Step 2. can’t be true in my example without opening the envelope.
There are 4 possible amounts in your example of which 2 are the smaller and 2 are the larger amount.
Thus, without opening any envelope, step 2 is true as the probability of A being either the smaller or the larger amount is 2/4 = 1/2.
You will have to show me why.
We know A can’t be a constant because we know if we played the game over and over we would not continually get the same amount in our envelope. As I’ve explained switching needs to work as a general strategy.
That is obvious in the setup of your example, but A is a constant in the TEP.
Yep but we don’t know which group we have and the probability of having either is 1/2. So we’ll gain $20 half of the time and lose $10 half of the time when we have $20 in our envelope.
But, as you pointed out earlier, we only get $20 half of the time. So, we only gain/lose half of half of the time which is 1/4 of the time.
They are not designed to be so, it just is so. The same goes for any way you care to pick the amounts in the two envelopes. The challenge is for you to find some way that contradicts this.
You can’t because there is no such way.
If you think you can then actually do it. Use numbers and say how they get selected.
And if you don’t…....................
Not in the context of your example which is a zero-sum fixed game with no degree of freedom.
However, the TEP is not like that.