Here’s a question: how many times do you have to riffle a deck of cards before it is completely shuffled? It’s a tricky one, but math has us covered: you need seven riffles.
We can calculate the number of orderings of a deck of cards using the notion of a permutation. To find all arrangements of 52 cards in a deck, we compute 52!, which happens to be a really big number.
Riffle seven times and you’ll have a sufficiently random ordering of cards, an ordering that has likely never existed before. In other words, it’s unlikely you’ll ever shuffle two decks the same.
I didn't want to accept it the first time i heard it is extremely unlikely that a random shuffle is very unlikely to have existed ever before. The numbers are clear, it just didn't feel right.
Same with the 24 words consistently giving unique private keys for Bitcoin...