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TL;DR - working out the number of draws it will take you get an Ace if you’re pulling cards randomly without replacing them. Just doing it as “an exercise to the reader” - sparked by some questions that came about in an Advent of Code discord server I’m in. I work out the expected number of draws to the first ‘success’ (drawing an Ace from a deck of cards, for example) from first principles, in a not-necessarily-rigorous-but-good-enough way (mathematicians don’t @ me....