Perspective on card shuffling

The largest U.S. manufacture of playing cards sells approx. 100,000,000
decks of playing cards per year. This can be expressed as 10⁸.

If each deck sold was fairly shuffled once every five seconds, then each deck
would be shuffled 86,400 times per day, or 31,536,000 times in a year.

That can be expressed as approximately 3.15 x 10⁷.

So if all the manufactured decks were shuffled each day, every five seconds,
the number of unique orderings would be 3.15 x 10⁷ x 10⁸ = 3.15 x 10¹⁵.

The number of ways a deck of cards can be ordered is 52! or approximately
8 x 10⁶⁷.

Assuming that each shuffle gives a new order to the cards then to get each
possible ordering of the playing cards would only take 2.5 * 10⁵² years. (8 x 10⁶⁷/3.15 x 10¹⁵.

Unfortunately, the Earth is only going to last a couple billion years or so
until the Sun runs out of fuel (2 x 10⁹)

8 x 10⁶⁷ (number of ways a deck of cards can be ordered)

80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

2.5 * 10⁵² (number of years to get every possible ordering of a deck of playing cards)

250,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

2 * 10 (number of years left in the life of Earth)

2,000,000,000