[t_mann]

The button may be 'correct' in its randomness under one meaningful definition of the word (draw the next element uniformly at random from the whole set on each click), but that's not the only plausible definition of randomness here. Another perfectly reasonable definition would be 'cycle through all elements in random order', ie similar to the randomness in a shuffled deck of cards (which is a reasonable analogy for a series of cartoon clips, and perfectly doable even without cookies, at least within the same session). So in this case, you wouldn't even have to sacrifice formal correctness to please your users, you'd just have to pick the right formal model that corresponds to the kind of randomness you want here.