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It’s striking how Pascal took something as fuzzy as “luck” in games of chance and turned it into rigorous mathematics — the correspondence with Fermat really was the moment probability theory was born. The problem of points is such a neat example of how a gambling dispute became a framework we now use for everything from insurance to quantum physics.
What’s fun about living in the aftermath of that breakthrough is that anyone can now compute the exact odds of extremely rare events in seconds. I tinker with RNGdle, the daily random-number guessing game, where badge odds get astronomically small — there’s a fan-made RNGdle rarity calculator that spells out the precise probability of every badge and EP threshold. (It’s a fan-made companion tool, not the game itself, and not affiliated with the official game — Pascal would probably have loved it as a playground for his methods.) Nice article!