One of my personal stumbling blocks, as an experimental scientist, has been the concept of true randomness. The core dilemma one faces is that truly random events sometimes must include non-random components. By chance alone, one must allow the possibility of cards being dealt in a bridge game so that each participant would have all of one suit, in the bidding order of 7 clubs, 7 diamonds, 7 hearts, and 7 spades (which would win the bid and be a lay down).
Now, what if we study rare events--which are believed to be non-random and predictable when they are understood? The established scientific approach is to reject a chance explanation by comparing rare events to random events--except a truly random comparison group might even be more "non-random" than the rare event group!
My solution to that kind of problem has been to redefine "truly random" as "truly unsystematic." Thus, for example, I'd reject bridge hands in which each player got all of one suit as "too systematic" and make it an automatic re-deal.
Something like that is what scientific investigators have been doing for a long time.