Yes the intention was clear, and I agree. I'm now wondering what the rigorous way to describe the phenomenon you describe is. Something like, as the number of

Yes the intention was clear, and I agree. I'm now wondering what the rigorous way to describe the phenomenon you describe is. Something like, as the number of realizations of a random variable increases, the probability of seeing a realization below a given threshold approaches one. This sounds a lot like some of the theory related to hypothesis testing but it's been too long.