jtwb / playingcards

Computationally verify a simple probability: given 8e67 permutations of a 52-card deck, every shuffled deck is effectively unique

Playing Cards

"[E]very time you shuffle a deck of cards, you are almost certainly creating an arrangement which the universe has never before seen." --- http://nowiknow.com/shuffled/

This project explores that statement.

Questions include:

• (A) Is it possible to compute enough random decks that you get a duplicate deck?
  • How do we guarantee 122 bits of real entropy to ensure fully-random shuffles?
  • We have the Generalized Birthday Paradox on our side - only need to visit ~10^33 decks before we start to see collisions
• (B) Is it possible to know when you have visited a duplicate deck? (There are 52!=8e67 possible decks)
• (C) What changes when we focus on Riffle Shuffles, which have much lower entropy than fully random shuffles?
  • Are we more likely to find non-unique states in this universe?