Quote:
|
Yes you are, because the outcomes are limited--it's like if you have four different colors of socks, and you choose five socks. Your fifth sock must match one of the other four.
|
Except, in this case, you’ve got four pairs of socks in a box, and you’re pulling them out one at a time and lining them up in that order. You have to get them in the exact same order, not just draw the same ones.
If you’ve got a red, green, blue, and orange sock; you could draw:
R G B O
R G O B
R B G O
R B O G
R O G B
R O B G
And that’s just what could happen if you draw the red sock first. It carries on for a total of 24 friendly, manageable permutations.
But the factorial of 52 is 8.065 817 517 094 39 x10 to the 67th power (roughly 8 with 67 zeroes). That's how many shuffles there are.
Any card of 52 could be in the first position, then for the 51 choices for the second card, there are 50 choices that could be the third card. But they might not be first, second, or third; they could be anywhere in the deck. The number of possible shuffles is so large that the human brain cannot comprehend it directly.
It’s not only
possible that the same shuffle has never happened, it’s the
most likely outcome; considering the number of permutations, and the number of chances we have had to crunch through them. Certainly you aren’t required to go through all of them to get a repeat, but…
...we’re talking about something like taking all the grains of sand in the world, throwing them up in the air, and having them all fall back down in the exact same place. That isn't going to happen very often, and if you don't have enough time to keep trying, it will never happen. We haven't had enough time to get the same shuffle twice. And before we get the chance, we'll be long gone. It will never happen.