The best illustrative example of how this pairing drastically lowers odds of two events being the same is the Birthday Paradox, where if you have just 72 people, there is a 99.9% chance two have the same birthday. (You wouldn't solve it this way, of course, the numbers are way too big.) And so on, forming an insanely huge web of pairs, each node representing a deck shuffled connecting to every other node. Then you move on to the second deck ever shuffled it pairs with every other deck ever shuffled to check if they are the same (except the first, which it has already been paired with). It becomes a node that gets to pair individually with every deck that has ever been shuffled after to check if they are the same.
To put it intuitively: Think of the first deck ever shuffled. I was about to type up this response and you saved me the trouble.
