Just trying to prevent my "false assumption" confirmation bias from growing - did you come to this thread as a result of https://news.ycombinator.com/item?id=41729586 or should I be attributing happenstance? Either is cool, no worries!
I'm an ex-PhD in mathematics. We're talking about two entirely separate things - finite numbers of samples from a probability distribution (what you are talking about) vs the measure of a subset of some finite number of objects (the probabilistic method).
On finite sets, all the stuff they're saying doesn't make sense completely.