Background

Given a 52-card deck, there are over 8.065817517 x 10⁶⁷ possible unique sequences (approx. 8 x 10⁶⁷, or 2²²⁵) to an entire deck. This is an enormous number, which when spelled out looks like this very long number:

80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000.

To understand why so many 52-card deck sequences are possible, think of it this way: the first card in the deck is one of 52 possible cards, the second is one of the remaining 51 cards, the third is one of the remaining 50, etc. So, for each of the 52 possible first cards, there are 51 possible second cards, and for each of the 52 x 51 first pairs of cards, there are 50 possible third cards. Continue with this logic to the last card, and you get: 52 x 51 x 50 x 49 ... x 4 x 3 x 2 x 1 possible card sequences (expressed mathematically as 52!, or 52 factorial) which when multiplied out, yields the huge number shown above.

In order to generate all the unique sequences possible in a 52-card deck, a random-number generation algorithm must be able to yield at least 52! unique random number sequences.