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  > No. In person I can see what the other party is thinking.

So when you have less knowledge about the other person you are more rude. I feel that's logically inconsistent.

  > The two are independent variables, man. I don't know
  > how to explain it any more clearly than that.

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

  > What's tripping people up is the idea that removing GG
  > from the possibilities doesn't affect the local probability
  > of either particular child being girl. It does. You must
  > reformulate.

Again, it's clear that you are talking about a different problem. Yes, the problem you are talking about has an answer of 1/2. No, it's not the problem we're talking about.

  > It's just hella hard to explain, ...

You will find many things difficult if you don't learn how to slow down, take time, be precise, and explain clearly. Be more like Feynman - take time to explain things clearly and precisely.

  > ... you must be one of the dolts ...

Ah.

  > The following, you can take or leave: probability is my
  > thing.  I got Monty Hall right when I was in 6th grade.
  > I was an AIME invitee, if you know what that is.  I got
  > 800 on the math SAT; 36 on the math ACT in freshman year.

Good for you. I speak for and contribute to the training of IOM teams, I've been an invited speaker at the Museum of Mathematics in New York, the Dutch National Mathematics days, Matematikbiennalen in Sweden, and more math masterclasses than I can count. This year I'm speaking in London, Switzerland, Belgium, and giving around 150 talks, masterclasses, and workshops. I have a Bachelors, Masters, and PhD.

  > None of these things mean anything, logically speaking,

Right.

  > I know. I say them only to encourage you (and only you,
  > because you're putting in effort) to consider what I'm
  > saying as fully as you're considering what the crowd is
  > saying.

Hmm. Well, thanks for the encouragement. I was only saying these things to point out that I have considered these things, and have some form in the area. I forgot to mention that I was at the G4G when the Tuesday Boy problem was first mentioned, and spent much of the evening with Tanya Khovanova, Gary Foshee, John Conway, Richard Guy, and others, talking about the various interpretations. I didn't talk about it with Martin Gardner when I spent an afternoon with him, we were talking about my work.

I mention these things only to point out that you might consider that you are wrong.

So, do you answer 1/3 for each of A, B, and C?

View on HN

> 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?

> 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.

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.

>> 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? > Yes. ... Going (invisibly) from 4 possible worlds > (including GG) to 3 changes the prob dist of the > remaining 3, by which I mean 2. If Monty must > guarantee you at least one boy, then there aren't > really 3 remaining possibilities. The unguaranteed > can be a boy, or it can be a girl. What is the > third?

> 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?

>> OK. Now B: >> > B: Now I hunt among couples with two children >> > until I find one that doesn't have two girls, >> > and I ask: what are the odds they have two >> > boys? >> Do you agree that it's 1/3? > Yes, I apparently misread that one too.