In certain circumstances, like when you're drawing from a limited pool, this becomes N^2 and unbounded - Imagine you're trying to shuffle a deck of cards. Selec

In certain circumstances, like when you're drawing from a limited pool, this becomes N^2 and unbounded - Imagine you're trying to shuffle a deck of cards. Select a card number, 1-52. The first draw, you're guaranteed to get a unique card, the second, you've got a 1/52 chance of having to generate a second number, all the way up to the final card you have a 1/52 chance of generating the final number you need, and you'll spin for quite a bit waiting for that to come up, with a possibility (if your RNG is bad) that you'll never get there. This gets amplified if you've got a larger set - If you draw from six decks, you'll go through an average of 156 'draws' before you get your final card... and the card before it almost as many! The nicer way to do this is to have two lists. Put all of your cards into the first list. Choose a number between 1 and the length of list 1, then remove that element from the list and add it to the end of list 2. Repeat until list 1 is empty. It's linear-time (with a linked list), and there's no chance of duplicates. But this isn't the scenario presented in the article - It's an algorithm for a very specialized version of a shuffle, where you need a random sample from an unbounded sequential (meaning, you don't know it's length ahead of time) list. The algorithm presented is for getting a good random sample from a dataset well beyond the size of memory, not for doing a perfect shuffle on a small list.