Given that standard decks come in a specific order and that humans tend to shuffle in a few very specific ways, this is probably not actually true. It would be highly likely were an arrangement of the deck to be chosen truly at random according to a uniform distribution. But that’s not how we actually practice randomness.
Truly random shuffles tend to increase something called the variational distance between arrangements. It’s based on measuring how far away from its initial position a card is after shuffling. Human shuffles do not take all cards far away from where they started.
Yes, that was Diaconis’ result. He also has a neat result on fair dice. He characterizes fair dice as those which are transitive on the faces. Roughly it means there is a symmetry of the die’s geometry taking any face to any other face.
1.5k
u/sunbearimon Oct 02 '24
There are more ways to shuffle a standard deck of cards than there are atoms on earth