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People who are otherwise smart often believe dumb things. History is littered with them. Which is why appeal to authority should always be regarded with skepticism.

This prayer example illustrates a series of fallacies and human biases. Confirmation bias, survivorship bias, apophenia, post-hoc reasoning... many ways we know our brains trick us.

Try this pre-registered, with large numbers and control groups.

Or just read the literature from people who did. Prayer does nothing.