Hello! I have been exploring LessWrong on a non-regular basis for a few months, and have recently been advised to create my own account.
I am a french aerospace student, who will (likely) start a PhD next year. I am particularly interested in mitigating xrisks, and would like to orient my career in such a direction. I enjoy ethics, epistemology, and philosophy of mind. A fact which I think is relevant: I am probably a bit less fond of bayesianism as most people here.
I am new on this website, and thus don't feel experienced enough to give global remarks on your post. For the same reason, please correct me if I am going against guidelines or acting in a way which is unusual on LessWrong.
I think I might have an explanation for your note:
4. In fact, the RMD looks like it might vary as a power law of sample size
Your samplings can probably be modeled through a random 1D symmetric motion, as suggested by your coin tossing example. This one is known to present a standard deviation proportional to the square-root of the sample size. The RMD should behave in a similar way, namely:
This is perfectly consistent with your graph: a factor 10000 on the x-axis gives a factor 1/100 on the y-axis.