> Why were you running a "computer simulation" of the
  > problem? Were you, even?

I was reconstructing what happened when Erdős was first told of the Monty Hall problem. He answered 1/2, and was very frustrated for a time. In the end he said something like "But you're not telling me the why!"

Moving on ...

  >> "The two" ?? What "two"? Your "explanations" are
  >> very unclear.

  > The only two there are: the two children. The sex
  > of one is independent from the sex of the other.

So we are assuming that this chap has exactly two children, and that their sexes are independent with probability 1/2.

  > Monty Hall is different because it precludes upfront
  > the possibility of there being any ratio other than
  > 1:2.  If we were, however, to say that any door could
  > have either a goat or a car, then it wouldn't matter
  > whether you stayed or switched.  Monty's elimination
  > of some other door would not inform you on the odds
  > of your door YOUR door. Yea or nay?

Yes, agreed.

  > The only way for Monty to give you any information at
  > all about whether to switch is if the rule binds him
  > to tell you something about the odds of the unchosen
  > doors.

Yes.

  > In the original problem, this happens, because the
  > ratio is bound 1:2.

OK.

  > In our revised problem, this does not happen - unless
  > he tells you he can't remove a door because neither
  > is a goat.

Yes.

  > Using this as an analogue to our children problem,
  > we've already precluded that possibility upfront
  > by eliminating GG, thus Monty can't provide us any
  > information because his B-G choice is unbound by
  > any rule.

I fail to see how that is in any way relevant. There are four equally likely possibilities for the children. If we label them older first then we have BB, BG, GB, GG. Only by labelling them in some consistent order to we get equally likely possibilities. The father says that at least one child is a boy. That eliminates the option of GG. Are you somehow suggesting that the probability distribution of the other options is changed by this?

If so, how? Just as Monty's choice gives no information about the door we have selected (and which therefore remains as chance 1/3 of being the winning door), telling us that it's not the case that both children are girls gives us no further information about the other three equally likely possibilities.

So in https://news.ycombinator.com/item?id=7022615 I asked you this ...

    A: So now let's take another experiment. I tell
       you I'm going to flip two coins until at least
       one of them is heads. I do that. Now I ask you
       to bet on whether or not there is a tail. What
       do you think are fair odds?
    B: ... 
    C: ...

    There are three options.

    1: Your answers to A, B, and C are not all the same;
    2: They are all the same, and not 1/3;
    3: They are all the same, and all 1/3.

In https://news.ycombinator.com/item?id=7022707 you answered:

  > The answer to all 3 is 1/2.

That turns out not to be the case. The answer to A is 1/3. Write a computer program to simulate it and then post it here. Seriously, don't just theorize about it, try it.