, $5 and $10. (Total $15). Imagine I pick $10 first. Oh, but then I look at $10 and $20. (Total $30). Sorry, this is wrong as wrong can be. Depending on what is picked first, the amounts change.

Correct is: if I have $5 and $10 and I pick $5 then the other amount is $10. And if I pick the $10, then the other is $5. That is the fact kwann wipes under the carpet.

StephenLawrence - 05 November 2012 12:26 AM

But he can do that and the amounts don’t change half way through when he does it because he’s comparing what would be the case if he were in the two different situations in the first place.

One must compare the situations separately, as I did here.

[ Edited: 05 November 2012 04:21 AM by GdB ]
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Posted: 05 November 2012 01:21 AM   [ Ignore ]   [ # 1557 ]
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GdB - 05 November 2012 01:13 AM

There is not ‘no need’, it is just wrong.

That won’t do as a solution to the problem.

Stephen

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Posted: 05 November 2012 02:51 AM   [ Ignore ]   [ # 1558 ]
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StephenLawrence - 05 November 2012 01:21 AM
GdB - 05 November 2012 01:13 AM

There is not ‘no need’, it is just wrong.

That won’t do as a solution to the problem.

The explanation follows after the sentence you quote.

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Posted: 05 November 2012 06:15 AM   [ Ignore ]   [ # 1559 ]
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GdB - 05 November 2012 02:51 AM
StephenLawrence - 05 November 2012 01:21 AM
GdB - 05 November 2012 01:13 AM

There is not ‘no need’, it is just wrong.

That won’t do as a solution to the problem.

The explanation follows after the sentence you quote.

No, the amounts don’t change depending upon what is picked because Kkwan is comparing two different situations that he might be in.

The question is what is wrong with doing that.

Post 1535 contains my thoughts and why I’m still puzzled. Have a go at answering it if you like.

Stephen

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Posted: 05 November 2012 09:21 AM   [ Ignore ]   [ # 1560 ]
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StephenLawrence - 05 November 2012 06:15 AM

No, the amounts don’t change depending upon what is picked because Kkwan is comparing two different situations that he might be in.

The question is what is wrong with doing that.

Post 1535 contains my thoughts and why I’m still puzzled. Have a go at answering it if you like.

That calculation was already don by Mingy Jongo, a long, long time ago.

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