Felipe Almeida Lessa
I wonder why Oleg's perfect shuffle[1] isn't on any standard library?
This is incorrect terminology: A perfect shuffle is one where the cards interleave in a 1:1:1:1:1... pattern, achieving exactly the same permutation of the deck each time. For example, a perfect shuffle of 52 cards where the top and bottom cards stay fixed has order 8: Do one eight times and the deck will return to its original ordering. Most people are incapable of executing a perfect shuffle, but various magicians have mastered this as sleight of hand. I am one of the authors of Dave Bayer, Persi Diaconis Trailing the dovetail shuffle to its lair Ann. Appl. Probab. 2 (1992), no. 2, 294-313 which found a closed form formula for the probabilities involved in riffle shuffles, how people shuffle e.g. playing bridge. This work was summarized as "seven shuffles suffice". I once watched my coauthor, Persi, perform a card trick as part of a talk, where he threw in a shuffle just to amuse himself before starting the trick. It happened to be a perfect shuffle, or the trick would have failed. I chortled eight hours later in a solemn moment in a modern dance concert, it took me this long to realize he had done this. What Oleg means is that his code achieves a uniform distribution after one pass.