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Splitting the money fairly required some notion of the probability of outcomes if the game would have been played until the end. This problem gave birth to the field of probability and laid the foundation for lots of fun things like life insurance, casino games, and scary financial derivatives. All that matters is that you lack knowledge in something. Aggregating Observations The real magic happens when we aggregate a lot of observations. What would happen if you flipped a coin times and counted the number of heads?
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