Benford's law is an amazing thing. If you know the probability distribution that classes of "natural" numbers should have, you can detect where people might be faking data: phony tax returns, bogus scientific studies, etc.

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When estimating the cost of a bunch of purchases, a useful heuristic is rounding to the nearest dollar. (In fact, on US income tax returns, one is allowed to omit the cents). If prices were uniformly distributed, the following two heuristics would be equally accurate: * Rounding each item up or down to the nearest dollar and summing * Rounding each...