I am glad that I came to the “no-advantage” conclusion, intuitively, about a hundred pages ago, and simply kept my envelope. I can’t remember what I spent it on.
I am glad that I came to the “no-advantage” conclusion, intuitively, about a hundred pages ago, and simply kept my envelope. I can’t remember what I spent it on.
Yeah, but you did not go into the trouble to convince others that you were right. Of course, that is a personality problem of mine. On the other side, explaining it, finding arguments, sharpens the mind, and sometimes increases the insight.
But glad you followed us all the time! You were a great moral support for me!
To the extent that your efforts to convince others that you are right are almost always rational, and very seldom snarky, I would consider it a strength rather than a problem. Obsessive behavior can sometimes be a good thing.
To the extent that your efforts to convince others that you are right are almost always rational, and very seldom snarky, I would consider it a strength rather than a problem. Obsessive behavior can sometimes be a good thing.
Just by the way Tim, this puzzle is not about being right about whether to switch or not.
The task is to answer correctly what is wrong with the following:
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.
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.
6. Thus the other envelope contains 2A with probability 1/2 and A/2 with probability 1/2.
7. So the expected value of the money in the other envelope is
8. This is greater than A, so I gain on average by swapping.
9. After the switch, I can denote that content by B and reason in exactly the same manner as above.
10. I will conclude that the most rational thing to do is to swap back again.
11. To be rational, I will thus end up swapping envelopes indefinitely.
12. As it seems more rational to open just any envelope than to swap indefinitely, we have a contradiction.
The puzzle: The puzzle is to find the flaw in the very compelling line of reasoning above.
[Just by the way Tim, this puzzle is not about being right about whether to switch or not…
The puzzle: The puzzle is to find the flaw in the very compelling line of reasoning above…
I recognized, early on, that it was beyond my processing power, or at least my motivation, to do so. Though I remain curious.
If you guys solved the puzzle, I commend you.
It was already solved very early. A is not a constant, and you cannot use it as such. Doing this wipes the fact under the carpet that the other envelope contains the other amount, which is not the same as ‘half or twice the amount you have’. In that formulation one leaves out that you originally had two envelopes to choose between. kkwan is just not using this fact.
[Just by the way Tim, this puzzle is not about being right about whether to switch or not…
The puzzle: The puzzle is to find the flaw in the very compelling line of reasoning above…
I recognized, early on, that it was beyond my processing power, or at least my motivation, to do so. Though I remain curious.
If you guys solved the puzzle, I commend you.
It was already solved very early. A is not a constant, and you cannot use it as such. Doing this wipes the fact under the carpet that the other envelope contains the other amount, which is not the same as ‘half or twice the amount you have’. In that formulation one leaves out that you originally had two envelopes to choose between. kkwan is just not using this fact.
I don’t believe this is good explanation at all. If we know the probability distribution we should do it Kkwan’s way.
Of course we can double or half our money by switching on any individual turn.
So you have to focus on not knowing the probability distribution and why that matters.
We’ll see, I’m assuming he is capable of being rational, reasonably smart and open to changing his mind, which I think are fair assumptions and descriptions of Kkwan that he would agree with.
BS. If you treat them separately, then do so:
Either your potential gain/loss is X when you describe the total amount as 3X, or it is X/2 when you describe the total amount as 3X/2. You do not treat the two descriptions separately, but as if they are one.
You cannot treat the situations separately because you don’t know what are actually in the two envelopes. It is either (X, 2X) or (X, 1/2X).
As I said: you do not use the knowledge you have, namely that the amounts are fixed. Show me where you use this information in your calculation.
And you did not answer my question: do you agree that for any two amounts (X,Y), the possible gain or loss by switching them is the same, namely X - Y?
The amounts in the two envelopes are fixed, but you don’t know whether it is (X, 2X) or (X, 1/2X).
For any two amounts, it is simpler to describe them as either (X, 2X) or (X, 1/2X) instead of (X, Y).
So, the potential gain/loss is X /1/2X.
