52!
52 factorial, the number of different ways a deck of 52 cards can wind up shuffled, is a big number, right? Way(!) short of a googol, never mind a googolplex, but still pretty incomprehensible.
Suppose you set a timer to count down 52! seconds (that's roughly 8.0658x10^67 seconds).
Now, stand on the equator, and take a step forward every billion years. (Don't worry, it's just a thought experiment.)
When you've circled the Earth once, take a drop of water from the Pacific Ocean, and keep going with the one step per billion years...
When the Pacific Ocean is empty, lay a sheet of paper down, refill the ocean and start over.
When your stack of paper reaches the sun, take a look at the timer.
The 3 left-most digits won't have changed. 8.063x10^67 seconds left to go. Repeat the whole process 1000 times to get 1/3 of the way through that time, with still 5.385x10^67 seconds left to go.
This is getting old, right? So now for a change of pace, start doing this instead, to use up the rest of that timer:
Shuffle a deck of cards and deal yourself 5 cards every billion years.
Each time you get a royal flush, buy a lottery ticket.
Each time that ticket wins the jackpot, throw a grain of sand in the Grand Canyon.
When the Grand Canyon's full, take one ounce of rock off Mount Everest, empty the canyon and carry on dealing for Royal Flushes once per billion years.
When Everest has been levelled, check the timer.
There's barely any change. 5.364x10^67 seconds left. You'll have to repeat this process 256 times to run out the timer.
Hard to believe such a big number lurks in that innocent looking deck of playing cards!
This is a paraphrasing of a blog entry I ran across a while ago and I just noticed I left it unfinished in the draft buffer. Too good to just clear, so I finished cleaning it up.
To see the longer original or if you're curious about some of the assumptions made:
https://czep.net/weblog/52cards.html