>>11209709well dice are usually assumed to be uniform distributons. but the CLT applies to almost any bounded probability distribution. so for example, if you had a bunch of very very loaded dice, or dice that were almost flat so only two sides would land, then even throwing a lot of those dice, you still get a gaussian distributed sum. and the gaussian shape gets more and more perfect the more dice you through. it's kinda intuitive but the fact that it works even for sums of very strange probability distributions is interesting.
so that means we see gaussians pop up in nature all over the place, like e.g. people's heights.
mysteriously, in QM a simple harmonic oscillator has a gaussian wavefunction for completely unrelated (?) reasons
