How many times do you need to shuffle a deck of cards before it’s truly random? (About seven good riffle shuffles.) How much uranium does it take to build a nuclear bomb? How does Google know which page you actually wanted?

These aren’t pub-trivia questions. They’re linked by a 100-year-old fight in Russia, where two mathematicians — one religious and conservative, the other combative and secular — turned probability theory into a battlefield. Out of their quarrel came ideas that echo through nuclear design, web search, and today’s predictive text. And it all started with coin flips.

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