Is java.util.Random really that random? How can I generate 52! (factorial) possible sequences?

Question

I\'ve been using Random (java.util.Random) to shuffle a deck of 52 cards. There are 52! (8.0658175e+67) possibilities. Yet, I\'ve found out that the seed for

Answer 1

A very simple algorithm is to apply SHA-256 to a sequence of integers incrementing from 0 upwards. (A salt can be appended if desired to "get a different sequence".) If we assume that the output of SHA-256 is "as good as" uniformly distributed integers between 0 and 2²⁵⁶ - 1 then we have enough entropy for the task.

To get a permutation from the output of SHA256 (when expressed as an integer) one simply needs to reduce it modulo 52, 51, 50... as in this pseudocode:

deck = [0..52]
shuffled = []
r = SHA256(i)

while deck.size > 0:
    pick = r % deck.size
    r = floor(r / deck.size)

    shuffled.append(deck[pick])
    delete deck[pick]