Imagine all eight billion people on Earth shuffling a deck once every second. Start them at the Big Bang, about 13.8 billion years ago, and let them carry on until today. Together they would have made about 3.5 × 1027 shuffles. They would still be nowhere near the end.
A 52-card deck has 52 choices for the first card, 51 for the second, 50 for the third, and so on. Multiply them all together, down to one, and you get 52! (“52 factorial”): about 8.07 × 1067 different orders. Written out in full, that is 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. Even at eight billion shuffles a second, making that many shuffles would take about 2 × 1040 times the age of the universe.
For another comparison, the Earth is estimated to contain about 1.3 × 1050 atoms. There are around 600 million billion times as many possible orders for a deck. The observable universe is estimated to contain between 1078 and 1082 atoms, more than the number of possible deck orders.
How much of this variety reaches your table? It depends on the shuffle.
If a deck is truly well shuffled, the order you are holding is almost certainly one nobody has held before. You are, in all likelihood, the first.
LeShuffler uses a built-in true random number generator, based on a live physical signal, to draw a slot for each card in an internal carousel. No formula or starting value is involved. The original order leaves no trace, and any of the 52! orders can come out.
A new deck starts in a fixed factory order. A light shuffle can leave traces of it.
In 1992, Dave Bayer and Persi Diaconis described a simple bet: move one card, riffle the deck, then bet even money that you can find the moved card within 26 guesses. Even after eight riffles, the person making that bet still has nearly a 10% advantage compared with a perfectly shuffled deck. They noted that people rarely riffle eight times in practice.
To check your own method, see “Is your deck shuffled enough?”, which explains a simple test you can do at home. You can also take the test directly.