No two card shuffles will EVER be the same.

[Flint]

That doesn’t sound right, does it? In all of human history, and all of human history to come, no matter how many times a deck of cards is shuffled, the same combination will never, ever, ever come up. How can that be? Well…

The 52 cards in a deck can be arranged in...
8,065,817,517,094,390,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
...different ways.

What if we were to put every person alive on the Earth, right now, on this shuffle project? According to the U.S. Census Bureau, the total population of the Earth, as of 02/04/08 at 15:40 GMT (EST+5) is 6,648,429,413.

So, each person would have to shuffle...
1,213,191,419,513,742,831,701,174,895,214,300,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
...decks of cards before all the possible shuffles were exhausted. What if we gave them a little time to work on that? How about 100 years…

If every person alive on the Earth, right now, shuffled continuously for the next hundred years, they would have to shuffle...
3,847,004,754,926,886,198,950,960,474,423,900,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000
...decks of cards, every second, before all the possible shuffles were exhausted.

We don’t seem to be getting any closer to achieving all those shuffle combinations. How long would it really take? Let’s put those 6,648,429,413 people on planet Earth to work, on a more realistic goal: shuffling one deck of cards every 10 seconds, 8 hours a day, 5 days a week, and see how long it takes.

360 shuffles per hour
2,880 shuffles per day
14,400 shuffles per week
5,256,000 shuffles per year
times 6,648,429,413 people is 34,944,144,994,728,000 shuffles per year!

We should see all those shuffle combinations coming up in about...
1,534,592,373,876,406,012,176,560,121,765,600,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
...years. Don’t hold your breath.