4 ms·

I don't think I saw is in the article, but what is the definition of a properly shuffled deck?

• fredhohman 8y ago
  Superficially, any arrangement of cards should be equally likely to exist, i.e., no one ordering should be favored over another. I'm a bit ill-equipped to go much further than that currently, but the Numberphile video linked in the post may help! There's also been research on this topic too that you get to from Wikipedia: https://en.wikipedia.org/wiki/Shuffling#Randomization https://en.wikipedia.org/wiki/Shuffling#Randomization
• GuB-42 8y ago
  Just on top of my head: a deck where the original order and shuffled order are completely uncorrelated. Or a deck where the shuffle process yields every possible order with equal probability. These two are equivalent if all cards are the same for the purpose of shuffling (no bias).
  • praptak 8y ago
    Can 7 riffles fully reverse the order of cards?
    • fredhohman 8y ago
      Not sure about that... but 8 perfect out shuffles will return a deck to its original order! (Thank you undergrad physics professor!) https://en.m.wikipedia.org/wiki/Out_shuffle https://en.m.wikipedia.org/wiki/Out_shuffle
    • edanm 8y ago
      Sure. Why couldn't it?
• rocqua 8y ago
  Like the others said, given any initial order, a 'proper shuffle procedure' gives the same probability to each other possible order of the deck. Note that this definition is about the process, not the end result. (One might say something about the end result using Kolmogorov complexity, but I know very little about that) It should also be said that the "7 normal riffle shuffles" mentioned earlier in the article is not a 'proper shuffle procedure' in the strict sense. For example, it seems to me that cards that were close together in the initial state are likely to remain closer together after 7 riffle shuffles than after a proper shuffle.