Take a standard deck of playing cards. Give it a good set of shuffles (six or seven should do). Congratulations! The order of your 52 cards has never been created before in human history.<\/p>\n\n\n\n
Of course, I can’t guarantee that your deck’s order is unique, but I can be pretty darn sure. The number of unique orderings of a deck of 52 cards is expressed mathematically as 52! (52 factorial). That’s 52 times 51 times 50 times 49 … all the way down to 1. This turns out to be a remarkably large number: 8.07 x 1067<\/sup>. There aren’t many numbers in the universe bigger than that (for example, it’s way more than the number of atoms that make up the Earth).<\/p>\n\n\n\n The 52-card deck has been around for about six or seven hundred years. Let’s be generous and assume that every human being alive over the past 700 years shuffled a deck 10 times a day (I think that once a day might be more accurate, but like I said, I’m being generous). So we have:<\/p>\n\n\n\n 1,200,000,000 x 255,675 x 10 = 3,068,100,000,000,000. Three quadrillion.<\/p>\n\n\n\n Which is a lot of shuffles. 3 x 1015<\/sup>. But it’s nowhere near 8.07 x 1067<\/sup>. To calculate the odds that your next shuffle will match any of the previous 3 quadrillion shuffles, just divide the two numbers. The result is one in 2.69 x 1052<\/sup>. Or<\/p>\n\n\n\n 1 in 26,900,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.<\/p>\n\n\n\n So yeah, it’s pretty safe to say that your shuffle is unique.<\/p>\n\n\n\n That’s just the odds of the “next” shuffle matching any of the previous ones. What about the probability any one of those 3 quadrillion shuffles matches some other one? If we compare every single shuffle with every other one, throughout history, has there ever been two that match? <\/p>\n\n\n\n Nope. The math is somewhat complicated, but the odds turn out to be, effectively, zero. Throughout history, every time a deck of cards is shuffled the resulting order has never been seen before.<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":"\n