shuffling

Persi Diaconis explains on Numberphile the mathematics of card shuffling, including why seven riffle shuffles are needed to randomize a deck and how different shuffles compare.

Vsauce explores math through card tricks and big numbers, including an animation of how enormous 52 factorial, the number of deck orderings, really is.

John Rauser's Strata 2014 keynote argues that programmers can learn statistics quickly by simulating random processes and shuffling data. He explains p-values through resampling rather than formulas.

Jake Vanderplas's PyCon 2016 talk shows how sampling-based methods such as simulation, shuffling and bootstrapping make statistics intuitive. His pitch is that if you can write a for-loop, you can do statistics.