Background: The Invention of Chess
The Shah of Persia, bored with dice games that rewarded chance, challenged the brightest minds of his time and place to invent a game that depended entirely on intellect. When he invited the inventor of chess to name his reward, the crafty inventor made what sounded like a modest request.
Give me just one grain of rice on the first square of the chessboard, please. And two grains of rice on the second square, four grains on the third square, eight on the fourth, and so on, and I will be satisfied.
The shah agreed and his ministers began to fulfill the simple request, gathering enough rice to cover the 64 squares of the board. By the time they reached the 14th square, they reported to the shah:
We ran out of rice before we reached the third row. By the time we reach the 40th square, we’ll need more than a trillion grains of rice. A few more squares and we’ll need all the rice on earth. A few more squares and we’ll need more rice than has ever been produced. By the time we reach the end of the board, we will need more rice than will be produced to the end of history.
The shah responded the only way his imagination allowed. He had the inventor beheaded.
In just a few seconds, I will create something unique in human history using an ordinary deck of 52 playing cards. I will shuffle them seven times, and the result will be a card order so unusual that the odds of it being generated by my shuffling are one in
Again, with no training or practice, never having performed this trick before, the odds that the cards I shuffle will end up in the order I shuffle them into will be:
1 in 80,658,175,170,943,878,571,660,636,856,403,766,975,289,
Can I do it?
Would you like to bet me?
According to J.B. Morley on The Old Bailey blog, “The chances that anyone has ever shuffled a pack of cards in the same way twice in the history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is ‘52 factorial’ otherwise known as 52! or 52 shriek.
This is 52 times 51 times 50 . . . all the way down to one. The result of this factoring is
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards.
If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they’d been doing that since the Big Bang, they’d only just now be starting to repeat shuffles.
How big is this number?
Someone shuffling a deck of cards once per second since the beginning of the universe believed to be about 14 billion years ago would not have shuffled the deck more than 1018 times.
Thus it is almost certain that any given configuration achieved through random shuffling has never appeared before in the history of shuffling!
For comparison’s sake: the number of stars in the universe: 1023.
Su, Francis E., et al. “Making History by Card Shuffling.” Math Fun Facts. .
100 Ways to Shuffle
We are Impossible.
I tell you about this trick, these numbers, the incomprehensible enormity of the odds against everyday occurrences to remind you, again, that we, the world, our ability to perceive anything at all, are almost entirely impossible.
We could have been thwarted at any time, at any stage of our development, and we’d never know we had been denied our brief awareness.
Yet we, and the world, and our awareness . . . in defiance of all the odds . . . undeniably exist.
So. Never despair. The impossible happens every day. It’s happening now all around us if we care to look at it.
Also, for Christ’s sake, stop taking life for granted.