kkwan, stop this bullshit. The TEP is clearly formulated:

Let us say you are given two indistinguishable envelopes, each of which contains a positive sum of money. One envelope contains twice as much as the other. You may pick one envelope and keep whatever amount it contains. You pick one envelope at random but before you open it you are offered the possibility to take the other envelope instead. Should you switch?

Full stop. Everything else is

your addition. So answer the above question in the above described situation.

That “one envelope contains twice as much as the other” does not mean **only** (X, 2X) but **either** (X, 2X) **or** (X, 1/2X) which are distinct events for any finite value of X.

You have misinterpreted the TEP as it is, for your convenience.

TEP is not defined as:

You are given one envelope. Now you are offered a second envelope, which can contain half or twice the amount in your envelope. Should you switch?

But that is the way you redefine TEP. You still owe me to show how you treat TEP and the above situation differently. Show me the calculations of both, and explain the difference to us. You are not able to do this, kkwan. For you, both situations are the same. But in the second is missing that you originally had the choice between the two envelopes, and that is exactly the fact you do not use in your ‘derivation’.

That is your perception of what you “think” is my “redefinition” of the TEP which is not so.

What a nonsense. How can be guaranteed that the amounts in the envelopes conform to ‘one amount is twice the other’, if there is not somebody, or some automaton programmed to put the amounts in the envelopes? For you there is no difference in how it is done. The only important thing is that you do not know what the factual amounts are.

Some entity put the amounts in the two envelopes (not you) and the amounts are either (X, 2X) or (X, 1/2X).

That is not the TEP as it is. Maybe I should point you to your first posting again, where you clearly state (well,

copyfrom Wikipedia…):The switching argument:

Now suppose you reason as follows:1. I denote by A the amount in my selected envelope.

2. The probability that A is the smaller amount is 1/2, and that it is the larger amount is also 1/2.

...Bold by me: everything following is part of the

reasoning, and not of thesetup.C’mon kkwan, I want to win $1000, why don’t you want to bet on it? Why are you so sure about yourself, and still do not take the chance to earn an easy $1000?

That was from the argument to switch in the wiki on the TEP, not from me, but if you were to follow through steps 3, 4 and 5 instead of selectively quoting only steps 1 and 2 for your convenience:

3. The other envelope may contain either 2A or A/2.

4. If A is the smaller amount the other envelope contains 2A.

5. If A is the larger amount the other envelope contains A/2.

3, 4 and 5 taken together mean either (A, 2A) or (A, 1/2A) are in the two envelopes which is **synonymous and equivalent** to: either (X, 2X) or (X, 1/2X) are in the two envelopes.

This is the complete description the TEP and it is the TEP as it is.

GdB, we are here to discuss the TEP, not to gamble. If you have any cogent arguments as to why the argument to switch is flawed thereby solving the puzzle and do not deride, insult or challenge me to gamble etc., I will be willing to consider them on their merits without prejudice.

The puzzle: The puzzle is to find the flaw in the very compelling line of reasoning above.