I decided I wanted to calculate the probabilty that in a group of randomly shuffled deck of cards, that two decks have the exact same order. No calculator I could find could handle that large of a number (52!!) until I found your online calculator.
Just because I think it's cool (and I would like someone to double check my math), I decided to make a worse case scenario and assume that every single person ever on this planet (estimated to be 100 billion people) shuffled a deck of cards once every second continuously for 100 years, what's the probability that two of those decks are the same? Here's the formula I used:
Which, written out looks a little more like: