A good way to think about probability is to accept that what you’re calculating isn’t really special.
The universe and maths don’t care that you shuffled the same deck twice. The probability I calculated is true for any 2 decks, not just the ones that are identical. Because we’re human we care about the edge case where they are identical but any one shuffle is equally as unlikely to turn up as all the others. You shuffled a deck once, and got one of 52! Results, and did it again, and got one of 52! Results. The chance of those 2 decks turning up is equally as mind-boggingly small as the identical case, but it’s not interesting to dopamine-driven brains.
A good way to think about probability is to accept that what you’re calculating isn’t really special.
The universe and maths don’t care that you shuffled the same deck twice. The probability I calculated is true for any 2 decks, not just the ones that are identical. Because we’re human we care about the edge case where they are identical but any one shuffle is equally as unlikely to turn up as all the others. You shuffled a deck once, and got one of 52! Results, and did it again, and got one of 52! Results. The chance of those 2 decks turning up is equally as mind-boggingly small as the identical case, but it’s not interesting to dopamine-driven brains.