T was trying (hard) to disabuse you of your ignorance, a noble enough goal, but clearly produced far more noise than signal. I'd like to be able to point to something specific and say, "right there you did something wrong, and you should have known it." I would have expected T to take some combination of the following two options:

1. Realize he's wrong. It's not reasonable to ask somebody to always be right. We're all wrong sometimes, but it is reasonable to insist an MO user have a minimum amount of receptiveness and mathematical competence. Granting that this is an intuition-twisting problem, he should still have become more aware of the possibility that he was wrong as you continued to correct him. In the process of pushing so hard in insisting that you're wrong, it's reasonable to expect somebody to calculate some small examples. In the case of a single family which stops after at most two children, E(G/(B+G)) is 3/8.
2. Give up on you. Even if he were right, his comments would still be mostly noise since he simply asserted that the proportion should be 1/2 and that the distributions are somehow symmetric. Even if he were generating new and correct arguments, you weren't being swayed by them. If 10 comments telling you you're wrong didn't make any progress, the eleventh is a mistake.

Dear Anton and Douglas,

I am a research mathematician, and after reading this thread I went back to read the discussion. I enjoyed reading it, I certainly learnt something from it, and I would not characterize T.'s comments as spam, although I can see why Douglas is bothered by them; since he disagrees with them, he clearly does not want to read the same objection 20 times over. My own feeling is that the best way to deal with such a situation (comments which one would prefer not to respond to) is to ignore them. If they continue to appear, then moderator intervention (hopefully in the form of a polite message to the commenter) seems appropriate. I would prefer that good faith mathematical remarks not be labelled as spam, though.

I think the ideal thing for T. would be to leave an answer of their own, explaining their point of view and possibly their objections to the answer they disagree with. This could be judged on its own merits, and could attract comments of its own if necessary (but which Douglas could also ignore if he wants to). But whether T. does this is, in the end, up to T.

Regards,

Matt

@Douglas: That was my attempt at a rhetorical device to focus on the situation from T's point of view. I don't think you're ignorant; I think your answer is wonderful. Moreover, I think you've handled this situation admirably. I have nothing to offer you but my support.

Even though I think T's actions were ... suboptimal, they were basically coherent and on topic. I believe they were aimed (but missed) at driving forward the mathematics, not at causing a stink. In other words, they don't merit a suspension or the threat of suspension. So I think the most reasonable thing to do is to arm T with the means of avoiding similar problems in the future. My comment above was an attempt to analyze (and invite others to analyze) what went wrong from T's point of view.

I emailed T, asking him to be aware that this issue came up and pointing him to this meta thread. I am now working on the assumption that T is reading this thread, but declining the urge to jump in and argue with you that his comments, even if they were wrong, were basically using MO for its intended purpose (or whatever else he's tempted to argue). I don't know if that assumption is correct, but it improves my opinion of T. What other moderator action are you asking for? As far as I can tell, this problem is on route to as good a solution as we can hope for. T has not continued to inhibit mathematical discussion.

As for the E[G/(G+B-1)] result, I think this is fundamentally a weakness (and strength) of the Q & A format. Even if the comment thread to your answer were much shorter, the result would still be buried there. Instead, I think you (or somebody else) should simply post another answer with the result. If you're worried that it will be buried under all the other answers, you can even edit your answer to link to the new answer. In general, the comments should be used to clarify, but if some really new or interesting thing comes up, it should spawn a new answer or question.