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2022/09/09 3:10:58
First edition 2014/11/08

# List of my pages written in English about the Two Envelopes Problem

Maybe flawsome sections of the English Wikipedia article 'Two envelopes problem' (revision at 21:12, 4 January 2021)
In my perception, the English language Wikipedia article 'Two envelopes problem' (revision at 21:12, 4 January 2021) has some points I think better to be corrected. Such points have increased from the revision 21:39, 23 November 2014.

An outline of the Two Envelopes Problem
The two envelopes problem is not so difficult and the two envelope paradox is not so mysterious.
But to my surprise, there are people who think that the correct expectation formula is E=(1/2)A + (1/2)2A.
This mystery was so big as I could not stop studying this.

The missing dollar riddle is as mysterious as the two envelope paradox.
The missing dollar riddle had been discussed in a famous paper on the two envelope paradox. I tried to resolve it and found that the riddle is as mysterious as the two envelope paradox.

Two envelopes problem : Which explanation is most easy to understand ?
There are some explanations which are easy to understand the two envelopes problem. Which explanation is best ?

Experiment for experiencing two envelopes problem
This page provides experiment about the probabilities which are concerned on the two envelopes problem.
I hope it help you to realize the characteristics of these probabilities.

Interesting web pages about the Two Envelopes Problem
Web pages which contain explanations that are easy to understand, or contain interesting variations of the problem, or contain interesting debate, or …

Two English language Wikipedia articles on the two envelope paradox
There are two English language Wikipedia articles on the two envelope paradox. The older article is hidden behind the redirection.

Remarkable revisions of the Wikipedia article "Two envelopes problem"
Some of the revisions of the English language Wikipedia article 'Two envelopes problem' surprised me.

Inconsistencies in the article 'Two envelopes problem' (revision of November 2014) of the English language Wikipedia.
In my perception, there are some inconsistencies in the article titled 'Two envelopes problem' (revision of November 2014) of the English language Wikipedia.

A fictional history of the two envelopes problem
I think that possibly we may be caught by inconsistent variable when we read the original of the two envelopes problem. So, I imagined the original of the problem and a fictional history of the two envelopes problem.

If amout of money is natural number the two envelopes problem is not established.
In this page, I tried to show if the amount of money is natural number then the two envelopes problem is not established.

Revers probreming of the two envelope paradox
I tried to create the most suitable problems for each solutions of the two envelopes problem. Variaty of the problems may reveal the credibility of each solutions.

My idea of cognitive psychological experiment about the two envelopes problem
This page shows my idea of psychological experiment about the cognitive fallacy which occurs on the two envelopes problem.

The Siegel paradox and the two envelope paradox
The Siegel paradox seems to resemble the two envelope paradox. How is the similarity?

Two methods for the proof of the equivalence of the envelopes of the two envelopes problem
There are two method to prove the equivalence of the envelopes of the two envelopes problem. One method uses the law of total expectation. The other method uses calculating formulas of conditional expectations.

An intuitive resolution of the two envelope paradox
I found a method which uses frequency instead of probability to prove the equivalence of the two envelopes. This method is not complete but more intuitive than standard method.

Two kinds of the Two Envelopes Problem
There are two kinds of the Two Envelopes Problem. One is DoublePairian's problem (Mathematician's problem) and the another is SinglePairian's problem (Philosopher's problem).
In this page I show the difference of these two kinds of problem.

The Mental Models for the Wallet Game
I think that the Inconsistent Valiable perhaps can occur on the Wallet Game.

Smullyan's paradox on the two envelopes problem
I have compared the structure of the Smullyan's paradox on the two envelopes problem and the structure of usual paradoxes on the two envelopes problem. And I have thought what fallacy is the cause of the Smullyan's paradox.

Incantations used by equivalent-expectationian on the two envelopes problem
"Equivalent-expectationian" is one of the "ian" except "SinglePairian" and "DoublePairian".  The subject of this page is incantations used by equivalent-expectationian on the two envelopes problem.

Is the principle of insufficient reason the cause of the paradox of the two envelope problem?
I doubt the theory that the principle of insufficient reason is the cause of the paradox of the two envelopes problem.

# Old pages

The following pages are old, and contents of them overlap with the other my page "An outline of the Two Envelopes Problem".

Theory of "E = (1/2)2a + (1/2)a" on The Two Envelope Paradox
This page show the mental model that is behind the theory of 'E = (1/2)2a + (1/2)a' on the Two Envelope Paradox,  and show there are different two mathematical problems on the Two Envelopes problem.

The relatives of IVT on the two envelopes problem
After studying the articles which advocate IVT (inconsistent variable theory) , I have found following facts.
• The articles which advocate IVT are less than my expectation.
• But there are many articles which claim that thinking two pairs of amount of money is the cause of the paradox. (There are many fashions to rationalize this opinion.)
• And there are some articles which claim that confusion of unconditional mean values and conditional mean values is the cause of the paradox.
The IVT is only one of these relatives.

The Way to the Inconsistent Variable Theory about Two Enveloe Paradox
I have read some articles written by SinglePairians and some Wikipedia articles that describe a resolution that was led in SinglePairian's viewpoint , and found that there may be two stages on the way to the Inconsistent Variable Theory.

# Terms

• inconsistent variable theory
It is as follows.
The variable symbol of the expectation formula denotes the smaller amount in one of the terms , while it denotes larger amount in the another term.
This mixture of different instances of a variable is the cause of the paradox.